423 lines
15 KiB
Python
423 lines
15 KiB
Python
|
from warnings import warn
|
||
|
import numpy as np
|
||
|
import scipy.ndimage as ndi
|
||
|
from .. import measure
|
||
|
from .._shared.utils import remove_arg
|
||
|
from .._shared.coord import ensure_spacing
|
||
|
|
||
|
|
||
|
def _get_high_intensity_peaks(image, mask, num_peaks, min_distance, p_norm):
|
||
|
"""
|
||
|
Return the highest intensity peak coordinates.
|
||
|
"""
|
||
|
# get coordinates of peaks
|
||
|
coord = np.nonzero(mask)
|
||
|
intensities = image[coord]
|
||
|
# Highest peak first
|
||
|
idx_maxsort = np.argsort(-intensities)
|
||
|
coord = np.transpose(coord)[idx_maxsort]
|
||
|
|
||
|
coord = ensure_spacing(coord, spacing=min_distance, p_norm=p_norm)
|
||
|
|
||
|
if len(coord) > num_peaks:
|
||
|
coord = coord[:num_peaks]
|
||
|
|
||
|
return coord
|
||
|
|
||
|
|
||
|
def _get_peak_mask(image, footprint, threshold, mask=None):
|
||
|
"""
|
||
|
Return the mask containing all peak candidates above thresholds.
|
||
|
"""
|
||
|
if footprint.size == 1 or image.size == 1:
|
||
|
return image > threshold
|
||
|
|
||
|
image_max = ndi.maximum_filter(image, footprint=footprint,
|
||
|
mode='constant')
|
||
|
|
||
|
out = image == image_max
|
||
|
|
||
|
# no peak for a trivial image
|
||
|
image_is_trivial = np.all(out) if mask is None else np.all(out[mask])
|
||
|
if image_is_trivial:
|
||
|
out[:] = False
|
||
|
if mask is not None:
|
||
|
# isolated pixels in masked area are returned as peaks
|
||
|
isolated_px = np.logical_xor(mask, ndi.binary_opening(mask))
|
||
|
out[isolated_px] = True
|
||
|
|
||
|
out &= image > threshold
|
||
|
return out
|
||
|
|
||
|
|
||
|
def _exclude_border(label, border_width):
|
||
|
"""Set label border values to 0.
|
||
|
|
||
|
"""
|
||
|
# zero out label borders
|
||
|
for i, width in enumerate(border_width):
|
||
|
if width == 0:
|
||
|
continue
|
||
|
label[(slice(None),) * i + (slice(None, width),)] = 0
|
||
|
label[(slice(None),) * i + (slice(-width, None),)] = 0
|
||
|
return label
|
||
|
|
||
|
|
||
|
def _get_threshold(image, threshold_abs, threshold_rel):
|
||
|
"""Return the threshold value according to an absolute and a relative
|
||
|
value.
|
||
|
|
||
|
"""
|
||
|
threshold = threshold_abs if threshold_abs is not None else image.min()
|
||
|
|
||
|
if threshold_rel is not None:
|
||
|
threshold = max(threshold, threshold_rel * image.max())
|
||
|
|
||
|
return threshold
|
||
|
|
||
|
|
||
|
def _get_excluded_border_width(image, min_distance, exclude_border):
|
||
|
"""Return border_width values relative to a min_distance if requested.
|
||
|
|
||
|
"""
|
||
|
|
||
|
if isinstance(exclude_border, bool):
|
||
|
border_width = (min_distance if exclude_border else 0,) * image.ndim
|
||
|
elif isinstance(exclude_border, int):
|
||
|
if exclude_border < 0:
|
||
|
raise ValueError("`exclude_border` cannot be a negative value")
|
||
|
border_width = (exclude_border,) * image.ndim
|
||
|
elif isinstance(exclude_border, tuple):
|
||
|
if len(exclude_border) != image.ndim:
|
||
|
raise ValueError(
|
||
|
"`exclude_border` should have the same length as the "
|
||
|
"dimensionality of the image.")
|
||
|
for exclude in exclude_border:
|
||
|
if not isinstance(exclude, int):
|
||
|
raise ValueError(
|
||
|
"`exclude_border`, when expressed as a tuple, must only "
|
||
|
"contain ints."
|
||
|
)
|
||
|
if exclude < 0:
|
||
|
raise ValueError(
|
||
|
"`exclude_border` can not be a negative value")
|
||
|
border_width = exclude_border
|
||
|
else:
|
||
|
raise TypeError(
|
||
|
"`exclude_border` must be bool, int, or tuple with the same "
|
||
|
"length as the dimensionality of the image.")
|
||
|
|
||
|
return border_width
|
||
|
|
||
|
|
||
|
@remove_arg("indices", changed_version="0.20")
|
||
|
def peak_local_max(image, min_distance=1, threshold_abs=None,
|
||
|
threshold_rel=None, exclude_border=True, indices=True,
|
||
|
num_peaks=np.inf, footprint=None, labels=None,
|
||
|
num_peaks_per_label=np.inf, p_norm=np.inf):
|
||
|
"""Find peaks in an image as coordinate list or boolean mask.
|
||
|
|
||
|
Peaks are the local maxima in a region of `2 * min_distance + 1`
|
||
|
(i.e. peaks are separated by at least `min_distance`).
|
||
|
|
||
|
If both `threshold_abs` and `threshold_rel` are provided, the maximum
|
||
|
of the two is chosen as the minimum intensity threshold of peaks.
|
||
|
|
||
|
.. versionchanged:: 0.18
|
||
|
Prior to version 0.18, peaks of the same height within a radius of
|
||
|
`min_distance` were all returned, but this could cause unexpected
|
||
|
behaviour. From 0.18 onwards, an arbitrary peak within the region is
|
||
|
returned. See issue gh-2592.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : ndarray
|
||
|
Input image.
|
||
|
min_distance : int, optional
|
||
|
The minimal allowed distance separating peaks. To find the
|
||
|
maximum number of peaks, use `min_distance=1`.
|
||
|
threshold_abs : float, optional
|
||
|
Minimum intensity of peaks. By default, the absolute threshold is
|
||
|
the minimum intensity of the image.
|
||
|
threshold_rel : float, optional
|
||
|
Minimum intensity of peaks, calculated as `max(image) * threshold_rel`.
|
||
|
exclude_border : int, tuple of ints, or bool, optional
|
||
|
If positive integer, `exclude_border` excludes peaks from within
|
||
|
`exclude_border`-pixels of the border of the image.
|
||
|
If tuple of non-negative ints, the length of the tuple must match the
|
||
|
input array's dimensionality. Each element of the tuple will exclude
|
||
|
peaks from within `exclude_border`-pixels of the border of the image
|
||
|
along that dimension.
|
||
|
If True, takes the `min_distance` parameter as value.
|
||
|
If zero or False, peaks are identified regardless of their distance
|
||
|
from the border.
|
||
|
indices : bool, optional
|
||
|
If True, the output will be an array representing peak
|
||
|
coordinates. The coordinates are sorted according to peaks
|
||
|
values (Larger first). If False, the output will be a boolean
|
||
|
array shaped as `image.shape` with peaks present at True
|
||
|
elements. ``indices`` is deprecated and will be removed in
|
||
|
version 0.20. Default behavior will be to always return peak
|
||
|
coordinates. You can obtain a mask as shown in the example
|
||
|
below.
|
||
|
num_peaks : int, optional
|
||
|
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
|
||
|
return `num_peaks` peaks based on highest peak intensity.
|
||
|
footprint : ndarray of bools, optional
|
||
|
If provided, `footprint == 1` represents the local region within which
|
||
|
to search for peaks at every point in `image`.
|
||
|
labels : ndarray of ints, optional
|
||
|
If provided, each unique region `labels == value` represents a unique
|
||
|
region to search for peaks. Zero is reserved for background.
|
||
|
num_peaks_per_label : int, optional
|
||
|
Maximum number of peaks for each label.
|
||
|
p_norm : float
|
||
|
Which Minkowski p-norm to use. Should be in the range [1, inf].
|
||
|
A finite large p may cause a ValueError if overflow can occur.
|
||
|
``inf`` corresponds to the Chebyshev distance and 2 to the
|
||
|
Euclidean distance.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : ndarray or ndarray of bools
|
||
|
|
||
|
* If `indices = True` : (row, column, ...) coordinates of peaks.
|
||
|
* If `indices = False` : Boolean array shaped like `image`, with peaks
|
||
|
represented by True values.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
The peak local maximum function returns the coordinates of local peaks
|
||
|
(maxima) in an image. Internally, a maximum filter is used for finding local
|
||
|
maxima. This operation dilates the original image. After comparison of the
|
||
|
dilated and original image, this function returns the coordinates or a mask
|
||
|
of the peaks where the dilated image equals the original image.
|
||
|
|
||
|
See also
|
||
|
--------
|
||
|
skimage.feature.corner_peaks
|
||
|
|
||
|
Examples
|
||
|
--------
|
||
|
>>> img1 = np.zeros((7, 7))
|
||
|
>>> img1[3, 4] = 1
|
||
|
>>> img1[3, 2] = 1.5
|
||
|
>>> img1
|
||
|
array([[0. , 0. , 0. , 0. , 0. , 0. , 0. ],
|
||
|
[0. , 0. , 0. , 0. , 0. , 0. , 0. ],
|
||
|
[0. , 0. , 0. , 0. , 0. , 0. , 0. ],
|
||
|
[0. , 0. , 1.5, 0. , 1. , 0. , 0. ],
|
||
|
[0. , 0. , 0. , 0. , 0. , 0. , 0. ],
|
||
|
[0. , 0. , 0. , 0. , 0. , 0. , 0. ],
|
||
|
[0. , 0. , 0. , 0. , 0. , 0. , 0. ]])
|
||
|
|
||
|
>>> peak_local_max(img1, min_distance=1)
|
||
|
array([[3, 2],
|
||
|
[3, 4]])
|
||
|
|
||
|
>>> peak_local_max(img1, min_distance=2)
|
||
|
array([[3, 2]])
|
||
|
|
||
|
>>> img2 = np.zeros((20, 20, 20))
|
||
|
>>> img2[10, 10, 10] = 1
|
||
|
>>> img2[15, 15, 15] = 1
|
||
|
>>> peak_idx = peak_local_max(img2, exclude_border=0)
|
||
|
>>> peak_idx
|
||
|
array([[10, 10, 10],
|
||
|
[15, 15, 15]])
|
||
|
|
||
|
>>> peak_mask = np.zeros_like(img2, dtype=bool)
|
||
|
>>> peak_mask[tuple(peak_idx.T)] = True
|
||
|
>>> np.argwhere(peak_mask)
|
||
|
array([[10, 10, 10],
|
||
|
[15, 15, 15]])
|
||
|
|
||
|
"""
|
||
|
if (footprint is None or footprint.size == 1) and min_distance < 1:
|
||
|
warn("When min_distance < 1, peak_local_max acts as finding "
|
||
|
"image > max(threshold_abs, threshold_rel * max(image)).",
|
||
|
RuntimeWarning, stacklevel=2)
|
||
|
|
||
|
border_width = _get_excluded_border_width(image, min_distance,
|
||
|
exclude_border)
|
||
|
|
||
|
threshold = _get_threshold(image, threshold_abs, threshold_rel)
|
||
|
|
||
|
if footprint is None:
|
||
|
size = 2 * min_distance + 1
|
||
|
footprint = np.ones((size, ) * image.ndim, dtype=bool)
|
||
|
else:
|
||
|
footprint = np.asarray(footprint)
|
||
|
|
||
|
if labels is None:
|
||
|
# Non maximum filter
|
||
|
mask = _get_peak_mask(image, footprint, threshold)
|
||
|
|
||
|
mask = _exclude_border(mask, border_width)
|
||
|
|
||
|
# Select highest intensities (num_peaks)
|
||
|
coordinates = _get_high_intensity_peaks(image, mask,
|
||
|
num_peaks,
|
||
|
min_distance, p_norm)
|
||
|
|
||
|
else:
|
||
|
_labels = _exclude_border(labels.astype(int, casting="safe"),
|
||
|
border_width)
|
||
|
|
||
|
if np.issubdtype(image.dtype, np.floating):
|
||
|
bg_val = np.finfo(image.dtype).min
|
||
|
else:
|
||
|
bg_val = np.iinfo(image.dtype).min
|
||
|
|
||
|
# For each label, extract a smaller image enclosing the object of
|
||
|
# interest, identify num_peaks_per_label peaks
|
||
|
labels_peak_coord = []
|
||
|
|
||
|
for label_idx, roi in enumerate(ndi.find_objects(_labels)):
|
||
|
|
||
|
if roi is None:
|
||
|
continue
|
||
|
|
||
|
# Get roi mask
|
||
|
label_mask = labels[roi] == label_idx + 1
|
||
|
# Extract image roi
|
||
|
img_object = image[roi]
|
||
|
# Ensure masked values don't affect roi's local peaks
|
||
|
img_object[np.logical_not(label_mask)] = bg_val
|
||
|
|
||
|
mask = _get_peak_mask(img_object, footprint, threshold, label_mask)
|
||
|
|
||
|
coordinates = _get_high_intensity_peaks(img_object, mask,
|
||
|
num_peaks_per_label,
|
||
|
min_distance,
|
||
|
p_norm)
|
||
|
|
||
|
# transform coordinates in global image indices space
|
||
|
for idx, s in enumerate(roi):
|
||
|
coordinates[:, idx] += s.start
|
||
|
|
||
|
labels_peak_coord.append(coordinates)
|
||
|
|
||
|
if labels_peak_coord:
|
||
|
coordinates = np.vstack(labels_peak_coord)
|
||
|
else:
|
||
|
coordinates = np.empty((0, 2), dtype=int)
|
||
|
|
||
|
if len(coordinates) > num_peaks:
|
||
|
out = np.zeros_like(image, dtype=bool)
|
||
|
out[tuple(coordinates.T)] = True
|
||
|
coordinates = _get_high_intensity_peaks(image, out,
|
||
|
num_peaks,
|
||
|
min_distance,
|
||
|
p_norm)
|
||
|
|
||
|
if indices:
|
||
|
return coordinates
|
||
|
else:
|
||
|
out = np.zeros_like(image, dtype=bool)
|
||
|
out[tuple(coordinates.T)] = True
|
||
|
return out
|
||
|
|
||
|
|
||
|
def _prominent_peaks(image, min_xdistance=1, min_ydistance=1,
|
||
|
threshold=None, num_peaks=np.inf):
|
||
|
"""Return peaks with non-maximum suppression.
|
||
|
|
||
|
Identifies most prominent features separated by certain distances.
|
||
|
Non-maximum suppression with different sizes is applied separately
|
||
|
in the first and second dimension of the image to identify peaks.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : (M, N) ndarray
|
||
|
Input image.
|
||
|
min_xdistance : int
|
||
|
Minimum distance separating features in the x dimension.
|
||
|
min_ydistance : int
|
||
|
Minimum distance separating features in the y dimension.
|
||
|
threshold : float
|
||
|
Minimum intensity of peaks. Default is `0.5 * max(image)`.
|
||
|
num_peaks : int
|
||
|
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
|
||
|
return `num_peaks` coordinates based on peak intensity.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
intensity, xcoords, ycoords : tuple of array
|
||
|
Peak intensity values, x and y indices.
|
||
|
"""
|
||
|
|
||
|
img = image.copy()
|
||
|
rows, cols = img.shape
|
||
|
|
||
|
if threshold is None:
|
||
|
threshold = 0.5 * np.max(img)
|
||
|
|
||
|
ycoords_size = 2 * min_ydistance + 1
|
||
|
xcoords_size = 2 * min_xdistance + 1
|
||
|
img_max = ndi.maximum_filter1d(img, size=ycoords_size, axis=0,
|
||
|
mode='constant', cval=0)
|
||
|
img_max = ndi.maximum_filter1d(img_max, size=xcoords_size, axis=1,
|
||
|
mode='constant', cval=0)
|
||
|
mask = (img == img_max)
|
||
|
img *= mask
|
||
|
img_t = img > threshold
|
||
|
|
||
|
label_img = measure.label(img_t)
|
||
|
props = measure.regionprops(label_img, img_max)
|
||
|
|
||
|
# Sort the list of peaks by intensity, not left-right, so larger peaks
|
||
|
# in Hough space cannot be arbitrarily suppressed by smaller neighbors
|
||
|
props = sorted(props, key=lambda x: x.max_intensity)[::-1]
|
||
|
coords = np.array([np.round(p.centroid) for p in props], dtype=int)
|
||
|
|
||
|
img_peaks = []
|
||
|
ycoords_peaks = []
|
||
|
xcoords_peaks = []
|
||
|
|
||
|
# relative coordinate grid for local neighbourhood suppression
|
||
|
ycoords_ext, xcoords_ext = np.mgrid[-min_ydistance:min_ydistance + 1,
|
||
|
-min_xdistance:min_xdistance + 1]
|
||
|
|
||
|
for ycoords_idx, xcoords_idx in coords:
|
||
|
accum = img_max[ycoords_idx, xcoords_idx]
|
||
|
if accum > threshold:
|
||
|
# absolute coordinate grid for local neighbourhood suppression
|
||
|
ycoords_nh = ycoords_idx + ycoords_ext
|
||
|
xcoords_nh = xcoords_idx + xcoords_ext
|
||
|
|
||
|
# no reflection for distance neighbourhood
|
||
|
ycoords_in = np.logical_and(ycoords_nh > 0, ycoords_nh < rows)
|
||
|
ycoords_nh = ycoords_nh[ycoords_in]
|
||
|
xcoords_nh = xcoords_nh[ycoords_in]
|
||
|
|
||
|
# reflect xcoords and assume xcoords are continuous,
|
||
|
# e.g. for angles:
|
||
|
# (..., 88, 89, -90, -89, ..., 89, -90, -89, ...)
|
||
|
xcoords_low = xcoords_nh < 0
|
||
|
ycoords_nh[xcoords_low] = rows - ycoords_nh[xcoords_low]
|
||
|
xcoords_nh[xcoords_low] += cols
|
||
|
xcoords_high = xcoords_nh >= cols
|
||
|
ycoords_nh[xcoords_high] = rows - ycoords_nh[xcoords_high]
|
||
|
xcoords_nh[xcoords_high] -= cols
|
||
|
|
||
|
# suppress neighbourhood
|
||
|
img_max[ycoords_nh, xcoords_nh] = 0
|
||
|
|
||
|
# add current feature to peaks
|
||
|
img_peaks.append(accum)
|
||
|
ycoords_peaks.append(ycoords_idx)
|
||
|
xcoords_peaks.append(xcoords_idx)
|
||
|
|
||
|
img_peaks = np.array(img_peaks)
|
||
|
ycoords_peaks = np.array(ycoords_peaks)
|
||
|
xcoords_peaks = np.array(xcoords_peaks)
|
||
|
|
||
|
if num_peaks < len(img_peaks):
|
||
|
idx_maxsort = np.argsort(img_peaks)[::-1][:num_peaks]
|
||
|
img_peaks = img_peaks[idx_maxsort]
|
||
|
ycoords_peaks = ycoords_peaks[idx_maxsort]
|
||
|
xcoords_peaks = xcoords_peaks[idx_maxsort]
|
||
|
|
||
|
return img_peaks, xcoords_peaks, ycoords_peaks
|