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QGIS/python/plugins/sextante/pymorph/mmorph.py
Juergen E. Fischer b86453a390 typo fixes and german function help update
2012-09-26 09:01:07 +02:00

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"""
==============
Module pymorph
==============
pymorph a powerful collection of state-of-the-art gray-scale morphological
tools that can be applied to image segmentation, non-linear filtering,
pattern recognition and image analysis.
- `add4dilate()` : Addition for dilation
- `addm()` : Addition of two images, with saturation.
- `areaclose()` : Area closing
- `areaopen()` : Area opening
- `asf()` : Alternating Sequential Filtering
- `asfrec()` : Reconstructive Alternating Sequential Filtering
- `bench()` : benchmarking main functions of the toolbox.
- `binary()` : Convert a gray-scale image into a binary image
- `blob()` : Blob measurements from a labeled image.
- `bshow()` : Generate a graphical representation of overlaid binary images.
- `cbisector()` : N-Conditional bisector.
- `cdilate()` : Dilate an image conditionally.
- `center()` : Center filter.
- `cerode()` : Erode an image conditionally.
- `close_holes()` : Close holes of binary and gray-scale images.
- `close()` : Morphological closing.
- `closerec()` : Closing by reconstruction.
- `closerecth()` : Close-by-Reconstruction Top-Hat.
- `closeth()` : Closing Top Hat.
- `concat()` : Concatenate two or more images along width, height or depth.
- `cthick()` : Image transformation by conditional thickening.
- `cthin()` : Image transformation by conditional thinning.
- `cwatershed()` : Detection of watershed from markers.
- `datatype()` : Return the image datatype string
- `dilate()` : Dilate an image by a structuring element.
- `dist()` : Distance transform.
- `drawv()` : Superpose points, rectangles and lines on an image.
- `edgeoff()` : Eliminate the objects that hit the image frame.
- `endpoints()` : Interval to detect end-points.
- `erode()` : Erode an image by a structuring element.
- `flood()` : Flooding filter- h,v,a-basin and dynamics (depth, area, volume)
- `frame()` : Create a frame image.
- `freedom()` : Control automatic data type conversion.
- `gdist()` : Geodesic Distance Transform.
- `gradm()` : Morphological gradient.
- `grain()` : Gray-scale statistics for each labeled region.
- `gray()` : Convert a binary image into a gray-scale image.
- `gshow()` : Apply binary overlays as color layers on a binary or gray-scale image
- `histogram()` : Find the histogram of the image f.
- `hmax()` : Remove peaks with contrast less than h.
- `hmin()` : Remove basins with contrast less than h.
- `homothick()` : Interval for homotopic thickening.
- `homothin()` : Interval for homotopic thinning.
- `img2se()` : Create a structuring element from a pair of images.
- `infcanon()` : Intersection of inf-generating operators.
- `infgen()` : Inf-generating.
- `infrec()` : Inf-reconstruction.
- `inpos()` : Minima imposition.
- `interot()` : Rotate an interval
- `intersec()` : Intersection of images.
- `intershow()` : Visualize an interval.
- `isbinary()` : Check for binary image
- `isolines()` : Apply an iso-line color table to a gray-scale image.
- `label()` : Label a binary image.
- `labelflat()` : Label the flat zones of gray-scale images.
- `lastero()` : Last erosion.
- `lblshow()` : Display a labeled image assigning a random color for each label.
- `limits()` : Get the possible minimum and maximum of an image.
- `mat2set()` : Converts image representation from matrix to set
- `maxleveltype()` : Returns the maximum value associated to an image datatype
- `neg()` : Negate an image.
- `open()` : Morphological opening.
- `openrec()` : Opening by reconstruction.
- `openrecth()` : Open-by-Reconstruction Top-Hat.
- `openth()` : Opening Top Hat.
- `opentransf()` : Open transform.
- `pad4n()` : pad4n
- `patspec()` : Pattern spectrum (also known as granulometric size density).
- `plot()` : Plot a function.
- `randomcolor()` : Apply a random color table to a gray-scale image.
- `regmax()` : Regional Maximum.
- `regmin()` : Regional Minimum (with generalized dynamics).
- `se2hmt()` : Create a Hit-or-Miss Template (or interval) from a pair of structuring elements.
- `se2interval()` : Create an interval from a pair of structuring elements.
- `sebox()` : Create a box structuring element.
- `secross()` : Diamond structuring element and elementary 3x3 cross.
- `sedilate()` : Dilate one structuring element by another
- `sedisk()` : Create a disk or a semi-sphere structuring element.
- `seline()` : Create a line structuring element.
- `sereflect()` : Reflect a structuring element
- `serot()` : Rotate a structuring element.
- `seshow()` : Display a structuring element as an image.
- `sesum()` : N-1 iterative Minkowski additions
- `set2mat()` : Converts image representation from set to matrix
- `setrans()` : Translate a structuring element
- `seunion()` : Union of structuring elements
- `skelm()` : Morphological skeleton (Medial Axis Transform).
- `skelmrec()` : Morphological skeleton reconstruction (Inverse Medial Axis Transform).
- `skiz()` : Skeleton of Influence Zone - also know as Generalized Voronoi Diagram
- `subm()` : Subtraction of two images, with saturation.
- `supcanon()` : Union of sup-generating or hit-miss operators.
- `supgen()` : Sup-generating (hit-miss).
- `suprec()` : Sup-reconstruction.
- `symdiff()` : Symmetric difference between two images
- `text()` : Create a binary image of a text.
- `thick()` : Image transformation by thickening.
- `thin()` : Image transformation by thinning.
- `threshad()` : Threshold (adaptive)
- `toggle()` : Image contrast enhancement or classification by the toggle operator.
- `union()` : Union of images.
- `watershed()` : Watershed detection.
- `to_int32()` : Convert an image to an int32 image.
- `to_uint16()` : Convert an image to a uint16 image.
- `to_uint8()` : Convert an image to an uint8 image.
"""
from __future__ import division
from pymorph_version import __version__, __version_info__
import sys, os
from PyQt4.uic.Compiler.qtproxies import QtGui
mydir = os.path.dirname(__file__)
try:
sys.imagepath += [os.path.join(mydir, 'data')]
except:
sys.imagepath = [os.path.join(mydir, 'data')]
__all__ = \
['concat'
,'limits'
,'center'
,'close_holes'
,'dist'
,'cdist'
,'edgeoff'
,'frame'
,'randomcolor'
,'isolines'
,'overlay'
,'histogram'
,'label'
,'neg'
,'threshad'
,'toggle'
,'addm'
,'areaclose'
,'areaopen'
,'asf'
,'asfrec'
,'binary'
,'blob'
,'cbisector'
,'cdilate'
,'cerode'
,'close'
,'closerec'
,'closerecth'
,'closeth'
,'cthick'
,'cthin'
,'cwatershed'
,'dilate'
,'drawv'
,'endpoints'
,'erode'
,'gdist'
,'gradm'
,'grain'
,'gray'
,'hmin'
,'hmax'
,'homothick'
,'homothin'
,'img2se'
,'infcanon'
,'infgen'
,'infrec'
,'inpos'
,'interot'
,'intersec'
,'intershow'
,'isbinary'
,'asbinary'
,'isequal'
,'labelflat'
,'lastero'
,'open'
,'openrec'
,'openrecth'
,'openth'
,'opentransf'
,'patspec'
,'regmax'
,'regmin'
,'se2interval'
,'se2hmt'
,'se2flatidx'
,'sebox'
,'secross'
,'sedisk'
,'seline'
,'serot'
,'seshow'
,'sesum'
,'setrans'
,'sereflect'
,'sedilate'
,'seunion'
,'skelm'
,'skelmrec'
,'skiz'
,'subm'
,'supcanon'
,'supgen'
,'suprec'
,'bshow'
,'symdif'
,'symdiff'
,'thick'
,'thin'
,'union'
,'watershed'
,'maxleveltype'
,'to_int32'
,'to_uint8'
,'to_uint16'
,'to_gray'
,'datatype'
,'add4dilate'
,'mat2set'
,'set2mat'
,'pad4n'
]
def concat(dim, *imgs):
"""
img = concat(dim, img0, img1, ...)
Concatenate two or more images along width, height or depth.
Concatenate two or more images in any of the dimensions: width,
height or depth. If the images do not match the dimension, a
larger image is create with zero pixels to accommodate them. The
images must have the same datatype.
Parameters
----------
dim : {'width', 'heigh', 'depth', 'w', 'h', 'd' }
Dimension along which to concatenate.
img0, img1, ... : Images to concatenate
Returns
-------
img : resulting image (of the same type as inputs).
"""
import numpy as np
import string
dimcode = string.lower(dim)[0]
if not imgs:
raise ValueError, 'pymorph.concat: received empty image list'
shapes = np.array([img.shape for img in imgs])
varies = shapes.var(0).astype(bool)
if (dimcode == 'w' and varies[0]) or \
(dimcode == 'h' and varies[1]) or \
(dimcode == 'd' and varies.any()):
max0,max1 = shapes.max(1)
imgs = list(imgs)
for (i,img),(s0,s1) in zip(enumerate(imgs), shapes):
if dimcode == 'w':
imgs[i] = np.zeros((s0,max1), img.dtype)
elif dimcode == 'h':
imgs[i] = np.zeros((max0,s1), img.dtype)
else:
imgs[i] = np.zeros((max0,max1), img.dtype)
imgs[i][:s0,:s1] = img
if dimcode == 'w':
return np.hstack(imgs)
elif dimcode == 'h':
return np.vstack(imgs)
elif dimcode == 'd':
return np.dstack(imgs)
else:
raise ValueError, 'pymorph.concat: Unknown direction "%s"' % dim
def limits(f):
"""
y = limits(f)
Get the possible minimum and maximum of an image.
The possible minimum and the possible maximum of an image depend
on its data type. These values are important to compute many
morphological operators (for instance, negate of an image). The
output is a vector, where the first element is the possible
minimum and the second, the possible maximum.
Parameters
----------
f : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
Returns
-------
y : Two element vector
the first element is the infimum, the second, the supremum.
"""
from numpy import array, bool, uint8, uint16, int32, int64
code = f.dtype
if code == bool: return array([0,1])
if code == uint8: return array([0,255])
if code == uint16: return array([0,65535])
if code == int32: return array([-2147483647,2147483647])
if code == int64: return array([-2**63,2**63-1])
raise ValueError('pymorph.limits: does not accept this typecode: %s' % code)
def center(f, b=None):
"""
centered = center(f, b={3x3 cross})
Center filter.
center() computes the morphological center of f w.r.t. to the
structuring element b.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
b : Structuring element (default: 3x3 cross).
Returns
-------
y : Image
"""
if b is None: b = secross()
while True:
beta1 = asf(f,'COC',b,1)
beta2 = asf(f,'OCO',b,1)
prev = f
f = union(intersec(y,beta1),beta2)
if isequal(prev,f):
return f
def close_holes(f, Bc=None):
"""
y = close_holes(f, Bc={3x3 cross})
Close holes of binary and gray-scale images.
`close_holes` creates the image `y` by closing the holes of the image
`f`, according with the connectivity defined by the structuring
element `Bc`.The images can be either binary or gray-scale.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bc : Connectivity (default: 3x3 cross).
Returns
-------
y : image (ndarray) of same type as `f`.
"""
if Bc is None: Bc = secross()
delta_f = frame(f)
return neg(infrec(delta_f, neg(f), Bc))
def dist(f, Bc=None, metric='euclidean'):
"""
y = dist(f, Bc={3x3 cross}, metric='euclidean')
Distance transform.
`dist` creates the distance image y of the binary image `f`. The
value of `y` at the pixel `x` is the distance of x to the complement
of f, that is, the distance of `x` to nearest point in the
complement of `f`. The distances available are based on the
Euclidean metrics and on metrics generated by a a regular graph,
that is characterized by a connectivity rule defined by the
structuring element `Bc`. The implementation of the Euclidean
algorithm is based on LotuZamp:01 .
Parameters
----------
f : ndarray of type bool
Input image
Bc : ndarray, optional
Connectivity structure element (default: 3x3 cross)
metric : {'euclidean' [default], 'euclidean2'}, optional
Metric to use.
Returns
-------
y : ndarray
distance image in uint16, or, if metric=='euclidean2', in int32
See Also
--------
cdist : conditional distance transform
mahotas.distance : in mahotas package, faster C++ implementation
scipy.ndimage.distance_transform_edt : in scipy, faster C implementation
"""
return cdist(f=f,g=None,Bc=Bc,metric=metric)
def cdist(f, g=None, Bc=None,metric=None):
"""
y = cdist(f, g, Bc=None, metric=None)
Conditional (geodesic) distance transform.
`cdist` creates the conditional distance image `y` of the binary image `f`.
y[y,x] = distance of (y,x) to foreground in a path through complement(c)
y[y,x] = 0, if f[y,x] == 0 or c[y,x] == 1
The distances available are based on the
Euclidean metrics and on metrics generated by a a regular graph,
that is characterized by a connectivity rule defined by the
structuring element Bc. The implementation of the Euclidean
algorithm is based on LotuZamp:01 .
Parameters
----------
f : Binary image.
g : Binary image.
Bc : Structuring Element Default: None (3x3 elementary
cross). (connectivity)
metric : Metric to use, one of ('euclidean', 'euclidean2'), 'euclidean' by default.
Returns
-------
y : ndarray
distance image in uint16, or, if metric=='euclidean2', in int32
"""
from string import lower
import numpy
from numpy import zeros, sqrt
if Bc is None: Bc = secross()
if metric is not None:
metric = lower(metric)
f = gray(f,'uint16')
y = intersec(f,0)
if g is not None:
g = (~g)*255
if (metric == 'euclidean') or (metric == 'euc2') or (metric == 'euclidean2'):
i=1
while not isequal(f,y):
a4 = -4*i+2
a2 = -2*i+1
b = to_int32([[a4,a2,a4],
[a2, 0,a2],
[a4,a2,a4]])
y=f
i+=1
if g is not None:
f = union(erode(f,b),g)
else:
f = erode(f,b)
if metric == 'euclidean':
f = to_uint16(sqrt(f)+0.5)
else:
if isequal(Bc, secross()):
b = to_int32([[-2147483647, -1, -2147483647],
[ -1, 0, -1],
[-2147483647, -1, -2147483647]])
elif isequal(Bc, sebox()):
b = to_int32([[-1,-1,-1],
[-1, 0,-1],
[-1,-1,-1]])
else: b = Bc # This seems wrong, but it's the original code
while not isequal(f,y):
y=f
f = union(erode(f,b),g)
if g is not None:
return y * (g==0)
return y
def edgeoff(f, Bc=None):
"""
y = edgeoff(f, Bc={3x3 cross})
Eliminate the objects that hit the image frame.
`edgeoff` creates the binary image `y` by eliminating the objects
(connected components) of the binary image `f` that hit the image
frame, according to the connectivity defined by the structuring
element `Bc`.
Parameters
----------
f : Binary image.
Bc : Structuring element (default: 3x3 cross)
Returns
-------
y : Binary image.
"""
if Bc is None: Bc = secross()
edge = frame(f)
return subm(f, infrec(edge, f, Bc))
def frame(f, Ht=1, Wt=1, Dt=0, framevalue=None, bgvalue=None):
"""
y = frame(f, Dt=1, Wt=1, Dt=0, framevalue={max of f.dtype}, bgvalue={min of f.dtype})
Create a frame image.
`frame creates an image `y`, with the same dimensions (W,H,D)
and same pixel type of the image `f`, such that the value of the
pixels in the image frame is `framevalue` and the value of the other
pixels is k2 . The thickness of the image frame is given by the
`HT`, `WT`, and `DT` parameters.
Parameters
----------
f : Input image
Ht : Height thickness (default 1)
Wt : Width thickness (default 1)
Dt : Depth thickness (default 0)
framevalue : Frame grey-level (default: max of f.dtype)
bgvalue : Background grey-level (default: min of f.dtype)
Returns
-------
y : image of same type as f .
"""
minf, maxf = limits(f)
if framevalue is None: framevalue = maxf
if bgvalue is None: bgvalue = minf
y = union(intersec(f, minf), bgvalue)
y[ : , :Wt] = framevalue
y[ : ,-Wt:] = framevalue
y[ :Ht, : ] = framevalue
y[-Ht:, : ] = framevalue
if len(f.shape) == 3:
y[:,:, :Dt] = framevalue
y[:,:,-Dt:] = framevalue
return y
def randomcolor(X):
"""
y = randomcolor(X)
Apply a random color table to a gray-scale image.
Zero is guaranteed to be mapped to black (i.e., (0,0,0) triplet)
Parameters
----------
X : 2d-array of uint8 of shape (h,w)
Labeled image.
Returns
-------
y : 3d-array of uint8 of shape (h, w, 3)
Color image.
"""
from numpy import take, reshape, shape, dstack
from numpy.random import rand
mmin = X.min()
mmax = X.max()
ncolors = mmax - mmin + 1
R = to_int32(rand(ncolors)*255)
G = to_int32(rand(ncolors)*255)
B = to_int32(rand(ncolors)*255)
if mmin == 0:
R[0],G[0],B[0] = 0,0,0
r = reshape(take(R, X.ravel() - mmin),X.shape)
g = reshape(take(G, X.ravel() - mmin),X.shape)
b = reshape(take(B, X.ravel() - mmin),X.shape)
return dstack((r,g,b))
def isolines(X, N=10):
"""
Y = isolines(X, N=10)
Apply an iso-contour color table to a gray-scale image.
Parameters
----------
X : 2d-array
Distance transform image.
N : integer, optional
Number of iso-contours (default: 10).
Returns
-------
Y : Gray-scale (uint8 or uint16) or binary image.
"""
from numpy import newaxis, ravel, ceil, zeros, ones, transpose, repeat, concatenate, arange, reshape, floor
def apply_lut(img, lut):
h,w=img.shape
return reshape(map(lut.__getitem__, img.ravel()),(h,w,3))
np = 1 # number of pixels by isoline
if len(X.shape) == 1: X = X[newaxis,:]
maxi, mini = X.max(), X.min()
d = int(ceil(256./N))
m = zeros(256)
m[0:256:d] = 1
m = transpose([m,m,m])
# lut gray
gray = floor(arange(N)*255. // (N-1) + 0.5).astype('B')
gray = repeat(gray, d)[0:256]
gray = transpose([gray,gray,gray])
# lut jet
r = concatenate((range(126,0,-4),zeros(64),range(0,255,4),255*ones(64),range(255,128,-4)))
g = concatenate((zeros(32),range(0,255,4),255*ones(64),range(255,0,-4),zeros(32)))
b = 255 - r
jet = transpose([r,g,b])
# apply lut
XX = floor((X-mini)*255. // maxi + 0.5).astype('B')
lut = (1-m)*gray + m*jet
return apply_lut(XX, lut)
def overlay(X, red=None, green=None, blue=None, magenta=None, yellow=None, cyan=None):
"""
Y = overlay(X, red=None, green=None, blue=None, magenta=None, yellow=None, cyan=None)
Apply binary overlays as color layers on a binary or gray-scale image
Parameters
----------
X : Gray-scale (uint8 or uint16) or binary image.
red : Red overlay, binary image(default: None)
green : Green overlay, binary image (default: None)
blue : blue overlay, binary image (default: None)
magenta : magenta overlay, binary image (default: None)
yellow : yellow overlay, binary image (default: None)
cyan : cyan overlay, binary image (default: None)
Returns
-------
Y : Color image (in HxWx3 format)
"""
from numpy import dstack
if isbinary(X): X = gray(X,'uint8')
r = X
g = X
b = X
if red is not None: # red 1 0 0
red = gray(asbinary(red),'uint8')
r = union(r,red)
g = intersec(g,neg(red))
b = intersec(b,neg(red))
if green is not None: # green 0 1 0
green = gray(asbinary(green),'uint8')
r = intersec(r,neg(green))
g = union(g,green)
b = intersec(b,neg(green))
if blue is not None: # blue 0 0 1
blue = gray(asbinary(blue),'uint8')
r = intersec(r,neg(blue))
g = intersec(g,neg(blue))
b = union(b,blue)
if magenta is not None: # magenta 1 0 1
magenta = gray(magenta,'uint8')
r = union(r,magenta)
g = intersec(g,neg(magenta))
b = union(b,magenta)
if yellow is not None: # yellow 1 1 0
#assert isbinary(yellow),'yellow must be binary overlay'
yellow = gray(asbinary(yellow),'uint8')
r = union(r,yellow)
g = union(g,yellow)
b = intersec(b,neg(yellow))
if cyan is not None: # cyan 0 1 1
#assert isbinary(cyan),'cyan must be binary overlay'
cyan = gray(asbinary(cyan),'uint8')
r = intersec(r,neg(cyan))
g = union(g,cyan)
b = union(b,cyan)
return dstack((r,g,b))
def histogram(f):
"""
h = histogram(f)
Find the histogram of the image f.
Finds the histogram of the image `f`.
For binary image the vector size is 2. For gray-scale uint8 and
uint16 images, the vector size is the maximum pixel value plus
one. h[0] gives the number of pixels with value 0.
Parameters
----------
f : Input image (of any integer type).
Returns
-------
h : Histogram in a uint16 or an int32 vector.
"""
import numpy as np
return np.histogram(f, np.arange(f.max() + 2))[0]
def label(f, Bc=None):
"""
y = label(f, Bc={3x3 cross})
Label a binary image.
`label` creates the image `y` by labeling the connect components
of a binary image `f`, according to the connectivity defined by
the structuring element `Bc`. The background pixels (with value
0) are not labeled. The maximum label value in the output image
gives the number of its connected components.
Parameters
----------
f : Binary image.
Bc : Connectivity (default: 3x3 cross)
Returns
-------
y : Image of same size as `f`.
If number of labels is less than 65535, the data type
is uint16, otherwise it is int32.
"""
if Bc is None: Bc = secross()
if not isbinary(f):
f = (f > 0)
f = pad4n(f, Bc, 0)
neighbours = se2flatidx(f,Bc)
labeled = f * 0
f = f.ravel()
labeledflat=labeled.ravel()
label = 1
queue = []
for i in xrange(f.size):
if f[i] and labeledflat[i] == 0:
labeledflat[i]=label
queue=[i+bi for bi in neighbours]
while queue:
ni=queue.pop()
if f[ni] and labeledflat[ni] == 0:
labeledflat[ni]=label
for n in neighbours+ni:
queue.append(n)
label += 1
return labeled[1:-1,1:-1] # revert the pad4n() call above
def neg(f):
"""
y = neg(f)
Negate an image.
`neg` returns an image `y` that is the negation (i.e., inverse or
involution) of the image `f`. In the binary case, `y` is the
complement of `f`.
Parameters
----------
f : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
Returns
-------
y : ndarray of same shape and dtype as `f`
"""
y = limits(f)[0] + limits(f)[1] - f
return y.astype(f.dtype)
def threshad(f, f1, f2=None):
"""
y = threshad(f, f1, f2=None)
Threshold (adaptive)
`threshad` creates the image y as the threshold of the image f
by the images `f1` and `f2`. A pixel in `y` has the value 1 when the
value of the corresponding pixel in `f` is between the values of
the corresponding pixels in `f1` and `f2`.
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
f1 : Lower value.
f2 : Upper value.
Returns
-------
y : Binary image.
"""
if f2 is None:
return f1 <= f
return (f1 <= f) & (f <= f2)
def toggle(f, f1, f2, gray_mode=True):
"""
y = toggle(f, f1, f2, gray_mode=True)
Toggle operator
Image contrast enhancement or classification by the toggle operator.
`toggle` creates the image `y` that is an enhancement or classification of
the image f by the toggle operator, with parameters `f1` and `f2`. If
`gray`, it performs an enhancement; otherwise, it performs a binary
classification.
In the enhancement, a pixel takes the value of the corresponding pixel in
`f1` or `f2`, according to a minimum distance criterion from `f` to `f1` or
`f` to `f2`. In the classification, the pixels in f nearest to `f1` receive
the value `0`, while the ones nearest to `f2` receive the value `1`.
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
f1 : Gray-scale (uint8 or uint16) image.
f2 : Gray-scale (uint8 or uint16) image.
gray_mode : boolean, optional
Whether to work in grey mode (default: True)
Returns
-------
y : ndaimge of same shape and dtype as f
"""
y = binary(subm(f,f1),subm(f2,f))
if gray_mode:
t = gray(y)
y = union(intersec(neg(t),f1),intersec(t,f2))
return y
def addm(f1, f2):
"""
y = addm(f1, f2)
Addition of two images, with saturation.
addm creates the image y by pixelwise addition of images f1
and f2 . When the addition of the values of two pixels saturates
the image data type considered, the greatest value of this type
is taken as the result of the addition.
Parameters
----------
f1 : Unsigned gray-scale (uint8 or uint16), signed (int32) or
binary image.
f2 : Unsigned gray-scale (uint8 or uint16), signed (int32) or
binary image. Or constant.
Returns
-------
y: Unsigned gray-scale (uint8 or uint16), signed (int32) or
binary image.
Examples
--------
::
f = to_uint8([255, 255, 0, 10, 0, 255, 250])
g = to_uint8([ 0, 40, 80, 140, 250, 10, 30])
print addm(f,g)
print addm(g, 100)
prints out
::
[255 255 80 150 250 255 255]
[100 140 180 240 255 110 130]
"""
from numpy import array, minimum, maximum
if type(f2) is array:
assert f1.dtype == f2.dtype, 'Cannot have different datatypes:'
y = maximum(minimum(f1.astype('d')+f2, limits(f1)[1]),limits(f1)[0])
return y.astype(f1.dtype)
def areaclose(f, a, Bc=None):
"""
y = areaclose(f, a, Bc={3x3 cross})
Area closing
`areaclose` removes any pore (i.e., background connected
component) with area less than `a` in binary image `f`. The
connectivity is given by the structuring element `Bc`. This
operator is generalized to gray-scale images by applying the
binary operator successively on slices of `f` taken from higher
threshold levels to lower threshold levels.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
a : Non negative integer.
Bc : Structuring element (default: 3x3 cross).
Returns
-------
y : Same type of f
"""
if Bc is None: Bc = secross()
return neg(areaopen(neg(f),a,Bc))
def areaopen(f, a, Bc=None):
"""
y = areaopen(f, a, Bc=None)
Area opening
`areaopen` removes any grain (i.e., connected component) with
area less than `a` of a binary image `f`. The connectivity is given
by the structuring element `Bc`. This operator is generalized to
gray-scale images by applying the binary operator successively
on slices of `f` taken from higher threshold levels to lower
threshold levels.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
a : Double non negative integer.
Bc : Structuring element (default: 3x3 cross).
Returns
-------
y : Same type of f
Examples
--------
::
f=binary(to_uint8([
[1, 1, 0, 0, 0, 0, 1],
[1, 0, 1, 1, 1, 0, 1],
[0, 0, 0, 0, 1, 0, 0]]))
y=areaopen(f,4,secross())
print y
example 2
::
f=to_uint8([
[10, 11, 0, 0, 0, 0, 20],
[10, 0, 5, 8, 9, 0, 15],
[10, 0, 0, 0, 10, 0, 0]])
y=areaopen(f,4,secross())
print y
::
a=readgray('form-1.tif')
b=areaopen(a,500)
show(a)
show(b)
::
a=readgray('bloodcells.tif')
b=areaopen(a, 500)
show(a)
show(b)
"""
if Bc is None: Bc = secross()
if isbinary(f):
fr = label(f,Bc) # binary area open, use area measurement
g = blob(fr,'area')
y = threshad(g,a)
else:
y = intersec(f,0)
zero = binary(y)
k1 = f.min()
k2 = f.max()
for k in xrange(k1,k2+1): # gray-scale, use thresholding decomposition
print float((k-k1)*100)/float(k2-k1)
fk = threshad(f,k)
fo = areaopen(fk,a,Bc)
if isequal(fo,zero):
break
y = union(y, gray(fo,datatype(f),k))
return y
def asf(f, seq="OC", B=None, n=1):
"""
y = asf(f, seq="OC", B={3x3 cross}, n=1)
Alternating Sequential Filtering
`asf` creates the image `y` by filtering the image `f` by n
iterations of the close and open alternating sequential filter
characterized by the structuring element `B`. The sequence of
opening and closing is controlled by the parameter `seq`. 'OC'
performs opening after closing, 'CO' performs closing after
opening, 'OCO' performs opening after closing after opening, and
'COC' performs closing after opening after closing.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
seq : Order of operations, one of ('OC', 'CO', 'OCO', 'COC'), default: 'OC'.
B : Structuring element (default: 3x3 cross).
n : integer, optional
Number of iterations (default: 1).
Returns
-------
y : Image
"""
from string import upper
if B is None: B = secross()
seq = upper(seq)
ops = { 'O' : open, 'C' : close }
ops = map(ops.get, reversed(seq))
for i in xrange(n):
Bn = sesum(B, i+1)
for op in ops:
f = op(f, Bn)
return f
def asfrec(f, seq="OC", B=None, Bc=None, N=1):
"""
y = asfrec(f, seq="OC", B={3x3 cross}, Bc={3x3 cross}, N=1)
Reconstructive Alternating Sequential Filtering
`asf` creates the image `y` by filtering the image `f` by `n`
iterations of the close by reconstruction and open by
reconstruction alternating sequential filter characterized by
the structuring element `B`. The structure element `Bc` is used in
the reconstruction. The sequence of opening and closing is
controlled by the parameter `seq`. 'OC' performs opening after
closing, and 'CO' performs closing after opening.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
seq : Order of operations, one of ('OC', 'CO'), default: 'OC'.
B : Structuring element (default: 3x3 cross).
Bc : Structuring element (default: 3x3 cross).
N : Number of iterations (default: 1).
Returns
-------
y : Same type of f
"""
from string import upper
if B is None: B = secross()
if Bc is None: Bc = secross()
seq = upper(seq)
assert seq in ('OC', 'CO'),'pymorph.asfrec: only accepts OC or CO for SEQ parameter'
firstop = closerec
secondop = openrec
if seq == 'CO':
firstop, secondop = secondop, firstop
for i in xrange(N):
Bn = sesum(B, i+1)
f = firstop(f, Bn, Bc)
f = secondop(f, Bn, Bc)
return f
def binary(f, k=1):
"""
y = binary(f, k=1)
Convert a gray-scale image into a binary image
`binary` converts a gray-scale image `f` into a binary image `y` by
a threshold rule. A pixel in `y` has the value 1 if and only if
the corresponding pixel in `f` has a value greater or equal to `k`.
Parameters
----------
f : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
k : integer, optional
Threshold used inclusively (default: 1)
Returns
-------
y : Binary image.
"""
from numpy import asanyarray
f = asanyarray(f)
return (f >= k)
def blob(f, measurement, output="image"):
"""
y = blob(f, measurement, output="image")
Blob measurements from a labeled image.
Take measurements from the labeled image f.
The measurements are:
- area,
- centroid,
- bounding rectangle.
`output` controls the output format:
image
the result is an image
data
the result is a double column vector with the measurement for each
blob.
The region with label zero is not measured as it is normally
the background. The measurement of region with label 1 appears
at the first row of the output.
Parameters
----------
f : Gray-scale (uint8 or uint16) image. Labeled image.
measurement : Measurement. One of ('area', 'centroid', 'boundingbox').
output : {'image' [default], 'data'}, optional
Output format: if 'image', returns a binary image; if 'data',
returns a vector of measurements
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
import numpy
from numpy import newaxis, ravel, zeros, sum, nonzero, array, asanyarray
from string import lower
measurement = lower(measurement)
output = lower(output)
if len(f.shape) == 1: f = f[newaxis,:]
assert measurement in ('area', 'centroid', 'boundingbox'), 'pymorph.blob: Unknown measurement type \'%s\'' % measurement
if output == 'data':
y = []
elif measurement == 'centroid':
y = zeros(f.shape,numpy.bool)
else:
y = zeros(f.shape,numpy.int32)
for obj_id in xrange(f.max()):
blob = (f == (obj_id+1))
if measurement == 'area':
area = blob.sum()
if output == 'data': y.append(area)
else : y += area*blob
elif measurement == 'centroid':
indy, indx = nonzero(blob)
cy = sum(indy) // len(indy)
cx = sum(indx) // len(indx)
if output == 'data': y.append( (cy, cx) )
else : y[cy, cx] = 1
elif measurement == 'boundingbox':
col, = nonzero(blob.any(0))
row, = nonzero(blob.any(1))
if output == 'data': y.append([col[0],row[0],col[-1]+1,row[-1]+1])
else:
y[row[0]:row[-1], col[0]] = 1
y[row[0]:row[-1],col[-1]] = 1
y[row[0], col[0]:col[-1]] = 1
y[row[-1],col[0]:col[-1]] = 1
return asanyarray(y)
def cbisector(f, B, n):
"""
y = cbisector(f, B, n)
N-Conditional bisector.
`cbisector` creates the binary image `y` by performing a filtering
of the morphological skeleton of the binary image `f`, relative
to the structuring element `B`. The strength of this filtering is
controlled by the parameter `n`. Particularly, if `n==0` , `y` is the
morphological skeleton of `f` itself.
Parameters
----------
f : Binary image.
B : Structuring element
n : filtering rate (positive integer)
Returns
-------
y : Binary image.
"""
y = intersec(f,0)
for i in xrange(n):
nb = sesum(B,i)
nbp = sesum(B,i+1)
f1 = erode(f,nbp)
f2 = cdilate(f1,f,B,n)
f3 = subm(erode(f,nb),f2)
y = union(y,f3)
return y
def cdilate(f, g, Bc=None, n=1):
"""
y = cdilate(f, g, Bc={3x3 cross}, n=1)
Conditional dilation
`cdilate` creates the image `y` by dilating the image `f` by the
structuring element `Bc` conditionally to the image `g`. This
operator may be applied recursively `n` times.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
g : Conditioning image. (Gray-scale or binary).
Bc : Structuring element (default: 3x3 cross)
n : Number of iterations (default: 1)
Returns
-------
y : Image
"""
if Bc is None: Bc = secross()
f = intersec(f,g)
for i in xrange(n):
prev = f
f = intersec(dilate(f, Bc), g)
if isequal(f, prev): break
return f
def cerode(f, g, Bc=None, n=1):
"""
y = cerode(f, g, Bc=None, n=1)
Conditional erosion
`cerode` creates the image `y` by eroding the image `f` by the
structuring element `Bc` conditionally to `g`. This operator may be
applied recursively `n` times.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
g : Conditioning image.
Bc : Structuring element (default: 3x3 cross)
n : Number of iterations (default: 1)
Returns
-------
y : Image
"""
if Bc is None: Bc = secross()
f = union(f,g)
for i in xrange(n):
prev = f
f = union(erode(f,Bc),g)
if isequal(f, prev): break
return f
def close(f, Bc =None):
"""
y = close(f, Bc={3x3 cross})
Morphological closing.
`close` creates the image `y` by the morphological closing of the
image `f` by the structuring element `Bc`. In the binary case, the
closing by a structuring element `Bc` may be interpreted as the
intersection of all the binary images that contain the image `f`
and have a hole equal to a translation of `Bc`. In the gray-scale
case, there is a similar interpretation taking the functions
umbra.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bc : Structuring Element Default: None (3x3 elementary cross).
Returns
-------
y : Image
"""
if Bc is None: Bc = secross()
return erode(dilate(f,Bc ),Bc )
def closerec(f, Bdil=None, Bc=None):
"""
y = closerec(f, Bdil=None, Bc=None)
Closing by reconstruction.
`closerec()` creates the image `y` by a sup-reconstruction (with
the connectivity defined by the structuring element `Bc`) of the
image `f` from its dilation by `Bdil`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image
Bdil : Dilation structuring element (default 3x3 elementary cross)
Bc : Connectivity structuring element (default: 3x3 elementary cross)
Returns
-------
y : Image (same type as f)
"""
if Bdil is None: Bdil = secross()
if Bc is None: Bc = secross()
return suprec(dilate(f,Bdil),f,Bc)
def closerecth(f, Bdil=None, Bc=None):
"""
y = closerecth(f, Bdil=None, Bc=None)
Close-by-Reconstruction Top-Hat.
`closerecth` creates the image `y` by subtracting the image `f` of
its closing by reconstruction, defined by the structuring
elements `Bc` and `Bdil`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bdil : Dilation structuring element (default: 3x3 cross)
Bc : Connectivity structuring element (default: 3x3 cross)
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
if Bdil is None: Bdil = secross()
if Bc is None: Bc = secross()
return subm(closerec(f, Bdil, Bc), f)
def closeth(f, B=None):
"""
y = closeth(f, B={3x3 cross})
Closing Top Hat.
`closeth` creates the image `y` by subtracting the image `f` of its
morphological closing by the structuring element `B`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
B : Structuring Element Default: None (3x3 elementary cross).
Returns
-------
y : ndarray of same shape and dtype as `f`
"""
if B is None: B = secross()
return subm(close(f, B), f)
def cthick(f, g, Iab=None, n=-1, theta=45, direction="clockwise"):
"""
y = cthick(f, g, Iab={Homothick interval}, n={infinite}, theta=45, direction="clockwise")
Image transformation by conditional thickening.
`cthick` creates the binary image `y` by performing a thickening
of the binary image `f` conditioned to the binary image `g`. The
number of iterations of the conditional thickening is `n` and in
each iteration the thickening is characterized by rotations of
`theta` of the interval `Iab`.
Parameters
----------
f : Binary image.
g : Binary image.
Iab : Interval (default: homothick).
n : Number of iterations, -1 for infinite (default: -1)
theta : Degrees of rotation, 45 (default), 90, or 180.
direction: 'clockwise' or 'anti-clockwise'.
Returns
-------
y : Binary image.
"""
from string import upper
if Iab is None: Iab = homothick()
if n == -1: n = f.size
assert isbinary(f), 'pymorph.cthick: f must be binary image'
direction = upper(direction)
for i in xrange(n):
prev = f
for t in xrange(0,360,theta):
sup = supgen(f, interot(Iab, t, direction))
f = intersec(union(f, sup),g)
if isequal(prev, f): break
return f
def cthin(f, g, Iab=None, n=-1, theta=45, direction="clockwise"):
"""
y = cthin(f, g, Iab={Homothin interval}, n={infinite}, theta=45, direction="clockwise")
Image transformation by conditional thinning.
`cthin` creates the binary image y by performing a thinning of
the binary image `f` conditioned to the binary image `g`. The
number of iterations of the conditional thinning is `n` and in
each iteration the thinning is characterized by rotations of
`theta` of the interval `Iab`.
Parameters
----------
f : Binary image.
g : Binary image.
Iab : Interval (default: homothin()).
n : Number of iterations, -1 for infinite (default: -1)
theta : Degrees of rotation, 45 (default), 90, or 180.
direction: 'clockwise' or 'anti-clockwise'.
Returns
-------
y : Binary image.
"""
from string import upper
if Iab is None: Iab = homothin()
assert isbinary(f),'f must be binary image'
direction = upper(direction)
if n == -1: n = f.size
for i in xrange(n):
prev = f
for t in xrange(0,360,theta):
sup = supgen(f, interot(iab, t, direction))
y = union(subm(f, sup),g)
if isequal(prev, f): break
return f
def cwatershed(f, markers, Bc=None, return_lines=False,is_gvoronoi=False):
"""
R = cwatershed(f, g, Bc=None, return_lines=False)
R,L = cwatershed(f, g, Bc=None, return_lines=True)
Detection of watershed from markers.
`cwatershed` creates the image `R` by detecting the domain of the
catchment basins of `f` indicated by the marker image `g`,
according to the connectivity defined by `Bc`.
If `return_lines`, `L` will be a labeled image of the catchment basins
domain or just a binary image that presents the watershed lines.
To know more about watershed and watershed from markers, see
BeucMeye:93. The implementation of this function is based on
LotuFalc:00.
WARNING: There is a common mistake related to the
marker image `g`. If this image contains only zeros and ones, but
it is not a binary image, the result will be an image with all
ones. If the marker image is binary, you have to set this
explicitly (e.g., `cwatershed(f,g>0)` or `cwatershed(f,g.astype(bool))`)
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
markers : Gray-scale (uint8 or uint16) or binary image. marker
image: binary or labeled.
Bc : Watershed connectivity (default: 3x3 cross)
return_lines : Whether to return lines as well as regions (default: False)
Returns
-------
R : Gray-scale (uint8 or uint16) or binary image.
L : Binary line image
See Also
--------
mahotas.cwatershed : implementation of same interface in C++
"""
from numpy import ones, zeros, nonzero, array, put, take, argmin, transpose, compress, concatenate, where, uint8
from heapq import heapify, heappush, heappop
if Bc is None: Bc = secross()
if isbinary(markers):
markers = label(markers,Bc)
status = pad4n(zeros(f.shape,uint8),Bc, 3)
f = pad4n(f,Bc,0) # pad input image with 0
y = pad4n(markers,Bc,0) # pad marker image with 0
if return_lines:
y1 = intersec(binary(y), 0)
y1flat=y1.ravel()
costM = limits(f)[1] * ones(f.shape) # cummulative cost function image
# get 1D displacement neighborhood pixels
Bi=se2flatidx(f,Bc)
status=status.ravel()
f=f.ravel()
costM=costM.ravel()
yflat=y.ravel()
initial, = where(yflat > 0)
costM[initial]=f[initial]
# I sort in order of insertion for the simple reason that that's what
# the original code intended to do (although that code was not functional)
hqueue=[(costM[idx],i,idx) for i,idx in enumerate(initial)]
heapify(hqueue)
while hqueue:
cost,_,pi = heappop(hqueue)
status[pi]=1 # make it a permanent label
for qi in Bi+pi: # for each neighbor of pi
if (status[qi] != 3): # not image border
if (status[qi] != 1): # if not permanent
if is_gvoronoi:
ncost=costM[pi]
else:
ncost=f[qi]
if ncost < costM[qi]:
costM[qi]=ncost
yflat[qi] = yflat[pi] # propagate the label
heappush(hqueue,(ncost,i,qi))
i += 1
elif (return_lines and
(yflat[qi] != yflat[pi]) and
(y1flat[qi] == 0) ):
y1flat[pi] = 1
y=y[1:-1,1:-1]
if return_lines:
y1=y1[1:-1,1:-1]
return y,y1
return y
def dilate(f, B=None):
"""
y = dilate(f, B={3x3 cross})
Dilate an image by a structuring element.
`dilate` performs the dilation of image `f` by the structuring
element `B`. Dilation is a neighbourhood operator that compares
locally `B` with `f`, according to an intersection rule. Since
Dilation is a fundamental operator to the construction of all
other morphological operators, it is also called an elementary
operator of Mathematical Morphology. When f is a gray-scale
image, `B` may be a flat or non-flat structuring element.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
B : Structuring element (default: 3x3 cross).
Returns
-------
y: Same type as `f`
"""
from numpy import maximum, newaxis, ones, int32
if B is None: B = secross()
if len(f.shape) == 1: f = f[newaxis,:]
if isbinary(f): B = asbinary(B)
h,w = f.shape
x,v = mat2set(B)
if len(x)==0:
y = (ones((h,w),int32) * limits(f)[0]).astype(f.dtype)
else:
if isbinary(v):
v = intersec(gray(v,'int32'),0)
mh,mw = max(abs(x)[:,0]),max(abs(x)[:,1])
y = (ones((h+2*mh,w+2*mw),int32) * limits(f)[0]).astype(f.dtype)
for i in xrange(x.shape[0]):
if v[i] > -2147483647:
y[mh+x[i,0]:mh+x[i,0]+h, mw+x[i,1]:mw+x[i,1]+w] = maximum(
y[mh+x[i,0]:mh+x[i,0]+h, mw+x[i,1]:mw+x[i,1]+w], add4dilate(f,v[i]))
y = y[mh:mh+h, mw:mw+w]
return y
def drawv(f, data, value, geometry):
"""
y = drawv(f, data, value, geometry)
Superpose points, rectangles and lines on an image.
`drawv` creates the image `y` by a superposition of points,
rectangles and lines of gray-level `value` on the image `f`. The
parameters for each geometrical primitive are defined by each line
in the `data` parameter. For points, they are represented by 2-D
coordinates. For lines, they are drawn with the same convention
used by points, with a straight line connecting them in the order
given by the data matrix. For rectangles and filled rectangles,
data should be an array of 2 x 2D points.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
data : Vector of coordinates.
value : Gray value(s) for drawing.
If it's a single value, then it will be used for all objects,
otherwise, it should be an array of same length as `data`.
geometry : { 'point', 'line', 'rect', 'frect' (filled rectangles)}
Returns
-------
y : Image of same type as `f`
"""
"""
- Examples
#
# example 1
#
f=to_uint8(zeros((3,5)))
pcoords=to_uint16([[0,2,4],
[0,0,2]])
pvalue=to_uint16([1,2,3])
print drawv(f,pcoords,pvalue,'point')
print drawv(f,pcoords,pvalue,'line')
rectcoords=to_uint16([[0],
[0],
[3],
[2]])
print drawv(f,rectcoords, to_uint16(5), 'rect')
#
# example 2
#
f=readgray('blob3.tif')
pc=blob(label(f),'centroid','data')
lines=drawv(intersec(f,0),transpose(pc),to_uint8(1),'line')
show(f,lines)
"""
from numpy import array, newaxis, zeros, put, ravel, arange, floor, int32, zeros_like
from string import lower
import itertools
geometry = lower(geometry)
if len(f.shape) == 1: f = f[newaxis,:]
value = array(value)
if value.shape == ():
value = itertools.repeat(value)
else:
assert (len(data) == len(value) or geometry == 'line'), \
'pymorph.drawv: Length of data does not match length of values'
assert ((len(data) == len(value)+1) or geometry != 'line'), \
'pymorph.drawv: Length of data does not match length of values -1 (for line option)'
res = zeros_like(f)
if geometry == 'point':
for (y,x), val in zip(data, value):
res[y,x] = val
elif geometry == 'line':
# Implement algorithm from
# http://en.wikipedia.org/wiki/Bresenham's_line_algorithm
# To match the Wikipedia version
# the coordinates are expressed in *x,y* convention!
for val,(x0,y0),(x1,y1) in itertools.izip(value,data[:-1], data[1:]):
steep = (abs(y1 - y0) > abs(x1 - x0))
if steep:
y0,x0 = x0,y0
y1,x1 = x1,y1
if x0 > x1:
x0,x1 = x1,x0
y0,y1 = y1,y0
deltax = x1 - x0
deltay = abs(y1 - y0)
error = deltax // 2
y = y0
ystep = (1 if y0 < y1 else -1)
for x in xrange(x0, x1+1):
if steep: res[y,x] = val
else: res[x,y] = val
error -= deltay
if error < 0:
y += ystep
error += deltax
elif geometry in ('frect', 'rect'):
for (y0,x0,y1,x1), val in zip(data, value):
assert y1 >= y0, 'pymorph.drawv: bad arguments'
assert x1 >= x0, 'pymorph.drawv: bad arguments'
if geometry == 'rect':
res[y0:y1+1, x0 ] = val
res[y0:y1+1, x1 ] = val
res[ y0 ,x0:x1+1] = val
res[ y1 ,x0:x1+1] = val
else:
res[y0:y1+1,x0:x1+1] = val
else:
assert False, "pymorph.drawv: geometry should be 'point', 'line', 'rect', or 'frect'."
return res
def endpoints(option="loop"):
"""
iab = endpoints(option="loop")
Interval to detect end-points.
`endpoints` creates an interval that is useful to detect
end-points of curves (i.e., one pixel thick connected
components) in binary images. It can be used to prune skeletons
and to mark objects transforming them in a single pixel or
closed loops if they have holes. There are two options
available: 'loop', deletes all points but preserves loops if used
in thin ; 'homotopic', deletes all points but preserves the last
single point or loops.
Parameters
----------
option : {'loop' [default], 'homotopic'}
type of interval
Returns
-------
Iab : Interval
"""
from string import lower
option = lower(option)
if option == 'loop':
return se2hmt(binary([[0,0,0],
[0,1,0],
[0,0,0]]),
binary([[0,0,0],
[1,0,1],
[1,1,1]]))
elif option == 'homotopic':
return se2hmt(binary([[0,1,0],
[0,1,0],
[0,0,0]]),
binary([[0,0,0],
[1,0,1],
[1,1,1]]))
from warnings import warn
warn('pymorph.endpoints: Did not understand argument "%s".' % option)
return None
def erode(f, b=None):
"""
y = erode(f, b={3x3 cross})
Erode an image by a structuring element.
`erode` performs the erosion of the image `f` by the structuring
element `b`. Erosion is a neighbourhood operator that compairs
locally `b` with `f`, according to an inclusion rule. Since erosion
is a fundamental operator to the construction of all other
morphological operators, it is called an elementary
operator of Mathematical Morphology. When `f` is a gray-scale
image, `b` may be a flat or non-flat structuring element.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
b : Structuring element (Default: 3x3 elementary cross).
Returns
-------
y : Image
See Also
--------
mahotas.erode : implementation of binary erosion
scipy.ndimage.grey_erosion : implementation of grey erosion
"""
if b is None: b = secross()
return neg(dilate(neg(f),sereflect(b)))
def gdist(f, g, Bc=None, metric=None):
"""
y = gdist(f, g, Bc=None, metric=None)
Geodesic Distance Transform.
`gdist` creates the geodesic distance image y of the binary
image `f` relative to the binary image `g`. The value of `y` at the
pixel `x` is the length of the smallest path between `x` and `f`. The
distances available are based on the Euclidean metrics and on
metrics generated by a neighbourhood graph, that is
characterized by a connectivity rule defined by the structuring
element `Bc`. The connectivity for defining the paths is
consistent with the metrics adopted to measure their length. In
the case of the Euclidean distance, the space is considered
continuos and, in the other cases, the connectivity is the one
defined by `Bc`.
Parameters
----------
f : Binary image.
g : Binary image. Marker image
Bc : Structuring Element Default: None (3x3 elementary
cross). (metric for distance).
metric: string default: none. 'euclidean' if specified.
Returns
-------
y : uint16 (distance image).
"""
if Bc is None: Bc = secross()
assert metric is None,'Does not support euclidean'
fneg,gneg = neg(f),neg(g)
y = gray(gneg,'uint16',1)
ero = intersec(y,0)
prev = y
i = 1
while not isequal(ero, prev):
prev = ero
ero = cerode(gneg,fneg,Bc,i)
y = addm(y,gray(ero,'uint16',1))
i += 1
return union(y,gray(ero,'uint16'))
def gradm(f, Bdil=None, Bero=None):
"""
y = gradm(f, Bdil={3x3 cross}, Bero={3x3 cross})
Morphological gradient.
`gradm` creates the image `y` by the subtraction of the erosion of
the image `f` by `Bero` of the dilation of `f` by `Bdil`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bdil : Structuring element for dilation (default: 3x3 cross).
Bero : Structuring element for erosion (default: 3x3 cross).
Returns
-------
y : Image of same type as `f`.
"""
if Bdil is None: Bdil = secross()
if Bero is None: Bero = secross()
return subm(dilate(f,Bdil),erode(f,Bero))
def grain(f, labels, measurement, option="image"):
"""
y = grain(f, labels, measurement, option="image")
Gray-scale statistics for each labeled region.
Computes gray-scale statistics of each grain in the image. The
grains regions are specified by the labeled image `labels` and the
gray-scale information is specified by the image `f`. The
statistics to compute is specified by the parameter measurement,
which has the same options as in function stats. The
parameter option defines the output format:
'image'
if the output is an uint16 image where each label value is changed to
the measurement value
'data'
a double column vector. In this case, the first element (index 0) is
the measurement of region 1. The region with label zero is not measure
as it is normally the background.
Parameters
----------
f : ndarray (gray-scale)
labels : ndarray of integer dtype
Labeled image. As usual, label 0 is backaground.
measurement : {'max', 'min', 'median', 'mean', 'sum', 'std', 'std1' }
Which measure to compute.
option : {'image' [default], 'data' }
Output format: if 'image', results as a gray-scale mosaic image
(default): if 'data', results a column vector of measurements.
Returns
-------
y: Gray-scale (uint8 or uint16) image.
Or an array with gray-scale statistics per region
"""
"""
- Examples
#
# example 1
1#
f=to_uint8([range(6),range(6),range(6)])
labels=labelflat(f)
grain(labels,f,'sum','data')
grain(labels,f,'sum')
#
# example 2
#
f=readgray('astablet.tif')
g=gradm(f)
marker=regmin(close(g))
ws=cwatershed(g,marker,sebox(),'regions')
g=grain(ws,f,'mean')
show(f)
show(g)
"""
from numpy import zeros_like, asarray, zeros, float32
from string import lower
measurement = lower(measurement)
is_data = (lower(option) == 'data')
if is_data:
y = []
else:
type = f.dtype
if measurement in ('mean', 'std'):
type = float32
y = zeros(labels.shape)
fdata = f.ravel()
labelsravel = labels.ravel()
for obj_id in xrange(labelsravel.max()):
pixels = fdata[labelsravel == (obj_id + 1)]
if measurement == 'max':
val = pixels.max()
elif measurement == 'min':
val = pixels.min()
elif measurement == 'sum':
val = pixels.sum()
elif measurement == 'mean':
val = pixels.mean()
elif measurement == 'std':
val = pixels.std()
elif measurement == 'std1':
print "'std1' is not implemented"
else:
print "measurement should be 'max', 'min', 'mean', 'sum', 'std', 'std1'."
if is_data:
y.append(val)
else:
y += val*(labels == (obj_id+1))
return asarray(y)
def gray(f, dtype="uint8", k=None):
"""
y = gray(f, dtype="uint8", k=None)
Convert a binary image into a gray-scale image.
`gray` converts a binary image into a gray-scale image of a
specified data type. The value `k` is assigned to the 1 pixels of
`f`, while the `0` pixels are assigned to the minimum value
associated to the specified data type.
Parameters
----------
f : Binary image.
dtype : { 'uint8' [default], 'uint16', 'int32' }
k : scalar, optional
Pixel value to assign to `True` pixels (default: max value for `dtype`).
Returns
-------
y : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
"""
from numpy import array
if k is None: k = maxleveltype(dtype)
if type(f) is list: f = binary(f)
assert isbinary(f), 'f must be binary'
if dtype == 'uint8' : y = to_uint8(f*k)
elif dtype == 'uint16': y = to_uint16(f*k)
elif dtype == 'int32' : y = to_int32(f*k) - to_int32(neg(f)*maxleveltype(dtype))
else:
assert 0, 'pymorph.gray: type not supported: %s' % dtype
return y
def hmin(f, h=1, Bc=None):
"""
y = hmin(f, h=1, Bc={3x3 cross})
Remove basins with contrast less than h.
`hmin` sup-reconstructs the gray-scale image `f` from the marker
created by the addition of the positive integer value `h` to `f`,
using the connectivity `Bc`. This operator removes connected
basins with contrast less than `h`. This function is very useful
for simplifying the basins of the image.
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
h : Contrast (default: 1).
Bc : Connectivity structuring element (default: 3x3 cross).
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
"""
Examples
#
# example 1
#
a = to_uint8([
[10, 3, 6, 18, 16, 15, 10],
[10, 9, 6, 18, 6, 5, 10],
[10, 9, 9, 15, 4, 9, 10],
[10, 10, 10, 10, 10, 10, 10]])
print hmin(a,1,sebox())
#
# example 2
#
f = readgray('r4x2_256.tif')
show(f)
fb = hmin(f,70)
show(fb)
show(regmin(fb))
"""
if Bc is None: Bc = secross()
g = addm(f, h)
return suprec(g, f, Bc);
def hmax(f, h=1, Bc=None):
"""
Remove peaks with contrast less than h.
y = hmax(f, h=1, Bc={3x3 cross})
`hmax` inf-reconstructs the gray-scale image f from the marker
created by the subtraction of the positive integer value h from
`f`, using connectivity `Bc`. This operator removes connected
peaks with contrast less than `h`.
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
h : Contrast (default: 1).
Bc : Connectivity structuring element (default: 3x3 cross).
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
"""
Examples
#
# example 1
#
a = to_uint8([
[4, 3, 6, 1, 3, 5, 2],
[2, 9, 6, 1, 6, 7, 3],
[8, 9, 3, 2, 4, 9, 4],
[3, 1, 2, 1, 2, 4, 2]])
print hmax(a,2,sebox())
#
# example 2
#
f = readgray('r4x2_256.tif')
show(f)
fb = hmax(f,50)
show(fb)
show(regmax(fb))
"""
if Bc is None: Bc = secross()
g = subm(f, h)
return infrec(g, f, Bc);
def homothick():
"""
Iab = homothick()
Interval for homotopic thickening.
`homothick` creates an interval that is useful for the homotopic
(i.e., that conserves the relation between objects and holes)
thickening of binary images.
Returns
-------
Iab: Interval
"""
return se2hmt(binary([[1,1,1],
[0,0,0],
[0,0,0]]),
binary([[0,0,0],
[0,1,0],
[1,1,1]]))
def homothin():
"""
Iab = homothin()
Interval for homotopic thinning.
`homothin` creates an interval that is useful for the homotopic
(i.e., that conserves the relation between objects and holes)
thinning of binary images.
Returns
-------
Iab : Interval
"""
return se2hmt(binary([[0,0,0],
[0,1,0],
[1,1,1]]),
binary([[1,1,1],
[0,0,0],
[0,0,0]]))
def img2se(fd, flat=True, f=None):
"""
B = img2se(fd, flat=True, f=None)
Create a structuring element from a pair of images.
`img2se` creates a flat structuring element `B` from the binary
image `fd` or creates a non-flat structuring element `B` from the
binary image `fd` and the gray-scale image `f`. `fd` represents the
domain of `B` and `f` represents the image of the points in `fd`.
Parameters
----------
fd : Binary image.
The image is in the matrix format where the origin (0,0) is at the
matrix center.
flat : boolean, optional
Whether to return a flat structuring element (default: True)
f : ndarray of type (uint8 or uint16, int32, or bool), optional
Returns
-------
B : Structuring Element
"""
from numpy import choose, ones
assert isbinary(fd),'pymorph.img2se: first parameter must be binary'
if flat:
return seshow(fd)
B = choose(fd, (limits(to_int32([0]))[0]*ones(fd.shape),f) )
return seshow(to_int32(B),'NON-FLAT')
def infcanon(f, Iab, theta=45, direction='clockwise'):
"""
y = infcanon(f, Iab, theta=45, direction='clockwise')
Intersection of inf-generating operators.
`infcanon` creates the image `y` by computing intersections of
transformations of the image `f` by inf-generating (i.e., dual of
the hit-or-miss) operators. These inf-generating operators are
characterized by rotations (in the clockwise or anti-clockwise
direction) of `theta` degrees of the interval `Iab`.
Parameters
----------
f : Binary image.
Iab : Interval
theta : Degrees of rotation (default: 45)
direction : { 'clockwise' [default], 'anti-clockwise' }
Returns
-------
y : Binary image.
"""
from string import upper
direction = upper(direction)
y = union(f,1)
for t in xrange(0,360,theta):
Irot = interot(Iab, t, direction)
y = intersec(y, infgen(f, Irot))
return y
def infgen(f, Iab):
"""
y = infgen(f, Iab)
Inf-generating.
`infgen` creates the image `y` by computing the transformation of
the image `f` by the inf-generating operator (or dual of the
hit-or-miss) characterized by the interval `Iab`.
Parameters
----------
f : Binary image.
Iab : Interval
Returns
-------
y: Binary image.
"""
A,Bc = Iab
return union(dilate(f, A),dilate(neg(f), Bc))
def infrec(f, g, Bc=None):
"""
y = infrec(f, g, Bc={3x3 cross})
Inf-reconstruction.
`infrec` creates the image `y` by an infinite number of recursive
iterations (iterations until stability) of the dilation of `f` by
Bc conditioned to `g`. We say the `y` is the inf-reconstruction of
g from the marker `f`. For algorithms and applications, see
Vinc:93b.
Parameters
----------
f : Marker image (gray or binary).
g : Conditioning image (gray or binary).
Bc : Connectivity Structuring element (default: 3x3 cross).
Returns
-------
y : Image
"""
"""
- Examples
#
# example 1
#
g=readgray('text_128.tif')
f=erode(g,seline(9,90))
y=infrec(f,g,sebox())
show(g)
show(f)
show(y)
#
# example 2
#
g=neg(readgray('n2538.tif'))
f=intersec(g,0)
f=draw(f,'LINE:40,30,60,30:END')
y30=cdilate(f,g,sebox(),30)
y=infrec(f,g,sebox())
show(g)
show(f)
show(y30)
show(y)
"""
if Bc is None: Bc = secross()
n = f.size
return cdilate(f, g, Bc, n);
def inpos(f, g, Bc=None):
"""
y = inpos(f, g, Bc={3x3 cross})
Minima imposition.
Minima imposition on `g` based on the marker `f`. `inpos` creates
an image `y` by filing the valleys of `g` that do not cover the
connect components of `f`. A remarkable property of `y` is that its
regional minima are exactly the connect components of `g`.
Parameters
----------
f : Binary image. Marker image.
g : Gray-scale (uint8 or uint16) image. input image.
Bc : connectivity structuring element (default: 3x3 cross).
Returns
-------
y : Gray-scale (uint8 or uint16) image.
"""
if Bc is None: Bc = secross()
assert isbinary(f), 'pymorph.inpos: first parameter must be binary image'
fg = gray(neg(f),datatype(g))
k = limits(g)[1] - 1
return suprec(fg, intersec(union(g, 1), k, fg), Bc)
def interot(Iab, theta=45, direction="clockwise"):
"""
Irot = interot(Iab, theta=45, direction="clockwise")
Rotate an interval
`interot` rotates the interval `Iab` by `theta`.
Parameters
----------
Iab : Interval
theta : Degrees of rotation. Should be a multiple of 45 degrees. If not,
the rotation is approximate (default: 45).
direction : { 'clockwise' [default], 'anti-clockwise' }
Returns
-------
Irot : Interval
Examples
--------
::
b1 = endpoints()
b2 = interot(b1)
print intershow(b1)
print intershow(b2)
"""
from string import lower
direction = lower(direction)
A,Bc = Iab
if direction != 'clockwise':
theta = 360 - theta
Irot = se2hmt(serot(A, theta),
serot(Bc,theta))
return Irot
def intersec(f1, f2, f3=None, f4=None, f5=None):
"""
y = intersec(f1, f2, f3=None, f4=None, f5=None)
Intersection of images.
`intersec` creates the image `y` by taking the pixelwise minimum
between the images `f1`, `f2`, `f3`, `f4`, and `f5` . When `f1`,
`f2`, `f3`, `f4`, and f5 are binary images, `y` is the intersection
of them.
Parameters
----------
f1 : Image (gray or binary) or constant.
f2 : Image (gray or binary) or constant.
f3 : Image (gray or binary) or constant, optional.
f4 : Image (gray or binary) or constant, optional.
f5 : Image (gray or binary) or constant, optional.
Returns
-------
y : Image
"""
"""
- Examples
#
# example 1
#
f=to_uint8([255, 255, 0, 10, 0, 255, 250])
g=to_uint8([ 0, 40, 80, 140, 250, 10, 30])
print intersec(f, g)
print intersec(f, 0)
#
# example 2
#
a = readgray('form-ok.tif')
b = readgray('form-1.tif')
c = intersec(a,b)
show(a)
show(b)
show(c)
#
# example 3
#
d = readgray('tplayer1.tif')
e = readgray('tplayer2.tif')
f = readgray('tplayer3.tif')
g = intersec(d,e,f)
show(d)
show(e)
show(f)
show(g)
"""
# Should this be intersect(f0, f1, *args) and take an arbitrary nr of inputs?
from numpy import minimum
y = minimum(f1,f2)
if f3 != None: y = minimum(y,f3)
if f4 != None: y = minimum(y,f4)
if f5 != None: y = minimum(y,f5)
return y.astype(f1.dtype)
def intershow(Iab):
"""
s = intershow(Iab)
Visualize an interval.
`intershow` creates a representation for an interval using `0`, `1`
and `.` (don't care).
Parameters
----------
Iab : Interval
Returns
-------
s : string representation of the interval.
Examples
--------
::
print intershow(homothick())
prints out
::
0 0 0
. 0 .
0 0 0
"""
from numpy import array, product, reshape, choose
from string import join
assert (type(Iab) is tuple) and (len(Iab) == 2),'pymorph.intershow: not proper format of hit-or-miss template'
A,B = Iab
s = ''
for y in xrange(A.shape[0]):
for x in xrange(A.shape[1]):
if A[y,x]:
s += '1 '
elif B[y,x]:
s += '0 '
else:
s += '. '
s += '\n'
return s
def isbinary(f):
"""
is_b = isbinary(f)
Check for binary image
`isbinary` returns True if the datatype of the input image is
binary. A binary image has just the values `0` and `1`.
Parameters
----------
f : Image
Returns
-------
is_b : bool
Whether `f` is a binary image
"""
return f.dtype == bool
def asbinary(f):
"""
fbin = asbinary(f)
Transforms f into a binary image
Parameters
----------
f : image of any type, consisting only of 0s and 1s.
Returns
-------
fbin : binary image
"""
import numpy
if isbinary(f): return f
assert ( (f == 0) | (f == 1) ).sum() == f.size, 'pymorph.asbinary: f has values that are not 0 or 1.'
return (f != 0)
def isequal(f1, f2):
"""
r_eq = isequal(f1, f2)
Check if two images are equal
`isequal` compares the images `f1` and f2 and returns `True`, if
`f1 and `f2` have the same size and `f1(x) == f2(x)`, for all pixel `x`;
otherwise, returns `False`.
Parameters
----------
f1 : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
f2 : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
Returns
-------
r_eq : Boolean
Whether the two images are equal
"""
import numpy
if f1.shape != f2.shape:
return False
return numpy.all(f1 == f2)
def labelflat(f, Bc=None, lambda_=0):
"""
y = labelflat(f, Bc=None, lambda_=0)
Label the flat zones of gray-scale images.
`labelflat` creates the image y by labeling the flat zones of `f`,
according to the connectivity defined by the structuring
element `Bc`. A flat zone is a connected region of the image
domain in which all the pixels have the same gray-level
(lambda=0). When lambda is different than zero, a quasi-flat
zone is detected where two neighboring pixels belong to the same
region if their difference gray-levels is smaller or equal
`lambda`. The minimum label of the output image is 1 and the
maximum is the number of flat-zones in the image.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bc : Structuring element, optional
Connectivity (efault: 3x3 elementary cross).
lambda_ : Default: 0. Connectivity given by ``|f(q)-f(p)|<=lambda_``.
Returns
-------
y: ndarray of same shape as `f`
If number of labels is less than 65535, the data type is uint16;
otherwise, it is int32.
"""
"""
f=to_uint8([
[5,5,8,3,0],
[5,8,8,0,2]])
g=labelflat(f)
print g
g1=labelflat(f,secross(),2)
print g1
#
# example 2
#
f=readgray('blob.tif')
d=dist(f,sebox(),'euclidean')
g= d /8
show(g)
fz=labelflat(g,sebox());
lblshow(fz)
print fz.max()
#
# example 3
#
f=readgray('pcb_gray.tif')
g=labelflat(f,sebox(),3)
show(f)
lblshow(g)
"""
from numpy import allclose, ravel, nonzero, array
import numpy as np
if Bc is None: Bc = secross()
assert not lambda_, 'pymorph.labelflat: only lambda_==0 is supported.'
label = 1
labeled = np.zeros(f.shape, np.uint16)
fmark = np.zeros_like(f)
Y,X = np.where(f)
for y,x in zip(Y,X):
if labeled[y,x]: continue
val = f[y,x]
fmark[y,x] = val
r = infrec(fmark, (f == val), Bc)
labeled[r] = label
fmark[y,x] = 0
label += 1
return labeled
def lastero(f, B=None):
"""
Last erosion.
y = lastero(f, B=None)
`lastero` creates the image y by computing the last erosion by
the structuring element B of the image f . The objects found in
y are the objects of the erosion by nB that can not be
reconstructed from the erosion by (n+1)B , where n is a generic
non negative integer. The image y is a proper subset of the
morphological skeleton by B of f .
Parameters
----------
f : Binary image.
B : Structuring Element (default: 3x3 elementary cross).
Returns
-------
y : Binary image.
"""
assert isbinary(f),'pymorph.lastero: can only process binary images'
if B is None: B = secross()
dt = dist(f,B)
return regmax(dt,B)
def open(f, b=None):
"""
y = open(f, b={3x3 cross})
Morphological opening.
`open` creates the image y by the morphological opening of the
image `f` by the structuring element `b`. In the binary case, the
opening by the structuring element `b` may be interpreted as the
union of translations of `b` included in `f`. In the gray-scale
case, there is a similar interpretation taking the functions
umbra.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
b : Structuring element (default: 3x3 elementary cross).
Returns
-------
y : Image
"""
if b is None: b = secross()
return dilate(erode(f,b),b)
def openrec(f, Bero=None, Bc=None):
"""
y = openrec(f, Bero={3x3 cross}, Bc={3x3 cross})
Opening by reconstruction.
`openrec` creates the image `y` by an inf-reconstruction of the
image `f` from its erosion by `bero`, using the connectivity
defined by `Bc`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bero : Eroding structuring element (default: 3x3 cross).
Bc : Connecting structuring element (default: 3x3 cross).
Returns
-------
y : Image (same type as f).
"""
if Bero is None: Bero = secross()
if Bc is None: Bc = secross()
return infrec(erode(f,Bero),f,Bc)
def openrecth(f, Bero=None, Bc=None):
"""
y = openrecth(f, Bero={3x3 cross}, Bc={3x3 cross})
Open-by-Reconstruction Top-Hat.
`openrecth` creates the image `y` by subtracting the open by
reconstruction of `f`, defined by the structuring elements `Bero` and
`Bc`, of `f` itself.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Bero : Erosion structuring element (default: 3x3 cross).
Bc : Connectivity structuring element (default: 3x3 cross).
Returns
-------
y : Image of same type as `f`.
"""
if Bero is None: Bero = secross()
if Bc is None: Bc = secross()
return subm(f, openrec(f, Bero, Bc))
def openth(f, b=None):
"""
y = openth(f, b={3x3 cross})
Opening Top Hat.
`openth` creates the image y by subtracting the morphological
opening of `f` by the structuring element `b` of `f` itself.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
b : Structuring element (default: 3x3 cross).
Returns
-------
y : Image of same type as `f`.
"""
"""
- Examples
#
a = readgray('keyb.tif')
show(a)
b = openth(a,sebox(3))
show(b)
"""
if b is None: b = secross()
return subm(f, open(f,b))
def opentransf(f, type='octagon', n=65535, Bc=None, Buser=None):
"""
y = opentransf(f, type='octagon', n=65535, Bc={3x3 cross}, Buser={3x3 cross})
Open transform.
Compute the open transform of a binary image. The value of the
pixels in the open transform is radius of the smallest disk, which
if used to open, nullifies that pixel.
The disk sequence must satisfy the following: if `r > s`, then `rB` is
`sB`-open, i.e. `open(rB,sB) == rB`. Note that the Euclidean
disk does not satisfy this property in the discrete grid. This
function also computes the reconstructive open transform by
adding the suffix '-rec' in the 'type' parameter.
Parameters
----------
f : binary image.
type : { 'octagon' [default], 'chessboard', 'citi-block', 'linear-h', 'linear-v', 'linear-45r', 'user' }
disk family.
n : integer, optional
Maximum disk radius (default: 65535).
Bc : Structuring element, optional
Connectivity for the reconstructive opening. Used if '-rec' suffix is
appended in the 'type' string. default: 3x3 cross
Buser : structure element, optional
user disk, used if 'type' is 'user'.
Returns
-------
y : Gray-scale (uint16) image.
"""
"""
- Examples
#
# example 1
#
f = binary([
[0,0,0,0,0,0,0,0],
[0,0,1,1,1,1,0,0],
[0,0,1,1,1,1,1,0],
[0,1,0,1,1,1,0,0],
[1,1,0,0,0,0,0,0]])
print opentransf( f, 'city-block')
print opentransf( f, 'linear-h')
print opentransf( f, 'linear-45r')
print opentransf( f, 'user',10,secross(),binary([0,1,1]))
print opentransf( f, 'city-block-rec')
#
# example 2
#
f=readgray('numbers.tif')
show(f)
g=opentransf(f,'OCTAGON')
show(g)
#
# example 3
#
b=sedisk(3,'2D','OCTAGON')
g1=open(f,b)
show(g1)
g2=(g > 3)
print g1 == g2
"""
import numpy as np
from string import lower
if Bc is None: Bc = secross()
if Buser is None: Buser = secross()
assert isbinary(f),'pymorph.opentransf: input image is not binary'
type = lower(type)
rec_flag = False
if type.endswith('-rec'):
rec_flag = True
type = type[:-len('-rec')]
disk_se = (type in ('octagon', 'chessboard', 'city-block'))
if disk_se:
n = min(n,min(f.shape))
elif type == 'linear-h':
se = binary([[1, 1, 1]])
n = min(n,f.shape[1])
elif type =='linear-v':
se = binary([
[1],
[1],
[1]])
n = min(n,f.shape[0])
elif type == 'linear-45r':
se = binary([
[0, 0, 1],
[0, 1, 0],
[1, 0, 0]])
n = min(n,min(f.shape))
elif type == 'linear-45l':
se = binary([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
n = min(n,min(f.shape))
elif type == 'user':
se = Buser
n = min(n,min(f.shape))
else:
assert False, \
'pymorph.opentransf: only accepts octagon, chessboard, \
city-block, linear-h, linear-v, linear-45r, linear-45l, or user as type, or with suffix -rec.'
y = np.zeros(f.shape, np.uint8)
for k in xrange(n):
prev = y
if disk_se:
a = open(f, sedisk(k, 2, type))
else:
a = open(f, sesum(se,k))
y = addm(y, gray(a,'uint16',1))
if isequal(y, prev):
break
if rec_flag:
return grain(label(f,Bc), y, 'max')
return y
def patspec(f, type='octagon', n=65535, Bc=None, Buser=None):
"""
h = patspec(f, type='octagon', n=65535, Bc={3x3 cross}, Buser=None)
Pattern spectrum (also known as granulometric size density).
Compute the Pattern Spectrum of a binary image. See Mara:89b .
The pattern spectrum is the histogram of the open transform, not
taking the zero values.
Parameters
----------
f : Binary image.
type : { 'octagon' [default], 'chessboard', 'citi-block', 'linear-h', 'linear-v', 'linear-45r', 'user' }
disk family.
n : integer, optional
Maximum disk radius (default: 65535).
Bc : Structuring element, optional
Connectivity for the reconstructive granulometry. Used if '-rec' suffix
is appended in the 'type' string. default: 3x3 cross
Buser : structure element, optional
user disk, used if 'type' is 'user'.
Returns
-------
h : ndarray
"""
if Bc is None: Bc = secross()
if Buser is None: Buser = secross()
assert isbinary(f),'pymorph.patspec: Error: input image is not binary'
g = opentransf(f,type,n,Bc,Buser)
h = histogram(g)
h = h[1:]
return h
def regmax(f, Bc=None):
"""
y = regmax(f, Bc={3x3 cross})
Regional Maximum.
`regmax` creates a binary image `y` by computing the regional
maxima of `f`, according to the connectivity defined by the
structuring element `Bc`. A regional maximum is a flat zone not
surrounded by flat zones of higher gray values.
Parameters
----------
f : Gray-scale image.
Bc : Connectivity structuring element (default: 3x3 cross).
Returns
-------
y : Binary image.
"""
if Bc is None: Bc = secross()
return regmin(neg(f),Bc)
def regmin(f, Bc=None, option="binary"):
"""
y = regmin(f, Bc=None, option="binary")
Regional Minimum (with generalized dynamics).
`regmin` creates a binary image by computing the regional
minima of `f`, according to the connectivity defined by the
structuring element `Bc`.
A regional minimum is a flat zone not surrounded by flat zones of
lower gray values. A flat zone is a maximal connected component of a
gray-scale image with same pixel values.
Parameters
----------
f : Gray-scale (uint8 or uint16) image.
Bc : Connectivity structuring element (default: 3x3 cross).
option : 'binary'
if 'binary', outputs a binary image. Currently, it must be set to
'binary'. Fortunately, that's the default.
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
Not Implemented
---------------
There are three output options: binary image; valued image; and
generalized dynamics. The dynamics of a regional minima is the
minimum height a pixel has to climb in a walk to reach another
regional minima with a higher dynamics. The area-dyn is the minimum
area a catchment basin has to raise to reach another regional minima
with higher area-dynamics. The volume-dyn is the minimum volume a
catchment basin has to raise to reach another regional minima with a
higher volume dynamics.
The dynamics concept was first introduced in Grimaud:92 and it is
the basic notion for the hierarchical or multiscale watershed
transform.
Controlled by option:
'value'
output a grayscale image with points at the regional minimum with the
pixel values of the input image
'dynamics'
output a grayscale image with points at the regional minimum with its
dynamics;
'area-dyn'
int32 image with the area-dynamics;
'volume-dyn'
int32 image with the volume-dynamics.
"""
"""
- Examples
#
# example 1
#
a = to_uint8([
[10, 10, 10, 10, 10, 10, 10],
[10, 9, 6, 18, 6, 5, 10],
[10, 9, 6, 18, 6, 5, 10],
[10, 9, 9, 15, 4, 9, 10],
[10, 9, 9, 15, 12, 10, 10],
[10, 10, 10, 10, 10, 10, 10]])
print regmin(a)
print regmin(a,secross(),'value')
print regmin(a,secross(),'dynamics')
#
# example 2
#
f1=readgray('bloodcells.tif')
m1=regmin(f1,sebox())
show(f1,m1)
f2=hmin(f1,70)
show(f2)
m2=regmin(f2,sebox())
show(f2,m2)
#
# example 3
#
f=readgray('cameraman.tif')
g=gradm(f)
mh=regmin(g,secross(),'dynamics')
ws1=cwatershed(g, binary(mh, 20))
ws2=cwatershed(g, binary(mh, 40))
show(ws1)
show(ws2)
"""
if option != 'binary':
raise ValueError, "pymorph.regmin only implements option 'binary'"
if Bc is None: Bc = secross()
fplus = addm(f,1)
g = subm(suprec(fplus,f,Bc),f)
return union(threshad(g,1),threshad(f,0,0))
def se2interval(a, b):
"""
Iab = se2interval(a, b)
Create an interval from a pair of structuring elements.
`se2interval` creates the interval [a,b] from the structuring
elements `a` and `b` such that `a` is less or equal `b`.
Parameters
----------
a : Structuring element left extremity
b : Structuring element right extremity
Returns
-------
Iab : Interval
"""
return a, neg(b)
def se2hmt(A, Bc):
"""
Iab = se2hmt(A, Bc)
Create a Hit-or-Miss Template (or interval) from a pair of
structuring elements.
`se2hmt` creates the Hit-or-Miss Template (HMT), also called
interval `[A,Bc]` from the structuring elements `A` and `Bc` such that
`A` is included in the complement of `Bc` . The only difference
between this function and `se2interval` is that here the second
structuring element is the complement of the one used in the
other function. The advantage of this function over
`se2interval` is that this one is more flexible in the use of
the structuring elements as they are not required to have the
same size.
Parameters
----------
A : Structuring Element Left extremity.
Bc : Structuring Element Complement of the right extremity.
Returns
-------
Iab : Interval
"""
return A, Bc
def se2flatidx(f,Bc):
"""
Bi = se2flatidx(f,Bc)
Transforms the Bc structuring element into an array of indices so that
f.flat[Bi[i]] corresponds to the i-th element where Bc is true
Equivalent of::
g = zeros(f.shape)
h,w=Bc.shape
g[:h,:w]=Bc
Bi, = where(g.ravel())
This is useful for implementing many functions. See the implementation of
`label()` for an example.
Parameters
----------
f : image
Bc : structuring element
Returns
-------
Bi : array of indice offsets.
"""
from numpy import array, where
h,w=Bc.shape
h //= 2
w //= 2
Bi=[]
for i,j in zip(*where(Bc)):
Bi.append( (j-w)+(i-h)*f.shape[1] )
return array(Bi)
def sebox(r=1):
"""
B = sebox(r=1)
Create a box structuring element.
`sebox` creates the structuring element B formed by r successive
Minkowski additions of the elementary square (i.e., the 3x3
square centered at the origin) with itself. If `R=0`, `B` is the
unitary set that contains the origin. If `R=1`, `B` is the
elementary square itself.
Parameters
----------
r : integer, optional
size of box (default: 1)
Returns
-------
B : Structuring Element
"""
return sesum(binary([[1,1,1],
[1,1,1],
[1,1,1]]),
r)
def secross(r=1):
"""
B = secross(r=1)
Diamond structuring element and elementary 3x3 cross.
`secross` creates the structuring element `B` formed by `r`
successive Minkowski additions of the elementary cross (i.e.,
the 3x3 cross centered at the origin) with itself. If `r=0`, `B` is
the unitary set that contains the origin. If `r=1` (the default),
`B` is the elementary cross itself.
Parameters
----------
r : integer, optional
radius (default: 1)
Returns
-------
B : Structuring Element
"""
return sesum(binary([[0,1,0],
[1,1,1],
[0,1,0]]),
r)
def sedisk(r=3, dim=2, metric="euclidean", flat=True, h=0):
"""
B = sedisk(r=3, dim=2, metric="euclidean", flat=True, h=0)
Create a disk or a semi-sphere structuring element.
`sedisk` creates a flat structuring element B that is disk under
the metric metric , centered at the origin and with radius r or
a non-flat structuring element that is a semi-sphere under the
metric metric, centered at (0, h) and with radius r . this
structuring element can be created on the 1D, 2D or 3D space.
Parameters
----------
r : Non-negative integer. Disk radius (default: 3)
dim : {1, 2 [default], 3}
dimension
metric : {'euclidean' [default], 'city-block', 'octagon', 'chessboard' }
flat : boolean, optional
default: True
h : double, optional
elevation of the center of the semi-sphere (default: 0).
Returns
-------
B : Structuring Element
"""
from string import lower
from numpy import resize, transpose, arange
from numpy import sqrt, arange, transpose, maximum
metric = lower(metric)
assert dim== 2, 'pymorph.sedisk: Supports only 2D structuring elements'
if flat: y = binary([[1]])
else: y = to_int32([[h]])
if r == 0: return y
if metric == 'city-block':
if flat:
b = secross(1)
else:
b = to_int32([[-2147483647, 0,-2147483647],
[ 0, 1, 0],
[-2147483647, 0,-2147483647]])
return sedilate(y,sesum(b,r))
elif metric == 'chessboard':
if flat:
b = sebox(1)
else:
b = to_int32([[1,1,1],
[1,1,1],
[1,1,1]])
return sedilate(y,sesum(b,r))
elif metric == 'octagon':
if flat:
b1,b2 = sebox(1),secross(1)
else:
b1 = to_int32([
[1,1,1],
[1,1,1],
[1,1,1]])
b2 = to_int32([
[-2147483647, 0, -2147483647],
[ 0, 1, 0],
[-2147483647, 0, -2147483647]])
if r == 1:
return b1
return sedilate(sedilate(y,sesum(b1,r//2)), sesum(b2,(r+1)//2))
elif metric == 'euclidean':
v = arange(-r,r+1)
x = resize(v, (len(v), len(v)))
y = transpose(x)
Be = binary(sqrt(x*x + y*y) <= (r+0.5))
if flat:
return Be
be = h + to_int32( sqrt( maximum((r+0.5)*(r+0.5) - (x*x) - (y*y),0)))
be = intersec(gray(Be,'int32'),be)
return be
else:
assert False,'Non valid metric'
return B
def seline(length=3, theta=0):
"""
B = seline(length=3, theta=0)
Create a line structuring element.
seline creates a structuring element B that is a line segment
that has an extremity at the origin, length `length` and angle
`theta` (0 degrees is east direction, clockwise). If `length==0` ,
it generates the origin.
Note that `length` is simply the number of on-pixels. Therefore, in
diagonal directions it is off by a factor of \sqrt{2}.
Parameters
----------
length : Length of line (default: 3)
theta : Degrees, clockwise (default: 0, i.e. east)
Returns
-------
B : Structuring Element
Examples
--------
::
>>> import pymorph
>>> pymorph.seline(2)
array([[0],
[1],
[1]], dtype=uint8)
>>> pymorph.seline(4)
array([[0],
[0],
[0],
[1],
[1],
[1],
[1]], dtype=uint8)
>>> pymorph.seline(3,45)
array([[0, 0, 0],
[0, 1, 1],
[0, 0, 1]], dtype=uint8)
"""
import numpy
from numpy import pi, tan, cos, sin, sign, floor, arange, transpose, array, ones
theta = pi*theta/180.
if abs(tan(theta)) <= 1:
s = sign(cos(theta))
x0 = arange(length) * cos(theta)
x1 = floor(x0 * tan(theta) + 0.5)
else:
s = sign(sin(theta))
x1 = arange(length) * sin(theta)
x0 = floor(x1 / tan(theta) + 0.5)
x = array(zip(x0, x1), int)
B = set2mat((x,))
return B
def serot(b, theta=45, direction="clockwise"):
"""
brot = serot(b, theta=45, direction="clockwise")
Rotate a structuring element.
`serot` rotates structuring element `b` by `theta` degrees.
Parameters
----------
B : Structuring Element
theta : Degrees of rotation. Should be a multiple of 45 degrees. If not,
the rotation is approximate (default: 45).
direction : { 'clockwise' [default], 'anti-clockwise' }
Returns
-------
brot : structuring element
"""
from string import lower
from numpy import array, transpose, concatenate
from numpy import cos, sin, pi
direction = lower(direction)
if direction == "anti-clockwise":
theta = -theta
theta = pi * theta/180.
ct = cos(theta)
st = sin(theta)
y,v = mat2set(b)
if len(y)==0: return binary([0])
x0 = y[:,1] * cos(theta) - y[:,0] * sin(theta)
x1 = y[:,1] * sin(theta) + y[:,0] * cos(theta)
x0 = to_int32((x0 +0.5)*(x0>=0) + (x0-0.5)*(x0<0))
x1 = to_int32((x1 +0.5)*(x1>=0) + (x1-0.5)*(x1<0))
x = transpose(array([transpose(x1),transpose(x0)]))
brot = set2mat((x,v))
return brot
def seshow(b, option="normal"):
"""
y = seshow(b, option="NORMAL")
Display a structuring element as an image.
`seshow` used with the option 'expand' generates an image `y` that
is a suitable graphical representation of the structuring
element `b`. This function is useful to convert a structuring
element to an image. The origin of the structuring element is at
the center of the image. If `b` is flat, y is binary, otherwise, y
is signed `int32 image. When using the option 'non-flat', the
output `y` is always a signed `int32` image.
Parameters
----------
b : Structuring element
option : { 'normal' [default], 'expand', 'non-flat' }
Mode
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
from string import upper
option = upper(option)
if option=='NON-FLAT':
y = to_int32([0])
if isbinary(b):
b = intersec(gray(b,'int32'),0)
elif option=='NORMAL':
if isbinary(b):
y = binary([1])
else:
y = to_int32([0])
elif option=='EXPAND':
assert isbinary(b), 'pymorph.seshow: \'expand\' option is only available with flat SE'
y = sedilate(binary([1]),b)
b1 = (y>=0)
b0 = erode(y,b)
return bshow(b1,y,b0)
else:
assert False, 'pymorph.seshow: not a valid flag: NORMAL, EXPAND or NON-FLAT'
return sedilate(y,b)
def sesum(B=None, N=1):
"""
Bn = sesum(B=None, N=1)
N-1 iterative Minkowski additions
`sesum` creates the structuring element `Bn` from `N - 1` iterative
Minkowski additions with the structuring element `B`.
Parameters
----------
B : Structuring element (Default: 3x3 elementary cross).
N : Non-negative integer. Default: 1.
Returns
-------
Bn : Structuring Element
"""
if B is None: B = secross()
if N==0:
if isbinary(B): return binary([[1]])
else: return to_int32([[0]]) # identity
NB = B
for i in xrange(N-1):
NB = sedilate(NB,B)
return NB
def setrans(Bi, t):
"""
Bo = setrans(Bi, t)
Translate a structuring element
setrans translates a structuring element by a specific value.
Parameters
----------
Bi : Structuring Element
t : translation amount
Returns
-------
Bo : Structuring element of same type as `Bi`
"""
x,v = mat2set(Bi)
Bo = set2mat((x+t,v))
return Bo.astype(Bi.dtype)
def sereflect(Bi):
"""
Bo = sereflect(Bi)
Reflect a structuring element
`sereflect` reflects a structuring element about the origin
Parameters
----------
Bi : Structuring Element
Returns
-------
Bo : Structuring element of same type as `Bi`
"""
return Bi[::-1, ::-1]
def sedilate(B1, B2):
"""
Bo = sedilate(B1, B2)
Dilate one structuring element by another
`sedilate` dilates an structuring element by another. The main
difference between this dilation and `dilate` is that the dilation
between structuring elements are not bounded, returning another
structuring element usually larger than anyone of them. This
gives the composition of the two structuring elements by
Minkowski addition.
Parameters
----------
B1 : Structuring Element
B2 : Structuring Element
Returns
-------
Bo: Structuring Element
"""
from numpy import newaxis, array, int32
assert (isbinary(B1) or (B1.dtype == int32)) and (isbinary(B2) or B2.dtype == int32), 'pymorph.sedilate: s.e. must be binary or int32'
if len(B1.shape) == 1: B1 = B1[newaxis,:]
if len(B2.shape) == 1: B2 = B2[newaxis,:]
if B1.dtype==int32 or B2.dtype == int32:
Bo = to_int32([limits(to_int32([0]))[0]])
if isbinary(B1):
B1 = gray(B1,'int32',0)
if isbinary(B2):
B2 = gray(B2,'int32',0)
else:
Bo = binary([0])
x,v = mat2set(B2)
if len(x):
for i in xrange(x.shape[0]):
s = add4dilate(B1,v[i])
st= setrans(s,x[i])
Bo = seunion(Bo,st)
return Bo
def seunion(B1, B2):
"""
B = seunion(B1, B2)
Union of structuring elements
`seunion` creates a structuring element from the union of two
structuring elements.
Parameters
----------
B1 : Structuring element
B2 : Structuring element
Returns
-------
B : structure element
union of B1 and B2
"""
from numpy import maximum, ones, asarray, newaxis, int32
assert B1.dtype == B2.dtype, 'Cannot have different datatypes:'
type1 = B1.dtype
if len(B1) == 0: return B2
if len(B1.shape) == 1: B1 = B1[newaxis,:]
if len(B2.shape) == 1: B2 = B2[newaxis,:]
if B1.shape != B2.shape:
inf = limits(B1)[0]
h1,w1 = B1.shape
h2,w2 = B2.shape
H,W = max(h1,h2),max(w1,w2)
Hc,Wc = (H-1)//2,(W-1)//2 # center
BB1,BB2 = asarray(B1),asarray(B2)
B1, B2 = inf * ones((H,W),int32), inf *ones((H,W),int32)
dh1s , dh1e = (h1-1)//2 , (h1-1)//2 + (h1+1)%2 # deal with even and odd dimensions
dw1s , dw1e = (w1-1)//2 , (w1-1)//2 + (w1+1)%2
dh2s , dh2e = (h2-1)//2 , (h2-1)//2 + (h2+1)%2
dw2s , dw2e = (w2-1)//2 , (w2-1)//2 + (w2+1)%2
B1[ Hc-dh1s : Hc+dh1e+1 , Wc-dw1s : Wc+dw1e+1 ] = BB1
B2[ Hc-dh2s : Hc+dh2e+1 , Wc-dw2s : Wc+dw2e+1 ] = BB2
B = maximum(B1,B2).astype(type1)
return B
def skelm(f, B=None, return_binary=True):
"""
y = skelm(f, B={3x3 cross}, return_binary=True)
Morphological skeleton (Medial Axis Transform).
`skelm` creates the image `y` by computing the morphological
skeleton by `B` of the image `f`. In this
case, the pixels of value 1 in y are center of maximal balls
(generated from B ) included in `f`. This is also called Medial
Axis. If `return_binary` is False, the non zeros pixels in `y` are the
radius plus 1 of the maximal balls. This is called Medial Axis
Transform or valued morphological skeleton.
Parameters
----------
f : Binary image.
B : Structuring Element Default: None (3x3 elementary
cross).
return_binary : boolean, optional
Whether to return a binary image of the medial axis (the default) or a
greyscale a binary image (medial axis); value: output a grayscale
image with values of the radius of the disk to reconstruct the
original image (medial axis transform).
Returns
-------
y : Gray-scale (uint8 or uint16) or binary image.
"""
"""
- Examples
#
# example 1
#
from numpy import ones
a=neg(frame(binary(ones((7,9)))))
print a
print skelm(a)
print skelm(a,sebox())
#
# example 2
#
a=readgray('pcbholes.tif')
b=skelm(a)
show(a)
show(b)
#
# example 3
#
c=skelm(a,secross(),'value')
show(c)
"""
from numpy import asarray
if B is None: B = secross()
assert isbinary(f),'pymorph.skelm: only works for binary images'
k1,k2 = limits(f)
y = gray(intersec(f, k1),'uint16')
iszero = asarray(y)
nb = sesum(B,0)
for r in xrange(1,65535):
ero = erode(f,nb)
if isequal(ero, iszero): break
f1 = openth(ero, B)
nb = sedilate(nb, B)
y = union(y, gray(f1,'uint16',r))
if return_binary:
return binary(y)
return y
def skelmrec(f, B=None):
"""
y = skelmrec(f, B={3x3 cross})
Morphological skeleton reconstruction
(inverse medial axis transform).
`skelmrec` reconstructs the valued morphological skeleton to
recover the original image.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
B : Structuring element (default: 3x3 cross).
Returns
-------
y : Binary image.
"""
"""
- Examples
#
from numpy import ones
a=neg(frame(binary(ones((7,9)))))
print a
b=skelm(a,secross(),'value')
print b
c=skelmrec(b,secross())
print c
"""
if B is None: B = secross()
y = binary(intersec(f, 0))
for r in xrange(f.max(),1,-1):
y = dilate(union(y,binary(f,r)), B)
return union(y, binary(f,1))
def skiz(f, Bc=None, return_lines=False, metric=None):
"""
labeled = skiz(f, Bc={3x3 cross}, return_lines=False, metric=None)
labeled,lines = skiz(f, Bc={3x3 cross}, return_lines=True, metric=None)
Skeleton of Influence Zone - also know as Generalized Voronoi Diagram
`skiz` creates the `labeled` image by detecting the lines which are
equidistant to two or more connected components of `f`, according
to the connectivity defined by `Bc`.
`labeled` will be a labeled image, while `lines` will be a binary image
of the lines between the regions Depending on with the flag
When the connected objects of `f` are single points, the `skiz` is the
Voronoi diagram.
Parameters
----------
f : Binary image.
Bc : Structuring Element (default: 3x3 cross).
Connectivity for the distance measurement.
return_lines : boolean, optional
Whether to return the lines separating regions in the image.
Default: False
metric : str, optional
default: 'euclidean'
Returns
-------
y : Gray-scale (uint8 or uint16) image.
lines : binary image.
only returned if `return_lines` is ``True``
"""
"""
- Examples
#
# example 1
#
f=readgray('blob2.tif')
y=skiz(f,sebox(),'LINES','EUCLIDEAN')
show(f,y)
#
# example 2
#
from numpy import zeros
f=binary(zeros((100,100)))
f[30,25],f[20,75],f[50,50],f[70,30],f[80,70] = 1,1,1,1,1
y = skiz(f,sebox(),'LINES','EUCLIDEAN')
show(f,y)
"""
from string import upper
if Bc is None: Bc = secross()
d = dist(neg(f), Bc, metric)
return cwatershed(d,f,Bc,return_lines)
def subm(f1, f2):
"""
y = subm(f1, f2)
Subtraction of two images, with saturation.
`subm` creates the image `y` by pixelwise subtraction of the image
`f2` from the image `f1`. When the subtraction of the values of two
pixels is negative, 0 is taken as the result of the subtraction.
When `f1` and `f2` are binary images, `y` represents the set
subtraction of `f2` from `f1`.
Parameters
----------
f1 : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image.
f2 : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image. Or constant.
Returns
-------
y : ndarray of same shape and dtype as `f1`
Examples
--------
::
f = to_uint8([255, 255, 0, 10, 20, 10, 0, 255, 255])
g = to_uint8([10, 20, 30, 40, 50, 40, 30, 20, 10])
print subm(f, g)
print subm(f, 100)
print subm(100, f)
::
a = readgray('boxdrill-C.tif')
b = readgray('boxdrill-B.tif')
c = subm(a,b)
show(a)
show(b)
show(c)
"""
from numpy import array, clip
if type(f2) is array:
if f1.dtype != f2.dtype:
raise TypeError('pymorph.subm(): arguments cannot have different datatypes')
bottom,top = limits(f1)
y = clip(f1.astype('d') - f2, bottom, top)
return y.astype(f1.dtype)
def supcanon(f, Iab, theta=45, direction="clockwise"):
"""
y = supcanon(f, Iab, theta=45, direction="clockwise")
Union of sup-generating or hit-miss operators.
`supcanon` creates the image `y` by computing the union of
transformations of the image `f` by sup-generating operators.
These hit-miss operators are characterized by rotations (in the
clockwise or anti-clockwise direction) of `theta` degrees of the
interval `Iab`.
Parameters
----------
f : Binary image.
Iab : Interval
theta : {45 [default], 90, 180 }
Angle of rotation in degrees.
direction : {'clockwise' [default], 'anti-clockwise'}
Direction of rotation
Returns
------
y : Binary image.
"""
y = intersec(f,0)
for t in xrange(0,360,theta):
Irot = interot(Iab, t, direction)
y = union(y, supgen(f, Irot))
return y
def supgen(f, interval):
"""
y = supgen(f, interval)
Sup-generating (hit-miss).
`supgen` creates the binary image `y` by computing the transformation of
the image f by the sup-generating operator characterized by the interval
`Iab`. The sup-generating operator is just a relaxed template matching,
where the criterion to keep a shape is that it be inside the interval
`Iab`. Note that we have the classical template matching when `a==b`. Note
also that the sup-generating operator is equivalent to the classical
hit-miss operator.
Parameters
----------
f : Binary image.
interval : Interval
Returns
-------
y : Binary image.
"""
"""
- Examples
#
# example 1
#
f=binary([
[0,0,1,0,0,1,1],
[0,1,0,0,1,0,0],
[0,0,0,1,1,0,0]])
i=endpoints()
print intershow(i)
g=supgen(f,i)
print g
#
# example 2
#
a=readgray('gear.tif')
b=supgen(a,endpoints())
show(a)
show(dilate(b))
"""
A,Bc = interval
return intersec(erode(f,A),
erode(neg(f),Bc))
def suprec(f, g, Bc=None):
"""
y = suprec(f, g, Bc={3x3 cross})
Sup-reconstruction.
`suprec` creates the image `y` by an infinite number of iterations
(until stability) of the erosion of `f` by `Bc` conditioned to `g`.
We say that y is the sup-reconstruction of `g` from the marker `f`.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
Marker image.
g : Gray-scale (uint8 or uint16) or binary image.
Conditioning image.
Bc : Connectivity structuring element (default: 3x3 cross)
Returns
-------
y : Image
"""
from numpy import product
if Bc is None: Bc = secross()
n = product(f.shape)
return cerode(f,g,Bc,n);
def bshow(f1, f2=None, f3=None, factor=17):
"""
y = bshow(f1, f2=None, f3=None, factor=17)
Generate a graphical representation of overlaid binary images.
Does **not** actually display the image anywhere!
Generate an expanded binary image as a graphical representation
of up to three binary input images. The 1-pixels of the first
image are represented by square contours, the pixels of the
optional second image are represented by circles and for the
third image they are represented by shaded squares. This
function is useful to create graphical illustration of small
images.
Parameters
----------
f1 : Binary image.
f2 : Binary image. Default: None.
f3 : Binary image. Default: None.
factor : Double Default: 17. Expansion factor for the output
image. Use odd values above 9.
Returns
-------
y : Binary image.
"""
import numpy
from numpy import newaxis, zeros, resize, transpose, floor, arange, array
if f1.shape == (): f1 = array([f1])
if len(f1.shape) == 1: f1 = f1[newaxis,:]
if f2 is not None and f1.shape != f2.shape or \
f3 is not None and f1.shape != f3.shape or \
f2 is not None and f3 is not None and f2.shape != f3.shape:
raise ValueError, 'pymorph.bshow: arguments must have the same shape'
s = factor
if factor < 9: s = 9
h,w = f1.shape
y = zeros((s*h, s*w),numpy.int32)
xc = resize(range(s), (s,s))
yc = transpose(xc)
r = int(floor((s-8)/2. + 0.5))
circle = (xc - s//2)**2 + (yc - s//2)**2 <= r**2
r = arange(s) % 2
fillrect = resize(array([r, 1-r]), (s,s))
fillrect[ 0 , : ] = 0
fillrect[s-1, : ] = 0
fillrect[ : , 0 ] = 0
fillrect[ : ,s-1] = 0
for i in xrange(h):
for j in xrange(w):
m, n = s*i, s*j
if f1 and f1[i,j]:
y[m ,n:n+s] = 1
y[m+s-1 ,n:n+s] = 1
y[m:m+s ,n ] = 1
y[m:m+s ,n+s-1] = 1
if f2 and f2[i,j]:
y[m:m+s, n:n+s] += circle
if f3 and f3[i,j]:
y[m:m+s, n:n+s] += fillrect
return (y > 0)
def symdiff(f1, f2):
"""
y = symdiff(f1, f2)
Symmetric difference between two images
`symdiff` creates the image y by taken the union of the subtractions of `f1`
from `f2` and `f2` from `f1`. When `f1` and `f2` are binary images, y
represents the set of points that are in `f1` and not in `f2` or that are
in `f2` and not in `f1`.
Parameters
----------
f1 : Gray-scale (uint8 or uint16) or binary image.
f2 : Gray-scale (uint8 or uint16) or binary image.
Returns
-------
y : Image
"""
"""
- Examples
#
# example 1
#
a = to_uint8([1, 2, 3, 4, 5])
b = to_uint8([5, 4, 3, 2, 1])
print symdiff(a,b)
#
# example 2
#
c = readgray('tplayer1.tif')
d = readgray('tplayer2.tif')
e = symdiff(c,d)
show(c)
show(d)
show(e)
"""
return union(subm(f1,f2),subm(f2,f1))
symdif = symdiff
def thick(f, Iab=None, n=-1, theta=45, direction="clockwise"):
"""
y = thick(f, Iab=None, n=-1, theta=45, direction="clockwise")
Image transformation by thickening.
`thick` creates the binary image `y` by performing a thickening of the
binary image `f`. The number of iterations of the thickening is `n` and
each iteration is performed by union of `f` with the points that are
detected in f by the hit-miss operators characterized by rotations of theta
degrees of the interval `Iab`.
Parameters
----------
f : Binary image.
Iab : Interval Default: None (homothick).
n : Number of iterations. Default: -1, i.e., infinite
theta : Degrees of rotation: 45 (default), 90, or 180.
direction : One of ('clockwise', 'anti-clockwise').
Returns
-------
y : Binary image.
"""
from numpy import product
if Iab is None: Iab = homothick()
assert isbinary(f),'f must be binary image'
if n == -1: n = product(f.shape)
y = f
zero = intersec(f,0)
for i in xrange(n):
aux = zero
for t in xrange(0,360,theta):
sup = supgen(y, interot(Iab, t, direction))
aux = union(aux, sup)
y = union(y, sup)
if isequal(aux,zero): break
return y
def thin(f, Iab=None, n=-1, theta=45, direction="clockwise"):
"""
y = thin(f, Iab={Homothin}, n={infinite}, theta=45, direction="clockwise")
Image transformation by thinning.
`thin` creates the binary image `y` by performing a thinning of the binary
image `f`. The number of iterations of the thinning is n and each iteration
is performed by subtracting the points that are detect in f by hit-miss
operators characterized by rotations of theta of the interval `Iab`. When
`n` is infinite and the interval is homothin (default conditions), thin
gives the skeleton by thinning.
Parameters
----------
f : Binary image.
Iab : Interval Default:(homothin).
n : Number of iterations. (default: -1, i.e. infinite)
theta : Double Default: 45. Degrees of rotation: 45, 90, or
180.
direction : One of ('clockwise', 'anti-clockwise'). default: clockwise.
Returns
-------
y : Binary image.
"""
"""
- Examples
#
f=readgray('scissors.tif')
f1=thin(f)
show(f,f1) # skeleton
f2=thin(f1,endpoints(),15) # prunning 15 pixels
show(f,f2) # prunned skeleton
"""
from numpy import product
from string import lower
if Iab is None: Iab = homothin()
direction = lower(direction)
assert isbinary(f),'f must be binary image'
if n == -1: n = product(f.shape)
y = f
zero = intersec(f,0)
for i in xrange(n):
aux = zero
for t in xrange(0,360,theta):
sup = supgen(y, interot(Iab, t, direction))
aux = union(aux, sup)
y = subm(y, sup)
if isequal(aux,zero): break
return y
def union(f1, f2, *args):
"""
y = union(f1, f2, f3=None, f4=None, f5=None, ...)
Union of images.
`union` creates the image `y` by taking the pixelwise maximum
between the images given. When the images are binary images,
y represents the union of them.
Parameters
----------
f1 : Gray-scale (uint8 or uint16) or binary image.
f2 : Gray-scale (uint8 or uint16) or binary image. Or constant
args : Gray-scale (uint8 or uint16) or binary images.
Returns
-------
y : Image
"""
"""
- Examples
#
# example 1
#
f=to_uint8([255, 255, 0, 10, 0, 255, 250])
print 'f=',f
g=to_uint8([ 0, 40, 80, 140, 250, 10, 30])
print 'g=',g
print union(f, g)
print union(f, 255)
#
# example 2
#
a = readgray('form-ok.tif')
b = readgray('form-1.tif')
c = union(a,b)
show(a)
show(b)
show(c)
#
# example 3
#
d = readgray('danaus.tif')
e = (d < 80)
f = union(d,gray(e))
show(d)
show(e)
show(f)
#
# example 4
#
g = readgray('tplayer1.tif')
h = readgray('tplayer2.tif')
i = readgray('tplayer3.tif')
j = union(g,h,i)
show(g)
show(h)
show(i)
show(j)
"""
from numpy import maximum
y = maximum(f1,f2)
for f in args:
y = maximum(y,f)
return y.astype(f1.dtype)
def watershed(f, Bc=None, return_lines=False):
"""
W = watershed(f, Bc={3x3 cross}, return_lines=False)
W,Wl = watershed(f, Bc={3x3 cross}, return_lines=True)
Watershed transform.
`watershed` creates the image y by detecting the domain of the
catchment basins of `f`, according to the connectivity defined by
`Bc`.
The implementation of this function is based on VincSoil:91.
Parameters
----------
f : Gray-scale (uint8 or uint16) or binary image.
return_lines : boolean
Whether to return the boundaries (default: False)
Returns
-------
W : labeled image
Wl : separation lines
"""
from string import upper
if Bc is None: Bc = secross()
return cwatershed(f,regmin(f,Bc),Bc,return_lines=return_lines)
def maxleveltype(type='uint8'):
"""
max = maxleveltype(type='uint8')
Returns the maximum value supported by a datatype
Parameters
----------
type : { 'uint8' [default], 'uint16', 'int32'}
Returns
-------
max : numeric value
The maximum level value of `type`
"""
if type == 'uint8': return 255
if type == 'binary': return 1
if type == 'uint16': return 65535
if type == 'int32': return 2147483647
assert False, 'pymorph.maxleveltype: does not support this data type:'+TYPE
def to_int32(f):
"""
Convert an image to an int32 image.
img = to_int32(f)
`to_int32` clips the input image between the values -2147483648 and
2147483647 and converts it to the signed 32-bit datatype.
Parameters
----------
f : Any image
Returns
-------
img : The converted image
"""
from numpy import int32, asanyarray
return asanyarray(f).astype(int32)
def to_uint8(f):
"""
img = to_uint8(f)
Convert an image to an uint8 image.
`to_uint8` clips the input image between the values 0 and 255 and
converts it to the unsigned 8-bit datatype.
Parameters
----------
f : Any image
Returns
-------
img : Gray-scale uint8 image. The converted image
Examples
--------
::
print to_uint8([-3, 0, 8, 600])
prints out
::
[ 0 0 8 255]
"""
from numpy import array, clip, uint8
img = array(clip(f,0,255),uint8)
return img
def to_uint16(f):
"""
img = to_uint16(f)
Convert an image to a uint16 image.
`to_uint16` clips the input image between the values 0 and 65535 and
converts it to the unsigned 16-bit datatype.
Parameters
----------
f : Any image
Returns
-------
img : The converted image
"""
from numpy import array, clip
img = array(clip(f,0,65535)).astype('H')
return img
def to_gray(f):
"""
g = to_gray(f)
Transform (possibly color) image to gray image.
If input file is a color RGB image, it is converted to gray-scale using the
equation:
I = 0.2989 * R + 0.587 * G + 0.114 * B
Parameters
----------
f : ndarray of shape HxWx3
color image.
Returns
-------
g : gray image of shape HxW same type as input
"""
import numpy as np
if len(f.shape) == 2:
return f
if len(f.shape) != 3:
raise ValueError, 'pymorph.to_gray: can only handle gray and color images'
r = f[:,:,0]
g = f[:,:,1]
b = f[:,:,2]
if np.all( (r == g) & (r == b) ):
return r
g = (0.2989 * r + 0.5870 * g + 0.1140 * b)
return g.astype(f.dtype)
def datatype(f):
"""
type = datatype(f)
Return the image datatype string
datatype returns a string that identifies the pixel datatype
of the image `f`.
Consider using f.dtype.
Parameters
----------
f : Unsigned gray-scale (uint8 or uint16), signed (int32) or binary image
Any image
Returns
-------
type : str
String representation of image type: 'binary',
'uint8', 'uint16' or 'int32'
"""
from numpy import bool, uint8, uint16, int32
code = f.dtype
if code == bool: type='binary'
elif code == uint8: type='uint8'
elif code == uint16: type='uint16'
elif code == int32: type='int32'
else:
assert 0,'Does not accept this typecode: %s' % code
return type
def add4dilate(f, c):
"""
a = add4dilate(f, c)
Addition for dilation. Assumes that the minimum value of dtype(f) is
to represent -inf (where -inf + c == -inf, for all c)
Parameters
----------
f : Gray-scale or binary image.
c : Gray-scale, binary image, or constant.
Returns
-------
a : f + c (but with correct implementation of -inf)
"""
from numpy import asarray, minimum, maximum, float64
if not c:
return f
y = asarray(f,float64) + c
k1,k2 = limits(f)
y = ((f==k1) * k1) + ((f!=k1) * y)
y = maximum(minimum(y,k2),k1)
return y.astype(f.dtype)
def mat2set(A):
"""
C,V = mat2set(A)
Converts image representation from matrix to set
Return tuple with array of pixel coordinates and array of
corresponding pixel values. The input image is in the matrix
format, like the structuring element, where the origin (0,0) is
at the center of the matrix.
Parameters
----------
A : ndarray
Image in matrix format, where the origin (0,0) is at the
center of the matrix.
Returns
-------
C : array of pixel coordinates
V : array of pixel values corresponding to the coordinates of C
See also
--------
set2mat : reverse function
"""
from numpy import take, ravel, nonzero, transpose, newaxis
if len(A.shape) == 1: A = A[newaxis,:]
offsets = nonzero(ravel(A) - limits(A)[0])[0]
if len(offsets) == 0: return ([],[])
h,w = A.shape
x = [0,1]
x[0] = offsets//w - (h-1)//2
x[1] = offsets%w - (w-1)//2
x = transpose(x)
return x,take(ravel(A),offsets)
def set2mat(A):
"""
M = set2mat(A)
Converts image representation from set to matrix
Return an image in the matrix format built from a tuple of an
array of pixel coordinates and a corresponding array of pixel
values
Parameters
----------
A : tuple (ndarray, ndarray) or tuple (ndarray,)
Tuple with array of pixel coordinates and optional array of
corresponding pixel values
Returns
-------
M : Image in matrix format, origin (0,0) at the matrix center
Examples
--------
::
coords = to_int32([ [0,0] , [-1,0] , [1,1]])
print set2mat( (coords,) )
prints out
::
[0,1,0]
[0,1,0]
[0,0,1]
"""
from numpy import put, ones, ravel, shape, newaxis, array, asarray, max, int32
import numpy as np
if len(A) == 2:
x, v = A
v = asarray(v)
elif len(A) == 1:
x = A[0]
v = np.ones((len(x),), np.uint8)
else:
raise TypeError, 'pymorph.set2mat: argument must be a tuple of length 1 or 2'
if len(x) == 0: return array([0]).astype(v.dtype)
if len(x.shape) == 1: x = x[newaxis,:]
dh,dw = abs(x).max(0)
h,w = (2*dh)+1, (2*dw)+1
M=ones((h,w),int32) * limits(v)[0]
offset = x[:,0] * w + x[:,1] + (dh*w + dw)
put(M,offset,v)
return M.astype(v.dtype)
def pad4n(f, Bc, value, scale=1):
"""
y = pad4n(f, Bc, value, scale=1)
pads f with value so that Bc can be applied scaled by scale.
Parameters
----------
f : Image
Bc : Structuring Element (connectivity).
value : dtype
value to pad borders with
scale : (default=1).
Returns
-------
y : The converted image
"""
from numpy import ones, array
if type(Bc) is not array:
Bc = seshow(Bc)
Bh, Bw = Bc.shape
assert Bh%2 and Bw%2, 'structuring element must be odd sized'
ch, cw = scale * Bh/2, scale * Bw/2
g = value * ones( f.shape + scale * (array(Bc.shape) - 1))
g[ ch: -ch, cw: -cw] = f
return g.astype(f.dtype)
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