"""
canny.py - Canny Edge detector
Reference: Canny, J., A Computational Approach To Edge Detection, IEEE Trans.
Pattern Analysis and Machine Intelligence, 8:679-714, 1986
"""
import numpy as np
import scipy.ndimage as ndi
from ..util.dtype import dtype_limits
from .._shared.filters import gaussian
from .._shared.utils import _supported_float_type, check_nD
from ._canny_cy import _nonmaximum_suppression_bilinear
def _preprocess(image, mask, sigma, mode, cval):
"""Generate a smoothed image and an eroded mask.
The image is smoothed using a gaussian filter ignoring masked
pixels and the mask is eroded.
Parameters
----------
image : array
Image to be smoothed.
mask : array
Mask with 1's for significant pixels, 0's for masked pixels.
sigma : scalar or sequence of scalars
Standard deviation for Gaussian kernel. The standard
deviations of the Gaussian filter are given for each axis as a
sequence, or as a single number, in which case it is equal for
all axes.
mode : str, {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}
The ``mode`` parameter determines how the array borders are
handled, where ``cval`` is the value when mode is equal to
'constant'.
cval : float, optional
Value to fill past edges of input if `mode` is 'constant'.
Returns
-------
smoothed_image : ndarray
The smoothed array
eroded_mask : ndarray
The eroded mask.
Notes
-----
This function calculates the fractional contribution of masked pixels
by applying the function to the mask (which gets you the fraction of
the pixel data that's due to significant points). We then mask the image
and apply the function. The resulting values will be lower by the
bleed-over fraction, so you can recalibrate by dividing by the function
on the mask to recover the effect of smoothing from just the significant
pixels.
"""
gaussian_kwargs = dict(sigma=sigma, mode=mode, cval=cval, preserve_range=False)
compute_bleedover = mode == 'constant' or mask is not None
float_type = _supported_float_type(image.dtype)
if mask is None:
if compute_bleedover:
mask = np.ones(image.shape, dtype=float_type)
masked_image = image
eroded_mask = np.ones(image.shape, dtype=bool)
eroded_mask[:1, :] = 0
eroded_mask[-1:, :] = 0
eroded_mask[:, :1] = 0
eroded_mask[:, -1:] = 0
else:
mask = mask.astype(bool, copy=False)
masked_image = np.zeros_like(image)
masked_image[mask] = image[mask]
# Make the eroded mask. Setting the border value to zero will wipe
# out the image edges for us.
s = ndi.generate_binary_structure(2, 2)
eroded_mask = ndi.binary_erosion(mask, s, border_value=0)
if compute_bleedover:
# Compute the fractional contribution of masked pixels by applying
# the function to the mask (which gets you the fraction of the
# pixel data that's due to significant points)
bleed_over = (
gaussian(mask.astype(float_type, copy=False), **gaussian_kwargs)
+ np.finfo(float_type).eps
)
# Smooth the masked image
smoothed_image = gaussian(masked_image, **gaussian_kwargs)
# Lower the result by the bleed-over fraction, so you can
# recalibrate by dividing by the function on the mask to recover
# the effect of smoothing from just the significant pixels.
if compute_bleedover:
smoothed_image /= bleed_over
return smoothed_image, eroded_mask
[文档]
def canny(
image,
sigma=1.0,
low_threshold=None,
high_threshold=None,
mask=None,
use_quantiles=False,
*,
mode='constant',
cval=0.0,
):
"""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].
mode : str, {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}
The ``mode`` parameter determines how the array borders are
handled during Gaussian filtering, where ``cval`` is the value when
mode is equal to 'constant'.
cval : float, optional
Value to fill past edges of input if `mode` is 'constant'.
Returns
-------
output : 2D array (image)
The binary edge map.
See also
--------
skimage.filters.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
--------
>>> from skimage import feature
>>> rng = np.random.default_rng()
>>> # Generate noisy image of a square
>>> im = np.zeros((256, 256))
>>> im[64:-64, 64:-64] = 1
>>> im += 0.2 * rng.random(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)
"""
# 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?
if np.issubdtype(image.dtype, np.int64) or np.issubdtype(image.dtype, np.uint64):
raise ValueError("64-bit integer images are not supported")
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 /= 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 /= dtype_max
if high_threshold < low_threshold:
raise ValueError("low_threshold should be lower then high_threshold")
# Image filtering
smoothed, eroded_mask = _preprocess(image, mask, sigma, mode, cval)
# Gradient magnitude estimation
jsobel = ndi.sobel(smoothed, axis=1)
isobel = ndi.sobel(smoothed, axis=0)
magnitude = isobel * isobel
magnitude += jsobel * jsobel
np.sqrt(magnitude, out=magnitude)
if use_quantiles:
low_threshold, high_threshold = np.percentile(
magnitude, [100.0 * low_threshold, 100.0 * high_threshold]
)
# Non-maximum suppression
low_masked = _nonmaximum_suppression_bilinear(
isobel, jsobel, magnitude, eroded_mask, low_threshold
)
# Double thresholding and edge tracking
#
# Segment the low-mask, then only keep low-segments that have
# some high_mask component in them
#
low_mask = low_masked > 0
strel = np.ones((3, 3), bool)
labels, count = ndi.label(low_mask, strel)
if count == 0:
return low_mask
high_mask = low_mask & (low_masked >= high_threshold)
nonzero_sums = np.unique(labels[high_mask])
good_label = np.zeros((count + 1,), bool)
good_label[nonzero_sums] = True
output_mask = good_label[labels]
return output_mask
