def conv_channel(cycle, vol, kernel, gpu_id=0, verbose=False):
if gpu_id >= 0:
# from chainer.functions import convolution_nd
import cupy as cp
from cupyx.scipy.ndimage import convolve
cp.cuda.Device(gpu_id).use()
kernel = cp.asarray(kernel)
cycle_conv = np.stack([ cp.asnumpy(convolve(cp.asarray(cycle[i]),kernel)) for i in range(len(cycle))])
## using chainer
# kernel = cp.asarray(kernel[np.newaxis,np.newaxis,:])
# cycle_conv = cp.asnumpy(convolution_nd(cp.asarray(cycle[:,np.newaxis,:]),kernel,pad=h))
if verbose:
print("normalising by local volume...")
# volume = cp.asnumpy(convolution_nd( cp.asarray((vol>-2048),dtype=np.float32)[np.newaxis,np.newaxis,:], cp.ones((1,1,h,h,h),dtype=np.float32) ))[0]
vkernel = cp.ones(kernel.shape,dtype=np.float32)/np.prod(kernel.shape)
volume = cp.asnumpy(convolve( cp.asarray((vol>-2048),dtype=np.float32), vkernel )[np.newaxis,:])
else:
from scipy.ndimage.filters import convolve
cycle_conv = np.stack([convolve(cycle[i],kernel) for i in range(len(cycle))])
if verbose:
print("normalising by local volume...")
vkernel = np.ones(kernel.shape,dtype=np.float32)/np.prod(kernel.shape)
volume = convolve( (vol>-2048).astype(np.float32), vkernel )[np.newaxis,:]
# normalise by volume
volume[:,vol<=-2048] = np.inf
return(cycle_conv / volume)
def diffuse_slime_trail():
cp.multiply(
SlimeWorld.cells,
SlimeWorld.trail_reduction_factor,
out=SlimeWorld.cells,
casting="unsafe",
)
convolve(SlimeWorld.cells,
SlimeWorld.trail_kernel,
output=SlimeWorld.cells)
def _interpolate_image(image, *, multichannel=False):
"""Replacing each pixel in ``image`` with the average of its neighbors.
Parameters
----------
image : ndarray
Input data to be interpolated.
multichannel : bool, optional
Whether the last axis of the image is to be interpreted as multiple
channels or another spatial dimension.
Returns
-------
interp : ndarray
Interpolated version of `image`.
"""
spatialdims = image.ndim if not multichannel else image.ndim - 1
conv_filter = ndi.generate_binary_structure(spatialdims,
1).astype(image.dtype)
conv_filter.ravel()[conv_filter.size // 2] = 0
conv_filter /= conv_filter.sum()
# CuPy Backend: refactored below to avoid for loop
if multichannel:
conv_filter = conv_filter[..., np.newaxis]
interp = ndi.convolve(image, conv_filter, mode='mirror')
return interp
def farid_v(image, *, mask=None):
"""Find the vertical edges of an image using the Farid transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Farid edge map.
Notes
-----
The kernel was constructed using the 5-tap weights from [1].
References
----------
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
multidimensional signals", IEEE Transactions on Image Processing
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
"""
check_nD(image, 2)
image = img_as_float(image)
result = ndi.convolve(image, cp.array(VFARID_WEIGHTS, dtype=image.dtype))
return _mask_filter_result(result, mask)
def farid_h(image, *, mask=None):
"""Find the horizontal edges of an image using the Farid transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Farid edge map.
Notes
-----
The kernel was constructed using the 5-tap weights from [1].
References
----------
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
multidimensional signals", IEEE Transactions on Image Processing
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
.. [2] Farid, H. and Simoncelli, E. P. "Optimally rotation-equivariant
directional derivative kernels", In: 7th International Conference on
Computer Analysis of Images and Patterns, Kiel, Germany. Sep, 1997.
"""
check_nD(image, 2)
image = img_as_float(image)
result = ndi.convolve(image, cp.array(HFARID_WEIGHTS, dtype=image.dtype))
return _mask_filter_result(result, mask)
def roberts_neg_diag(image, mask=None):
"""Find the cross edges of an image using the Roberts' Cross operator.
The kernel is applied to the input image to produce separate measurements
of the gradient component one orientation.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Robert's edge map.
Notes
-----
We use the following kernel::
0 1
-1 0
"""
check_nD(image, 2)
image = img_as_float(image)
# CuPy Backend: allow float16 & float32 filtering
weights = cp.array(ROBERTS_ND_WEIGHTS, dtype=image.dtype)
result = ndi.convolve(image, weights)
return _mask_filter_result(result, mask)
def test_image_shape():
"""Test that shape of output image in deconvolution is same as input.
This addresses issue #1172.
"""
point = cp.zeros((5, 5), np.float)
point[2, 2] = 1.0
psf = ndi.gaussian_filter(point, sigma=1.0)
# image shape: (45, 45), as reported in #1172
image = cp.asarray(test_img[65:165, 215:315]) # just the face
image_conv = ndi.convolve(image, psf)
deconv_sup = restoration.wiener(image_conv, psf, 1)
deconv_un = restoration.unsupervised_wiener(image_conv, psf)[0]
# test the shape
assert image.shape == deconv_sup.shape
assert image.shape == deconv_un.shape
# test the reconstruction error
sup_relative_error = cp.abs(deconv_sup - image) / image
un_relative_error = cp.abs(deconv_un - image) / image
cp.testing.assert_array_less(cp.median(sup_relative_error), 0.1)
cp.testing.assert_array_less(cp.median(un_relative_error), 0.1)
def laplace(image, ksize=3, mask=None):
"""Find the edges of an image using the Laplace operator.
Parameters
----------
image : ndarray
Image to process.
ksize : int, optional
Define the size of the discrete Laplacian operator such that it
will have a size of (ksize,) * image.ndim.
mask : ndarray, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : ndarray
The Laplace edge map.
Notes
-----
The Laplacian operator is generated using the function
skimage.restoration.uft.laplacian().
"""
image = img_as_float(image)
# TODO: File an upstream bug for scikit-image. ksize does not appear to
# actually be used and is hard-coded to 3 in `laplacian`.
if ksize != 3:
raise NotImplementedError("only ksize=3 is supported")
# Create the discrete Laplacian operator - We keep only the real part of
# the filter
laplace_op = laplacian(image.ndim, None, dtype=image.dtype)
result = ndi.convolve(image, laplace_op)
return _mask_filter_result(result, mask)
def set_args(self, dtype):
if np.dtype(dtype).kind in "iu":
im1 = skimage.data.camera()
else:
im1 = skimage.data.camera() / 255.0
im1 = im1.astype(dtype)
if len(self.shape) == 3:
im1 = im1[..., np.newaxis]
im1 = cp.array(im1)
n_tile = [
math.ceil(s / im_s) for s, im_s in zip(self.shape, im1.shape)
]
slices = tuple([slice(s) for s in self.shape])
imaged = cp.tile(im1, n_tile)[slices]
psfd = cp.ones((5, ) * imaged.ndim) / 25
imaged = ndi.convolve(imaged, psfd)
image = cp.asnumpy(imaged)
psf = cp.asnumpy(psfd)
self.args_cpu = (image, psf)
self.args_gpu = (imaged, psfd)
def gabor(image, frequency, theta=0, bandwidth=1, sigma_x=None,
sigma_y=None, n_stds=3, offset=0, mode='reflect', cval=0):
"""Return real and imaginary responses to Gabor filter.
The real and imaginary parts of the Gabor filter kernel are applied to the
image and the response is returned as a pair of arrays.
Gabor filter is a linear filter with a Gaussian kernel which is modulated
by a sinusoidal plane wave. Frequency and orientation representations of
the Gabor filter are similar to those of the human visual system.
Gabor filter banks are commonly used in computer vision and image
processing. They are especially suitable for edge detection and texture
classification.
Parameters
----------
image : 2-D array
Input image.
frequency : float
Spatial frequency of the harmonic function. Specified in pixels.
theta : float, optional
Orientation in radians. If 0, the harmonic is in the x-direction.
bandwidth : float, optional
The bandwidth captured by the filter. For fixed bandwidth, ``sigma_x``
and ``sigma_y`` will decrease with increasing frequency. This value is
ignored if ``sigma_x`` and ``sigma_y`` are set by the user.
sigma_x, sigma_y : float, optional
Standard deviation in x- and y-directions. These directions apply to
the kernel *before* rotation. If `theta = pi/2`, then the kernel is
rotated 90 degrees so that ``sigma_x`` controls the *vertical*
direction.
n_stds : scalar, optional
The linear size of the kernel is n_stds (3 by default) standard
deviations.
offset : float, optional
Phase offset of harmonic function in radians.
mode : {'constant', 'nearest', 'reflect', 'mirror', 'wrap'}, optional
Mode used to convolve image with a kernel, passed to `ndi.convolve`
cval : scalar, optional
Value to fill past edges of input if ``mode`` of convolution is
'constant'. The parameter is passed to `ndi.convolve`.
Returns
-------
real, imag : arrays
Filtered images using the real and imaginary parts of the Gabor filter
kernel. Images are of the same dimensions as the input one.
References
----------
.. [1] https://en.wikipedia.org/wiki/Gabor_filter
.. [2] https://web.archive.org/web/20180127125930/http://mplab.ucsd.edu/tutorials/gabor.pdf
Examples
--------
>>> import cupy as cp
>>> from cucim.skimage.filters import gabor
>>> from skimage import data, io
>>> from matplotlib import pyplot as plt # doctest: +SKIP
>>> image = cp.array(data.coins())
>>> # detecting edges in a coin image
>>> filt_real, filt_imag = gabor(image, frequency=0.6)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(cp.asnumpy(filt_real)) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
>>> # less sensitivity to finer details with the lower frequency kernel
>>> filt_real, filt_imag = gabor(image, frequency=0.1)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(cp.asnumpy(filt_real) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
""" # noqa
check_nD(image, 2)
float_dtype = cp.promote_types(image.dtype, cp.float16)
g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, n_stds,
offset, float_dtype=float_dtype)
filtered = ndi.convolve(image, g, mode=mode, cval=cval)
return filtered.real, filtered.imag
def estimate_sigma(arr, disable_background_masking=False, N=0):
"""Standard deviation estimation from local patches
Parameters
----------
arr : 3D or 4D ndarray
The array to be estimated
disable_background_masking : bool, default False
If True, uses all voxels for the estimation, otherwise, only non-zeros
voxels are used. Useful if the background is masked by the scanner.
N : int, default 0
Number of coils of the receiver array. Use N = 1 in case of a SENSE
reconstruction (Philips scanners) or the number of coils for a GRAPPA
reconstruction (Siemens and GE). Use 0 to disable the correction factor,
as for example if the noise is Gaussian distributed. See [1] for more
information.
Returns
-------
sigma : ndarray
standard deviation of the noise, one estimation per volume.
Notes
-------
This function is the same as manually taking the standard deviation of the
background and gives one value for the whole 3D array.
It also includes the coil-dependent correction factor of Koay 2006
(see [1]_, equation 18) with theta = 0.
Since this function was introduced in [2]_ for T1 imaging,
it is expected to perform ok on diffusion MRI data, but might oversmooth
some regions and leave others un-denoised for spatially varying noise
profiles. Consider using :func:`piesno` to estimate sigma instead if visual
inaccuracies are apparent in the denoised result.
References
----------
.. [1] Koay, C. G., & Basser, P. J. (2006). Analytically exact correction
scheme for signal extraction from noisy magnitude MR signals.
Journal of Magnetic Resonance), 179(2), 317-22.
.. [2] Coupe, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot,
C., 2008. An optimized blockwise nonlocal means denoising filter for 3-D
magnetic resonance images, IEEE Trans. Med. Imaging 27, 425-41.
"""
k = np.zeros((3, 3, 3), dtype=np.int8)
k[0, 1, 1] = 1
k[2, 1, 1] = 1
k[1, 0, 1] = 1
k[1, 2, 1] = 1
k[1, 1, 0] = 1
k[1, 1, 2] = 1
k = cp.asarray(k)
# Precomputed factor from Koay 2006, this corrects the bias of magnitude
# image
correction_factor = {
0: 1, # No correction
1: 0.42920367320510366,
4: 0.4834941393603609,
6: 0.4891759468548269,
8: 0.49195420135894175,
12: 0.4946862482541263,
16: 0.4960339908122364,
20: 0.4968365823718557,
24: 0.49736907650825657,
32: 0.49803177052530145,
64: 0.49901964176235936,
}
if N in correction_factor:
factor = correction_factor[N]
else:
raise ValueError("N = {0} is not supported! Please choose amongst \
{1}".format(N, sorted(list(correction_factor.keys()))))
if arr.ndim == 3:
arr = arr[..., None]
elif arr.ndim != 4:
raise ValueError("Array shape is not supported!", arr.shape)
if disable_background_masking:
mask = None
else:
mask = arr[..., 0].astype(np.bool)
# TODO: make upstream PR at dipy with this binary erosion bug fix
# erode mask by the convolution kernel shape
mask = ndi.binary_erosion(mask,
structure=cp.ones(k.shape[:3],
dtype=np.bool))
# TODO: make upstream PR at dipy that avoids an explicit loop over slices
conv_out = cp.empty(arr.shape, dtype=np.float64)
ndi.convolve(arr, k[..., np.newaxis], output=conv_out)
mean_block = arr - conv_out / 6
if mask is None:
tmp = mean_block.reshape((-1, mean_block.shape[-1]))
else:
tmp = mean_block[mask]
tmp *= math.sqrt(6 / 7)
tmp *= tmp
sigma = cp.sqrt(cp.mean(tmp, axis=0) / factor)
return sigma
def perimeter_crofton(image, directions=4):
"""Calculate total Crofton perimeter of all objects in binary image.
Parameters
----------
image : (N, M) ndarray
2D image. If image is not binary, all values strictly greater than zero
are considered as the object.
directions : 2 or 4, optional
Number of directions used to approximate the Crofton perimeter. By
default, 4 is used: it should be more accurate than 2.
Computation time is the same in both cases.
Returns
-------
perimeter : float
Total perimeter of all objects in binary image.
Notes
-----
This measure is based on Crofton formula [1], which is a measure from
integral geometry. It is defined for general curve length evaluation via
a double integral along all directions. In a discrete
space, 2 or 4 directions give a quite good approximation, 4 being more
accurate than 2 for more complex shapes.
Similar to :func:`~.measure.perimeter`, this function returns an
approximation of the perimeter in continuous space.
References
----------
.. [1] https://en.wikipedia.org/wiki/Crofton_formula
.. [2] S. Rivollier. Analyse d’image geometrique et morphometrique par
diagrammes de forme et voisinages adaptatifs generaux. PhD thesis,
2010.
Ecole Nationale Superieure des Mines de Saint-Etienne.
https://tel.archives-ouvertes.fr/tel-00560838
"""
if image.ndim != 2:
raise NotImplementedError(
"`perimeter_crofton` supports 2D images only")
# as image could be a label image, transform it to binary image
image = (image > 0).astype(cp.uint8)
image = cp.pad(image, pad_width=1, mode="constant")
XF = ndi.convolve(
image,
cp.array([[0, 0, 0], [0, 1, 4], [0, 2, 8]]),
mode="constant",
cval=0,
)
h = cp.bincount(XF.ravel(), minlength=16)
# definition of the LUT
# fmt: off
if directions == 2:
coefs = [
0, np.pi / 2, 0, 0, 0, np.pi / 2, 0, 0, np.pi / 2, np.pi, 0, 0,
np.pi / 2, np.pi, 0, 0
]
else:
sq2 = math.sqrt(2)
coefs = [
0, np.pi / 4 * (1 + 1 / sq2), np.pi / (4 * sq2), np.pi / (2 * sq2),
0, np.pi / 4 * (1 + 1 / sq2), 0, np.pi / (4 * sq2), np.pi / 4,
np.pi / 2, np.pi / (4 * sq2), np.pi / (4 * sq2), np.pi / 4,
np.pi / 2, 0, 0
]
# fmt: on
total_perimeter = cp.asarray(coefs) @ h
return total_perimeter
def perimeter(image, neighbourhood=4):
"""Calculate total perimeter of all objects in binary image.
Parameters
----------
image : (N, M) ndarray
2D binary image.
neighbourhood : 4 or 8, optional
Neighborhood connectivity for border pixel determination. It is used to
compute the contour. A higher neighbourhood widens the border on which
the perimeter is computed.
Returns
-------
perimeter : float
Total perimeter of all objects in binary image.
References
----------
.. [1] K. Benkrid, D. Crookes. Design and FPGA Implementation of
a Perimeter Estimator. The Queen's University of Belfast.
http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc
Examples
--------
>>> from skimage import data, util
>>> from skimage.measure import label
>>> # coins image (binary)
>>> img_coins = data.coins() > 110
>>> # total perimeter of all objects in the image
>>> perimeter(img_coins, neighbourhood=4) # doctest: +ELLIPSIS
7796.867...
>>> perimeter(img_coins, neighbourhood=8) # doctest: +ELLIPSIS
8806.268...
"""
if image.ndim != 2:
raise NotImplementedError("`perimeter` supports 2D images only")
if neighbourhood == 4:
strel = STREL_4
else:
strel = STREL_8
strel = cp.asarray(strel)
image = image.astype(cp.uint8)
eroded_image = ndi.binary_erosion(image, strel, border_value=0)
border_image = image - eroded_image
perimeter_weights = cp.zeros(50, dtype=cp.double)
perimeter_weights[[5, 7, 15, 17, 25, 27]] = 1
perimeter_weights[[21, 33]] = math.sqrt(2)
perimeter_weights[[13, 23]] = (1 + math.sqrt(2)) / 2
perimeter_image = ndi.convolve(
border_image,
cp.array([[10, 2, 10], [2, 1, 2], [10, 2, 10]]),
mode="constant",
cval=0,
)
# You can also write
# return perimeter_weights[perimeter_image].sum()
# but that was measured as taking much longer than bincount + cp.dot (5x
# as much time)
perimeter_histogram = cp.bincount(perimeter_image.ravel(), minlength=50)
total_perimeter = perimeter_histogram @ perimeter_weights
return total_perimeter
def euler_number(image, connectivity=None):
"""Calculate the Euler characteristic in binary image.
For 2D objects, the Euler number is the number of objects minus the number
of holes. For 3D objects, the Euler number is obtained as the number of
objects plus the number of holes, minus the number of tunnels, or loops.
Parameters
----------
image: (N, M) ndarray or (N, M, D) ndarray.
2D or 3D images.
If image is not binary, all values strictly greater than zero
are considered as the object.
connectivity : int, optional
Maximum number of orthogonal hops to consider a pixel/voxel
as a neighbor.
Accepted values are ranging from 1 to input.ndim. If ``None``, a full
connectivity of ``input.ndim`` is used.
4 or 8 neighborhoods are defined for 2D images (connectivity 1 and 2,
respectively).
6 or 26 neighborhoods are defined for 3D images, (connectivity 1 and 3,
respectively). Connectivity 2 is not defined.
Returns
-------
euler_number : int
Euler characteristic of the set of all objects in the image.
Notes
-----
The Euler characteristic is an integer number that describes the
topology of the set of all objects in the input image. If object is
4-connected, then background is 8-connected, and conversely.
The computation of the Euler characteristic is based on an integral
geometry formula in discretized space. In practice, a neighbourhood
configuration is constructed, and a LUT is applied for each
configuration. The coefficients used are the ones of Ohser et al.
It can be useful to compute the Euler characteristic for several
connectivities. A large relative difference between results
for different connectivities suggests that the image resolution
(with respect to the size of objects and holes) is too low.
References
----------
.. [1] S. Rivollier. Analyse d’image geometrique et morphometrique par
diagrammes de forme et voisinages adaptatifs generaux. PhD thesis,
2010. Ecole Nationale Superieure des Mines de Saint-Etienne.
https://tel.archives-ouvertes.fr/tel-00560838
.. [2] Ohser J., Nagel W., Schladitz K. (2002) The Euler Number of
Discretized Sets - On the Choice of Adjacency in Homogeneous
Lattices. In: Mecke K., Stoyan D. (eds) Morphology of Condensed
Matter. Lecture Notes in Physics, vol 600. Springer, Berlin,
Heidelberg.
Examples
--------
>>> import numpy as np
>>> SAMPLE = np.zeros((100,100,100));
>>> SAMPLE[40:60, 40:60, 40:60]=1
>>> euler_number(SAMPLE) # doctest: +ELLIPSIS
1...
>>> SAMPLE[45:55,45:55,45:55] = 0;
>>> euler_number(SAMPLE) # doctest: +ELLIPSIS
2...
>>> SAMPLE = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],
... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],
... [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0],
... [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1],
... [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]])
>>> euler_number(SAMPLE) # doctest:
0
>>> euler_number(SAMPLE, connectivity=1) # doctest:
2
""" # noqa
# as image can be a label image, transform it to binary
image = (image > 0).astype(int)
image = cp.pad(image, pad_width=1, mode="constant")
# check connectivity
if connectivity is None:
connectivity = image.ndim
# config variable is an adjacency configuration. A coefficient given by
# variable coefs is attributed to each configuration in order to get
# the Euler characteristic.
if image.ndim == 2:
config = cp.array([[0, 0, 0], [0, 1, 4], [0, 2, 8]])
if connectivity == 1:
coefs = EULER_COEFS2D_4
else:
coefs = EULER_COEFS2D_8
bins = 16
else: # 3D images
if connectivity == 2:
raise NotImplementedError(
"For 3D images, Euler number is implemented "
"for connectivities 1 and 3 only")
# fmt: off
config = cp.array([[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, 1, 4], [0, 2, 8]],
[[0, 0, 0], [0, 16, 64], [0, 32, 128]]])
# fmt: on
if connectivity == 1:
coefs = EULER_COEFS3D_26[::-1]
else:
coefs = EULER_COEFS3D_26
bins = 256
# XF has values in the 0-255 range in 3D, and in the 0-15 range in 2D,
# with one unique value for each binary configuration of the
# 27-voxel cube in 3D / 8-pixel square in 2D, up to symmetries
XF = ndi.convolve(image, config, mode="constant", cval=0)
h = cp.bincount(XF.ravel(), minlength=bins)
coefs = cp.asarray(coefs)
if image.ndim == 2:
return coefs @ h
else:
return int(0.125 * coefs @ h)
def fftconvolve(arr1, arr2):
#return cpx.scipy.signal.convolve(arr1, arr2)
return ndimage.convolve(arr1, arr2)