def apply_hysteresis_threshold(image, low, high):
"""Apply hysteresis thresholding to ``image``.
This algorithm finds regions where ``image`` is greater than ``high``
OR ``image`` is greater than ``low`` *and* that region is connected to
a region greater than ``high``.
Parameters
----------
image : array, shape (M,[ N, ..., P])
Grayscale input image.
low : float, or array of same shape as ``image``
Lower threshold.
high : float, or array of same shape as ``image``
Higher threshold.
Returns
-------
thresholded : array of bool, same shape as ``image``
Array in which ``True`` indicates the locations where ``image``
was above the hysteresis threshold.
Examples
--------
>>> import cupy as cp
>>> from cucim.skimage.filters import apply_hysteresis_threshold
>>> image = cp.asarray([1, 2, 3, 2, 1, 2, 1, 3, 2])
>>> apply_hysteresis_threshold(image, 1.5, 2.5).astype(int)
array([0, 1, 1, 1, 0, 0, 0, 1, 1])
References
----------
.. [1] J. Canny. A computational approach to edge detection.
IEEE Transactions on Pattern Analysis and Machine Intelligence.
1986; vol. 8, pp.679-698.
:DOI:`10.1109/TPAMI.1986.4767851`
"""
low = cp.asarray(low) # asarray to allow scalar low
# ensure low always below high
low = cp.clip(low, a_min=None, a_max=high)
mask_low = image > low
mask_high = image > high
# Connected components of mask_low
labels_low, num_labels = ndi.label(mask_low)
# Check which connected components contain pixels from mask_high
# CuPy Backend: refactored in the same style as features.canny to avoid
# slow call to cupyx.scipy.ndimage.sum
nonzero_sums = cp.unique(labels_low[mask_high])
connected_to_high = cp.zeros((num_labels + 1, ), bool)
connected_to_high[nonzero_sums] = True
thresholded = connected_to_high[labels_low]
return thresholded
def remove_small_objects_gpu(mask: cupy.ndarray, min_size: int) -> None:
""" See scikit-image remove_small_objects()
N.B.
Input array can be a binary mask (bool type) or
labeled mask (int type).
This is a inplace operation.
"""
_check_dtype_supported(mask)
ccs, _ = label(mask) if mask.dtype == bool else mask
component_sizes = cupy.bincount(ccs.ravel())
too_small = component_sizes < min_size
too_small_mask = too_small[ccs]
mask[too_small_mask] = 0
def keep_largest_connected_component_gpu(mask: cupy.ndarray, ) -> None:
""" Keep the largest connected component.
Remove small connected components, only keep the largest
connected component (excluding background).
N.B.
Input array can be a binary mask (bool type) or
labeled mask (int type).
This is a inplace operation.
"""
_check_dtype_supported(mask)
ccs, _ = label(mask) if mask.dtype == bool else mask
component_sizes = cupy.bincount(ccs.ravel())
if len(component_sizes) == 1: # just background
return
largest_cc_index = cupy.argmax(component_sizes[1:]) + 1
mask[ccs != largest_cc_index] = 0
def canny(image,
sigma=1.,
low_threshold=None,
high_threshold=None,
mask=None,
use_quantiles=False):
"""Edge filter an image using the Canny algorithm.
Parameters
-----------
image : 2D array
Grayscale input image to detect edges on; can be of any dtype.
sigma : float, optional
Standard deviation of the Gaussian filter.
low_threshold : float, optional
Lower bound for hysteresis thresholding (linking edges).
If None, low_threshold is set to 10% of dtype's max.
high_threshold : float, optional
Upper bound for hysteresis thresholding (linking edges).
If None, high_threshold is set to 20% of dtype's max.
mask : array, dtype=bool, optional
Mask to limit the application of Canny to a certain area.
use_quantiles : bool, optional
If True then treat low_threshold and high_threshold as quantiles of the
edge magnitude image, rather than absolute edge magnitude values. If
True, then the thresholds must be in the range [0, 1].
Returns
-------
output : 2D array (image)
The binary edge map.
See also
--------
skimage.sobel
Notes
-----
The steps of the algorithm are as follows:
* Smooth the image using a Gaussian with ``sigma`` width.
* Apply the horizontal and vertical Sobel operators to get the gradients
within the image. The edge strength is the norm of the gradient.
* Thin potential edges to 1-pixel wide curves. First, find the normal
to the edge at each point. This is done by looking at the
signs and the relative magnitude of the X-Sobel and Y-Sobel
to sort the points into 4 categories: horizontal, vertical,
diagonal and antidiagonal. Then look in the normal and reverse
directions to see if the values in either of those directions are
greater than the point in question. Use interpolation to get a mix of
points instead of picking the one that's the closest to the normal.
* Perform a hysteresis thresholding: first label all points above the
high threshold as edges. Then recursively label any point above the
low threshold that is 8-connected to a labeled point as an edge.
References
-----------
.. [1] Canny, J., A Computational Approach To Edge Detection, IEEE Trans.
Pattern Analysis and Machine Intelligence, 8:679-714, 1986
:DOI:`10.1109/TPAMI.1986.4767851`
.. [2] William Green's Canny tutorial
https://en.wikipedia.org/wiki/Canny_edge_detector
Examples
--------
>>> import cupy as cp
>>> from cucim.skimage import feature
>>> # Generate noisy image of a square
>>> im = cp.zeros((256, 256))
>>> im[64:-64, 64:-64] = 1
>>> im += 0.2 * cp.random.rand(*im.shape)
>>> # First trial with the Canny filter, with the default smoothing
>>> edges1 = feature.canny(im)
>>> # Increase the smoothing for better results
>>> edges2 = feature.canny(im, sigma=3)
"""
#
# The steps involved:
#
# * Smooth using the Gaussian with sigma above.
#
# * Apply the horizontal and vertical Sobel operators to get the gradients
# within the image. The edge strength is the sum of the magnitudes
# of the gradients in each direction.
#
# * Find the normal to the edge at each point using the arctangent of the
# ratio of the Y sobel over the X sobel - pragmatically, we can
# look at the signs of X and Y and the relative magnitude of X vs Y
# to sort the points into 4 categories: horizontal, vertical,
# diagonal and antidiagonal.
#
# * Look in the normal and reverse directions to see if the values
# in either of those directions are greater than the point in question.
# Use interpolation to get a mix of points instead of picking the one
# that's the closest to the normal.
#
# * Label all points above the high threshold as edges.
# * Recursively label any point above the low threshold that is 8-connected
# to a labeled point as an edge.
#
# Regarding masks, any point touching a masked point will have a gradient
# that is "infected" by the masked point, so it's enough to erode the
# mask by one and then mask the output. We also mask out the border points
# because who knows what lies beyond the edge of the image?
#
check_nD(image, 2)
dtype_max = dtype_limits(image, clip_negative=False)[1]
if low_threshold is None:
low_threshold = 0.1
elif use_quantiles:
if not (0.0 <= low_threshold <= 1.0):
raise ValueError("Quantile thresholds must be between 0 and 1.")
else:
low_threshold = low_threshold / dtype_max
if high_threshold is None:
high_threshold = 0.2
elif use_quantiles:
if not (0.0 <= high_threshold <= 1.0):
raise ValueError("Quantile thresholds must be between 0 and 1.")
else:
high_threshold = high_threshold / dtype_max
_gaussian = functools.partial(gaussian, sigma=sigma)
def fsmooth(x, mode='constant'):
return img_as_float(_gaussian(x, mode=mode))
if mask is None:
smoothed = fsmooth(image, mode='reflect')
# mask that is ones everywhere except the borders
eroded_mask = cp.ones(image.shape, dtype=bool)
eroded_mask[:1, :] = 0
eroded_mask[-1:, :] = 0
eroded_mask[:, :1] = 0
eroded_mask[:, -1:] = 0
else:
smoothed = smooth_with_function_and_mask(image, fsmooth, mask)
#
# Make the eroded mask. Setting the border value to zero will wipe
# out the image edges for us.
#
s = generate_binary_structure(2, 2)
eroded_mask = binary_erosion(mask, s, border_value=0)
jsobel = ndi.sobel(smoothed, axis=1)
isobel = ndi.sobel(smoothed, axis=0)
abs_isobel = cp.abs(isobel)
abs_jsobel = cp.abs(jsobel)
magnitude = cp.hypot(isobel, jsobel)
eroded_mask = eroded_mask & (magnitude > 0)
# TODO: implement custom kernel to compute local maxima
#
# --------- Find local maxima --------------
#
# Assign each point to have a normal of 0-45 degrees, 45-90 degrees,
# 90-135 degrees and 135-180 degrees.
#
local_maxima = cp.zeros(image.shape, bool)
isobel_gt_0 = isobel >= 0
jsobel_gt_0 = jsobel >= 0
isobel_lt_0 = isobel <= 0
jsobel_lt_0 = jsobel <= 0
abs_isobel_lt_jsobel = abs_isobel <= abs_jsobel
abs_isobel_gt_jsobel = abs_isobel >= abs_jsobel
# ----- 0 to 45 degrees ------
pts_plus = isobel_gt_0 & jsobel_gt_0
pts_minus = isobel_lt_0 & jsobel_lt_0
pts_tmp = (pts_plus | pts_minus) & eroded_mask
pts = pts_tmp & abs_isobel_gt_jsobel
# Get the magnitudes shifted left to make a matrix of the points to the
# right of pts. Similarly, shift left and down to get the points to the
# top right of pts.
c1 = magnitude[1:, :][pts[:-1, :]]
c2 = magnitude[1:, 1:][pts[:-1, :-1]]
m = magnitude[pts]
w = abs_jsobel[pts] / abs_isobel[pts]
c_plus = _fused_comparison(w, c1, c2, m)
c1 = magnitude[:-1, :][pts[1:, :]]
c2 = magnitude[:-1, :-1][pts[1:, 1:]]
c_minus = _fused_comparison(w, c1, c2, m)
local_maxima[pts] = c_plus & c_minus
# ----- 45 to 90 degrees ------
# Mix diagonal and vertical
#
pts = pts_tmp & abs_isobel_lt_jsobel
c1 = magnitude[:, 1:][pts[:, :-1]]
c2 = magnitude[1:, 1:][pts[:-1, :-1]]
m = magnitude[pts]
w = abs_isobel[pts] / abs_jsobel[pts]
c_plus = _fused_comparison(w, c1, c2, m)
c1 = magnitude[:, :-1][pts[:, 1:]]
c2 = magnitude[:-1, :-1][pts[1:, 1:]]
c_minus = _fused_comparison(w, c1, c2, m)
local_maxima[pts] = c_plus & c_minus
# ----- 90 to 135 degrees ------
# Mix anti-diagonal and vertical
#
pts_plus = isobel_lt_0 & jsobel_gt_0
pts_minus = isobel_gt_0 & jsobel_lt_0
pts_tmp = (pts_plus | pts_minus) & eroded_mask
pts = pts_tmp & abs_isobel_lt_jsobel
c1a = magnitude[:, 1:][pts[:, :-1]]
c2a = magnitude[:-1, 1:][pts[1:, :-1]]
m = magnitude[pts]
w = abs_isobel[pts] / abs_jsobel[pts]
c_plus = _fused_comparison(w, c1a, c2a, m)
c1 = magnitude[:, :-1][pts[:, 1:]]
c2 = magnitude[1:, :-1][pts[:-1, 1:]]
c_minus = _fused_comparison(w, c1, c2, m)
local_maxima[pts] = c_plus & c_minus
# ----- 135 to 180 degrees ------
# Mix anti-diagonal and anti-horizontal
#
pts = pts_tmp & abs_isobel_gt_jsobel
c1 = magnitude[:-1, :][pts[1:, :]]
c2 = magnitude[:-1, 1:][pts[1:, :-1]]
m = magnitude[pts]
w = abs_jsobel[pts] / abs_isobel[pts]
c_plus = _fused_comparison(w, c1, c2, m)
c1 = magnitude[1:, :][pts[:-1, :]]
c2 = magnitude[1:, :-1][pts[:-1, 1:]]
c_minus = _fused_comparison(w, c1, c2, m)
local_maxima[pts] = c_plus & c_minus
#
# ---- If use_quantiles is set then calculate the thresholds to use
#
if use_quantiles:
high_threshold = cp.percentile(magnitude, 100.0 * high_threshold)
low_threshold = cp.percentile(magnitude, 100.0 * low_threshold)
#
# ---- Create two masks at the two thresholds.
#
high_mask = local_maxima & (magnitude >= high_threshold)
low_mask = local_maxima & (magnitude >= low_threshold)
#
# Segment the low-mask, then only keep low-segments that have
# some high_mask component in them
#
labels, count = ndi.label(low_mask, structure=cp.ones((3, 3), bool))
if count == 0:
return low_mask
nonzero_sums = cp.unique(labels[high_mask])
good_label = cp.zeros((count + 1, ), bool)
good_label[nonzero_sums] = True
output_mask = good_label[labels]
return output_mask
def remove_small_objects(ar, min_size=64, connectivity=1, in_place=False):
"""Remove objects smaller than the specified size.
Expects ar to be an array with labeled objects, and removes objects
smaller than min_size. If `ar` is bool, the image is first labeled.
This leads to potentially different behavior for bool and 0-and-1
arrays.
Parameters
----------
ar : ndarray (arbitrary shape, int or bool type)
The array containing the objects of interest. If the array type is
int, the ints must be non-negative.
min_size : int, optional (default: 64)
The smallest allowable object size.
connectivity : int, {1, 2, ..., ar.ndim}, optional (default: 1)
The connectivity defining the neighborhood of a pixel. Used during
labelling if `ar` is bool.
in_place : bool, optional (default: False)
If ``True``, remove the objects in the input array itself.
Otherwise, make a copy.
Raises
------
TypeError
If the input array is of an invalid type, such as float or string.
ValueError
If the input array contains negative values.
Returns
-------
out : ndarray, same shape and type as input `ar`
The input array with small connected components removed.
Examples
--------
>>> import cupy as cp
>>> from cucim.skimage import morphology
>>> a = cp.array([[0, 0, 0, 1, 0],
... [1, 1, 1, 0, 0],
... [1, 1, 1, 0, 1]], bool)
>>> b = morphology.remove_small_objects(a, 6)
>>> b
array([[False, False, False, False, False],
[ True, True, True, False, False],
[ True, True, True, False, False]])
>>> c = morphology.remove_small_objects(a, 7, connectivity=2)
>>> c
array([[False, False, False, True, False],
[ True, True, True, False, False],
[ True, True, True, False, False]])
>>> d = morphology.remove_small_objects(a, 6, in_place=True)
>>> d is a
True
"""
# Raising type error if not int or bool
_check_dtype_supported(ar)
if in_place:
out = ar
else:
out = ar.copy()
if min_size == 0: # shortcut for efficiency
return out
if out.dtype == bool:
selem = ndi.generate_binary_structure(ar.ndim, connectivity)
ccs = cp.zeros_like(ar, dtype=cp.int32)
ndi.label(ar, selem, output=ccs)
else:
ccs = out
try:
component_sizes = cp.bincount(ccs.ravel())
except ValueError:
raise ValueError("Negative value labels are not supported. Try "
"relabeling the input with `scipy.ndimage.label` or "
"`skimage.morphology.label`.")
if len(component_sizes) == 2 and out.dtype != bool:
warn("Only one label was provided to `remove_small_objects`. "
"Did you mean to use a boolean array?")
too_small = component_sizes < min_size
too_small_mask = too_small[ccs]
out[too_small_mask] = 0
return out