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import numpy as np
import scipy.ndimage as ndi
from .. import measure
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, kind="stable")
coord = np.transpose(coord)[idx_maxsort]
if np.isfinite(num_peaks):
max_out = int(num_peaks)
else:
max_out = None
if min_distance > 1:
coord = ensure_spacing(
coord, spacing=min_distance, p_norm=p_norm, max_out=max_out
)
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='nearest')
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
def peak_local_max(
image,
min_distance=1,
threshold_abs=None,
threshold_rel=None,
exclude_border=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.
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 or None, optional
Minimum intensity of peaks. By default, the absolute threshold is
the minimum intensity of the image.
threshold_rel : float or None, 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.
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
The coordinates of the peaks.
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 images, this function returns the coordinates
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].copy()
# 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
)
return coordinates
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.intensity_max)[::-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 neighborhood 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 neighborhood suppression
ycoords_nh = ycoords_idx + ycoords_ext
xcoords_nh = xcoords_idx + xcoords_ext
# no reflection for distance neighborhood
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 neighborhood
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
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