from warnings import warn 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 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