485 lines
16 KiB
Python
485 lines
16 KiB
Python
|
import warnings
|
||
|
|
from itertools import cycle
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy import ndimage as ndi
|
||
|
|
|
||
|
|
from .._shared.utils import check_nD
|
||
|
|
|
||
|
|
__all__ = ['morphological_chan_vese',
|
||
|
|
'morphological_geodesic_active_contour',
|
||
|
|
'inverse_gaussian_gradient',
|
||
|
|
'circle_level_set',
|
||
|
|
'disk_level_set',
|
||
|
|
'checkerboard_level_set'
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
class _fcycle(object):
|
||
|
|
|
||
|
|
def __init__(self, iterable):
|
||
|
|
"""Call functions from the iterable each time it is called."""
|
||
|
|
self.funcs = cycle(iterable)
|
||
|
|
|
||
|
|
def __call__(self, *args, **kwargs):
|
||
|
|
f = next(self.funcs)
|
||
|
|
return f(*args, **kwargs)
|
||
|
|
|
||
|
|
|
||
|
|
# SI and IS operators for 2D and 3D.
|
||
|
|
_P2 = [np.eye(3),
|
||
|
|
np.array([[0, 1, 0]] * 3),
|
||
|
|
np.flipud(np.eye(3)),
|
||
|
|
np.rot90([[0, 1, 0]] * 3)]
|
||
|
|
_P3 = [np.zeros((3, 3, 3)) for i in range(9)]
|
||
|
|
|
||
|
|
_P3[0][:, :, 1] = 1
|
||
|
|
_P3[1][:, 1, :] = 1
|
||
|
|
_P3[2][1, :, :] = 1
|
||
|
|
_P3[3][:, [0, 1, 2], [0, 1, 2]] = 1
|
||
|
|
_P3[4][:, [0, 1, 2], [2, 1, 0]] = 1
|
||
|
|
_P3[5][[0, 1, 2], :, [0, 1, 2]] = 1
|
||
|
|
_P3[6][[0, 1, 2], :, [2, 1, 0]] = 1
|
||
|
|
_P3[7][[0, 1, 2], [0, 1, 2], :] = 1
|
||
|
|
_P3[8][[0, 1, 2], [2, 1, 0], :] = 1
|
||
|
|
|
||
|
|
|
||
|
|
def sup_inf(u):
|
||
|
|
"""SI operator."""
|
||
|
|
|
||
|
|
if np.ndim(u) == 2:
|
||
|
|
P = _P2
|
||
|
|
elif np.ndim(u) == 3:
|
||
|
|
P = _P3
|
||
|
|
else:
|
||
|
|
raise ValueError("u has an invalid number of dimensions "
|
||
|
|
"(should be 2 or 3)")
|
||
|
|
|
||
|
|
erosions = []
|
||
|
|
for P_i in P:
|
||
|
|
erosions.append(ndi.binary_erosion(u, P_i))
|
||
|
|
|
||
|
|
return np.array(erosions, dtype=np.int8).max(0)
|
||
|
|
|
||
|
|
|
||
|
|
def inf_sup(u):
|
||
|
|
"""IS operator."""
|
||
|
|
|
||
|
|
if np.ndim(u) == 2:
|
||
|
|
P = _P2
|
||
|
|
elif np.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:
|
||
|
|
dilations.append(ndi.binary_dilation(u, P_i))
|
||
|
|
|
||
|
|
return np.array(dilations, dtype=np.int8).min(0)
|
||
|
|
|
||
|
|
|
||
|
|
_curvop = _fcycle([lambda u: sup_inf(inf_sup(u)), # SIoIS
|
||
|
|
lambda u: inf_sup(sup_inf(u))]) # ISoSI
|
||
|
|
|
||
|
|
|
||
|
|
def _check_input(image, init_level_set):
|
||
|
|
"""Check that shapes of `image` and `init_level_set` match."""
|
||
|
|
check_nD(image, [2, 3])
|
||
|
|
|
||
|
|
if len(image.shape) != len(init_level_set.shape):
|
||
|
|
raise ValueError("The dimensions of the initial level set do not "
|
||
|
|
"match the dimensions of the image.")
|
||
|
|
|
||
|
|
|
||
|
|
def _init_level_set(init_level_set, image_shape):
|
||
|
|
"""Auxiliary function for initializing level sets with a string.
|
||
|
|
|
||
|
|
If `init_level_set` is not a string, it is returned as is.
|
||
|
|
"""
|
||
|
|
if isinstance(init_level_set, str):
|
||
|
|
if init_level_set == 'checkerboard':
|
||
|
|
res = checkerboard_level_set(image_shape)
|
||
|
|
# TODO: remove me in 0.19.0
|
||
|
|
elif init_level_set == 'circle':
|
||
|
|
res = circle_level_set(image_shape)
|
||
|
|
elif init_level_set == 'disk':
|
||
|
|
res = disk_level_set(image_shape)
|
||
|
|
else:
|
||
|
|
raise ValueError("`init_level_set` not in "
|
||
|
|
"['checkerboard', 'circle', 'disk']")
|
||
|
|
else:
|
||
|
|
res = init_level_set
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def circle_level_set(image_shape, center=None, radius=None):
|
||
|
|
"""Create a circle level set with binary values.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image_shape : tuple of positive integers
|
||
|
|
Shape of the image
|
||
|
|
center : tuple of positive integers, optional
|
||
|
|
Coordinates of the center of the circle given in (row, column). If not
|
||
|
|
given, it defaults to the center of the image.
|
||
|
|
radius : float, optional
|
||
|
|
Radius of the circle. If not given, it is set to the 75% of the
|
||
|
|
smallest image dimension.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array with shape `image_shape`
|
||
|
|
Binary level set of the circle with the given `radius` and `center`.
|
||
|
|
|
||
|
|
Warns
|
||
|
|
-----
|
||
|
|
Deprecated:
|
||
|
|
.. versionadded:: 0.17
|
||
|
|
|
||
|
|
This function is deprecated and will be removed in scikit-image 0.19.
|
||
|
|
Please use the function named ``disk_level_set`` instead.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
checkerboard_level_set
|
||
|
|
"""
|
||
|
|
warnings.warn("circle_level_set is deprecated in favor of "
|
||
|
|
"disk_level_set."
|
||
|
|
"circle_level_set will be removed in version 0.19",
|
||
|
|
FutureWarning, stacklevel=2)
|
||
|
|
|
||
|
|
return disk_level_set(image_shape, center=center, radius=radius)
|
||
|
|
|
||
|
|
|
||
|
|
def disk_level_set(image_shape, *, center=None, radius=None):
|
||
|
|
"""Create a disk level set with binary values.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image_shape : tuple of positive integers
|
||
|
|
Shape of the image
|
||
|
|
center : tuple of positive integers, optional
|
||
|
|
Coordinates of the center of the disk given in (row, column). If not
|
||
|
|
given, it defaults to the center of the image.
|
||
|
|
radius : float, optional
|
||
|
|
Radius of the disk. If not given, it is set to the 75% of the
|
||
|
|
smallest image dimension.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array with shape `image_shape`
|
||
|
|
Binary level set of the disk with the given `radius` and `center`.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
checkerboard_level_set
|
||
|
|
"""
|
||
|
|
|
||
|
|
if center is None:
|
||
|
|
center = tuple(i // 2 for i in image_shape)
|
||
|
|
|
||
|
|
if radius is None:
|
||
|
|
radius = min(image_shape) * 3.0 / 8.0
|
||
|
|
|
||
|
|
grid = np.mgrid[[slice(i) for i in image_shape]]
|
||
|
|
grid = (grid.T - center).T
|
||
|
|
phi = radius - np.sqrt(np.sum((grid)**2, 0))
|
||
|
|
res = np.int8(phi > 0)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def checkerboard_level_set(image_shape, square_size=5):
|
||
|
|
"""Create a checkerboard level set with binary values.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image_shape : tuple of positive integers
|
||
|
|
Shape of the image.
|
||
|
|
square_size : int, optional
|
||
|
|
Size of the squares of the checkerboard. It defaults to 5.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array with shape `image_shape`
|
||
|
|
Binary level set of the checkerboard.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
circle_level_set
|
||
|
|
"""
|
||
|
|
|
||
|
|
grid = np.mgrid[[slice(i) for i in image_shape]]
|
||
|
|
grid = (grid // square_size)
|
||
|
|
|
||
|
|
# Alternate 0/1 for even/odd numbers.
|
||
|
|
grid = grid & 1
|
||
|
|
|
||
|
|
checkerboard = np.bitwise_xor.reduce(grid, axis=0)
|
||
|
|
res = np.int8(checkerboard)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def inverse_gaussian_gradient(image, alpha=100.0, sigma=5.0):
|
||
|
|
"""Inverse of gradient magnitude.
|
||
|
|
|
||
|
|
Compute the magnitude of the gradients in the image and then inverts the
|
||
|
|
result in the range [0, 1]. Flat areas are assigned values close to 1,
|
||
|
|
while areas close to borders are assigned values close to 0.
|
||
|
|
|
||
|
|
This function or a similar one defined by the user should be applied over
|
||
|
|
the image as a preprocessing step before calling
|
||
|
|
`morphological_geodesic_active_contour`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) or (L, M, N) array
|
||
|
|
Grayscale image or volume.
|
||
|
|
alpha : float, optional
|
||
|
|
Controls the steepness of the inversion. A larger value will make the
|
||
|
|
transition between the flat areas and border areas steeper in the
|
||
|
|
resulting array.
|
||
|
|
sigma : float, optional
|
||
|
|
Standard deviation of the Gaussian filter applied over the image.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
gimage : (M, N) or (L, M, N) array
|
||
|
|
Preprocessed image (or volume) suitable for
|
||
|
|
`morphological_geodesic_active_contour`.
|
||
|
|
"""
|
||
|
|
gradnorm = ndi.gaussian_gradient_magnitude(image, sigma, mode='nearest')
|
||
|
|
return 1.0 / np.sqrt(1.0 + alpha * gradnorm)
|
||
|
|
|
||
|
|
|
||
|
|
def morphological_chan_vese(image, iterations, init_level_set='checkerboard',
|
||
|
|
smoothing=1, lambda1=1, lambda2=1,
|
||
|
|
iter_callback=lambda x: None):
|
||
|
|
"""Morphological Active Contours without Edges (MorphACWE)
|
||
|
|
|
||
|
|
Active contours without edges implemented with morphological operators. It
|
||
|
|
can be used to segment objects in images and volumes without well defined
|
||
|
|
borders. It is required that the inside of the object looks different on
|
||
|
|
average than the outside (i.e., the inner area of the object should be
|
||
|
|
darker or lighter than the outer area on average).
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) or (L, M, N) array
|
||
|
|
Grayscale image or volume to be segmented.
|
||
|
|
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.
|
||
|
|
lambda1 : float, optional
|
||
|
|
Weight parameter for the outer region. If `lambda1` is larger than
|
||
|
|
`lambda2`, the outer region will contain a larger range of values than
|
||
|
|
the inner region.
|
||
|
|
lambda2 : float, optional
|
||
|
|
Weight parameter for the inner region. If `lambda2` is larger than
|
||
|
|
`lambda1`, the inner region will contain a larger range of values than
|
||
|
|
the outer region.
|
||
|
|
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
|
||
|
|
--------
|
||
|
|
circle_level_set, checkerboard_level_set
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
|
||
|
|
This is a version of the Chan-Vese algorithm that uses morphological
|
||
|
|
operators instead of solving a partial differential equation (PDE) for the
|
||
|
|
evolution of the contour. The set of morphological operators used in this
|
||
|
|
algorithm are proved to be infinitesimally equivalent to the Chan-Vese PDE
|
||
|
|
(see [1]_). However, morphological operators are do not suffer from the
|
||
|
|
numerical stability issues typically found in PDEs (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`
|
||
|
|
"""
|
||
|
|
|
||
|
|
init_level_set = _init_level_set(init_level_set, image.shape)
|
||
|
|
|
||
|
|
_check_input(image, init_level_set)
|
||
|
|
|
||
|
|
u = np.int8(init_level_set > 0)
|
||
|
|
|
||
|
|
iter_callback(u)
|
||
|
|
|
||
|
|
for _ in range(iterations):
|
||
|
|
|
||
|
|
# inside = u > 0
|
||
|
|
# outside = u <= 0
|
||
|
|
c0 = (image * (1 - u)).sum() / float((1 - u).sum() + 1e-8)
|
||
|
|
c1 = (image * u).sum() / float(u.sum() + 1e-8)
|
||
|
|
|
||
|
|
# Image attachment
|
||
|
|
du = np.gradient(u)
|
||
|
|
abs_du = np.abs(du).sum(0)
|
||
|
|
aux = abs_du * (lambda1 * (image - c1)**2 - lambda2 * (image - c0)**2)
|
||
|
|
|
||
|
|
u[aux < 0] = 1
|
||
|
|
u[aux > 0] = 0
|
||
|
|
|
||
|
|
# Smoothing
|
||
|
|
for _ in range(smoothing):
|
||
|
|
u = _curvop(u)
|
||
|
|
|
||
|
|
iter_callback(u)
|
||
|
|
|
||
|
|
return u
|
||
|
|
|
||
|
|
|
||
|
|
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 = np.percentile(image, 40)
|
||
|
|
|
||
|
|
structure = np.ones((3,) * len(image.shape), dtype=np.int8)
|
||
|
|
dimage = np.gradient(image)
|
||
|
|
# threshold_mask = image > threshold
|
||
|
|
if balloon != 0:
|
||
|
|
threshold_mask_balloon = image > threshold / np.abs(balloon)
|
||
|
|
|
||
|
|
u = np.int8(init_level_set > 0)
|
||
|
|
|
||
|
|
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 = np.zeros_like(image)
|
||
|
|
du = np.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
|