def binary_dilation(image, selem=None, out=None):
"""Return fast binary morphological dilation of an image.
This function returns the same result as greyscale dilation but performs
faster for binary images.
Morphological dilation sets a pixel at ``(i,j)`` to the maximum over all
pixels in the neighborhood centered at ``(i,j)``. Dilation enlarges bright
regions and shrinks dark regions.
Parameters
----------
image : ndarray
Binary input image.
selem : ndarray, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped structuring element (connectivity=1).
out : ndarray of bool, optional
The array to store the result of the morphology. If None is
passed, a new array will be allocated.
Returns
-------
dilated : ndarray of bool or uint
The result of the morphological dilation with values in
``[False, True]``.
"""
if out is None:
out = cp.empty(image.shape, dtype=cp.bool_)
ndi.binary_dilation(image, structure=selem, output=out)
return out
def test_01_01_circle(self):
"""Test that the Canny filter finds the outlines of a circle"""
i, j = cp.mgrid[-200:200, -200:200].astype(float) / 200
c = cp.abs(cp.sqrt(i * i + j * j) - 0.5) < 0.02
result = feature.canny(c.astype(float), 4, 0, 0,
cp.ones(c.shape, bool))
#
# erode and dilate the circle to get rings that should contain the
# outlines
#
# TODO: grlee77: only implemented brute_force=True, so added that to
# these tests
cd = binary_dilation(c, iterations=3, brute_force=True)
ce = binary_erosion(c, iterations=3, brute_force=True)
cde = cp.logical_and(cd, cp.logical_not(ce))
self.assertTrue(cp.all(cde[result]))
#
# The circle has a radius of 100. There are two rings here, one
# for the inside edge and one for the outside. So that's
# 100 * 2 * 2 * 3 for those places where pi is still 3.
# The edge contains both pixels if there's a tie, so we
# bump the count a little.
point_count = cp.sum(result)
self.assertTrue(point_count > 1200)
self.assertTrue(point_count < 1600)
def inf_sup(u):
"""IS operator."""
if cnp.ndim(u) == 2:
P = _P2
elif cnp.ndim(u) == 3:
P = _P3
else:
raise ValueError("u has an invalid number of dimensions "
"(should be 2 or 3)")
dilations = []
for P_i in P:
d = ndi.binary_dilation(u, cp.asarray(P_i)).astype(np.int8, copy=False)
dilations.append(d)
return cp.stack(dilations, axis=0).min(0)
def test_01_02_circle_with_noise(self):
"""Test that the Canny filter finds the circle outlines
in a noisy image"""
cp.random.seed(0)
i, j = cp.mgrid[-200:200, -200:200].astype(float) / 200
c = cp.abs(cp.sqrt(i * i + j * j) - 0.5) < 0.02
cf = c.astype(float) * 0.5 + cp.random.uniform(size=c.shape) * 0.5
result = F.canny(cf, 4, 0.1, 0.2, cp.ones(c.shape, bool))
#
# erode and dilate the circle to get rings that should contain the
# outlines
#
cd = binary_dilation(c, iterations=4, brute_force=True)
ce = binary_erosion(c, iterations=4, brute_force=True)
cde = cp.logical_and(cd, cp.logical_not(ce))
self.assertTrue(cp.all(cde[result]))
point_count = cp.sum(result)
self.assertTrue(point_count > 1200)
self.assertTrue(point_count < 1600)
def test_mask():
vol = cp.zeros((30, 30, 30))
vol[15, 15, 15] = 1
struct = generate_binary_structure(3, 1)
# TODO: remove brute_force=True once non-brute force implemented for CuPy
voln = binary_dilation(vol,
structure=struct,
iterations=4,
brute_force=True).astype("f4")
initial = cp.sum(voln > 0)
mask = voln.copy()
thresh = otsu(mask)
mask = mask > thresh
initial_otsu = cp.sum(mask > 0)
assert_array_equal(initial_otsu, initial)
mins, maxs = bounding_box(mask)
voln_crop = crop(mask, mins, maxs)
initial_crop = cp.sum(voln_crop > 0)
assert_array_equal(initial_crop, initial)
applymask(voln, mask)
final = cp.sum(voln > 0)
assert_array_equal(final, initial)
# Test multi_median.
img = cp.arange(25).reshape(5, 5)
img_copy = img.copy()
medianradius = 2
median_test = multi_median(img, medianradius, 3)
assert_array_equal(img, img_copy)
medarr = ((medianradius * 2) + 1, ) * img.ndim
median_control = median_filter(img, medarr)
median_control = median_filter(median_control, medarr)
median_control = median_filter(median_control, medarr)
assert_array_equal(median_test, median_control)
def morphological_geodesic_active_contour(
gimage,
iterations,
init_level_set="circle",
smoothing=1,
threshold="auto",
balloon=0,
iter_callback=lambda x: None,
):
"""Morphological Geodesic Active Contours (MorphGAC).
Geodesic active contours implemented with morphological operators. It can
be used to segment objects with visible but noisy, cluttered, broken
borders.
Parameters
----------
gimage : (M, N) or (L, M, N) array
Preprocessed image or volume to be segmented. This is very rarely the
original image. Instead, this is usually a preprocessed version of the
original image that enhances and highlights the borders (or other
structures) of the object to segment.
`morphological_geodesic_active_contour` will try to stop the contour
evolution in areas where `gimage` is small. See
`morphsnakes.inverse_gaussian_gradient` as an example function to
perform this preprocessing. Note that the quality of
`morphological_geodesic_active_contour` might greatly depend on this
preprocessing.
iterations : uint
Number of iterations to run.
init_level_set : str, (M, N) array, or (L, M, N) array
Initial level set. If an array is given, it will be binarized and used
as the initial level set. If a string is given, it defines the method
to generate a reasonable initial level set with the shape of the
`image`. Accepted values are 'checkerboard' and 'circle'. See the
documentation of `checkerboard_level_set` and `circle_level_set`
respectively for details about how these level sets are created.
smoothing : uint, optional
Number of times the smoothing operator is applied per iteration.
Reasonable values are around 1-4. Larger values lead to smoother
segmentations.
threshold : float, optional
Areas of the image with a value smaller than this threshold will be
considered borders. The evolution of the contour will stop in this
areas.
balloon : float, optional
Balloon force to guide the contour in non-informative areas of the
image, i.e., areas where the gradient of the image is too small to push
the contour towards a border. A negative value will shrink the contour,
while a positive value will expand the contour in these areas. Setting
this to zero will disable the balloon force.
iter_callback : function, optional
If given, this function is called once per iteration with the current
level set as the only argument. This is useful for debugging or for
plotting intermediate results during the evolution.
Returns
-------
out : (M, N) or (L, M, N) array
Final segmentation (i.e., the final level set)
See Also
--------
inverse_gaussian_gradient, circle_level_set, checkerboard_level_set
Notes
-----
This is a version of the Geodesic Active Contours (GAC) algorithm that uses
morphological operators instead of solving partial differential equations
(PDEs) for the evolution of the contour. The set of morphological operators
used in this algorithm are proved to be infinitesimally equivalent to the
GAC PDEs (see [1]_). However, morphological operators are do not suffer
from the numerical stability issues typically found in PDEs (e.g., it is
not necessary to find the right time step for the evolution), and are
computationally faster.
The algorithm and its theoretical derivation are described in [1]_.
References
----------
.. [1] A Morphological Approach to Curvature-based Evolution of Curves and
Surfaces, Pablo Márquez-Neila, Luis Baumela, Luis Álvarez. In IEEE
Transactions on Pattern Analysis and Machine Intelligence (PAMI),
2014, :DOI:`10.1109/TPAMI.2013.106`
"""
image = gimage
init_level_set = _init_level_set(init_level_set, image.shape)
_check_input(image, init_level_set)
if threshold == "auto":
threshold = cp.percentile(image, 40)
structure = cp.ones((3, ) * len(image.shape), dtype=cp.int8)
dimage = cnp.gradient(image)
# threshold_mask = image > threshold
if balloon != 0:
threshold_mask_balloon = image > threshold / cp.abs(balloon)
u = (init_level_set > 0).astype(cp.int8)
iter_callback(u)
for _ in range(iterations):
# Balloon
if balloon > 0:
aux = ndi.binary_dilation(u, structure)
elif balloon < 0:
aux = ndi.binary_erosion(u, structure)
if balloon != 0:
u[threshold_mask_balloon] = aux[threshold_mask_balloon]
# Image attachment
aux = cp.zeros_like(image)
du = cnp.gradient(u)
for el1, el2 in zip(dimage, du):
aux += el1 * el2
u[aux > 0] = 1
u[aux < 0] = 0
# Smoothing
for _ in range(smoothing):
u = _curvop(u)
iter_callback(u)
return u
def median_otsu(input_volume,
vol_idx=None,
median_radius=4,
numpass=4,
autocrop=False,
dilate=None):
"""Simple brain extraction tool method for images from DWI data.
It uses a median filter smoothing of the input_volumes `vol_idx` and an
automatic histogram Otsu thresholding technique, hence the name
*median_otsu*.
This function is inspired from Mrtrix's bet which has default values
``median_radius=3``, ``numpass=2``. However, from tests on multiple 1.5T
and 3T data from GE, Philips, Siemens, the most robust choice is
``median_radius=4``, ``numpass=4``.
Parameters
----------
input_volume : ndarray
3D or 4D array of the brain volume.
vol_idx : None or array, optional.
1D array representing indices of ``axis=3`` of a 4D `input_volume`.
None is only an acceptable input if ``input_volume`` is 3D.
median_radius : int
Radius (in voxels) of the applied median filter (default: 4).
numpass: int
Number of pass of the median filter (default: 4).
autocrop: bool, optional
if True, the masked input_volume will also be cropped using the
bounding box defined by the masked data. Should be on if DWI is
upsampled to 1x1x1 resolution. (default: False).
dilate : None or int, optional
number of iterations for binary dilation
Returns
-------
maskedvolume : ndarray
Masked input_volume
mask : 3D ndarray
The binary brain mask
Notes
-----
Copyright (C) 2011, the scikit-image team
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
3. Neither the name of skimage nor the names of its contributors may be
used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
"""
xp = get_array_module(input_volume, vol_idx)
if len(input_volume.shape) == 4:
if vol_idx is not None:
b0vol = xp.mean(input_volume[..., xp.asarray(vol_idx)], axis=3)
else:
raise ValueError("For 4D images, must provide vol_idx input")
else:
b0vol = input_volume
# Make a mask using a multiple pass median filter and histogram
# thresholding.
mask = multi_median(b0vol, median_radius, numpass)
thresh = otsu(mask)
mask = mask > thresh
if dilate is not None:
cross = generate_binary_structure(3, 1)
# only brute_force iterations have been implemented in cupy
kwargs = dict(brute_force=True) if xp == cp else {}
mask = binary_dilation(mask, cross, iterations=dilate, **kwargs)
# Auto crop the volumes using the mask as input_volume for bounding box
# computing.
if autocrop:
mins, maxs = bounding_box(mask)
mask = crop(mask, mins, maxs)
croppedvolume = crop(input_volume, mins, maxs)
maskedvolume = applymask(croppedvolume, mask)
else:
maskedvolume = applymask(input_volume, mask)
return maskedvolume, mask