"""Convex Hull.""" from itertools import product import numpy as np from scipy.spatial import ConvexHull from ..measure.pnpoly import grid_points_in_poly from ._convex_hull import possible_hull from ..measure._label import label from ..util import unique_rows from .._shared.utils import warn __all__ = ['convex_hull_image', 'convex_hull_object'] def _offsets_diamond(ndim): offsets = np.zeros((2 * ndim, ndim)) for vertex, (axis, offset) in enumerate(product(range(ndim), (-0.5, 0.5))): offsets[vertex, axis] = offset return offsets def convex_hull_image(image, offset_coordinates=True, tolerance=1e-10): """Compute the convex hull image of a binary image. The convex hull is the set of pixels included in the smallest convex polygon that surround all white pixels in the input image. Parameters ---------- image : array Binary input image. This array is cast to bool before processing. offset_coordinates : bool, optional If ``True``, a pixel at coordinate, e.g., (4, 7) will be represented by coordinates (3.5, 7), (4.5, 7), (4, 6.5), and (4, 7.5). This adds some "extent" to a pixel when computing the hull. tolerance : float, optional Tolerance when determining whether a point is inside the hull. Due to numerical floating point errors, a tolerance of 0 can result in some points erroneously being classified as being outside the hull. Returns ------- hull : (M, N) array of bool Binary image with pixels in convex hull set to True. References ---------- .. [1] https://blogs.mathworks.com/steve/2011/10/04/binary-image-convex-hull-algorithm-notes/ """ ndim = image.ndim if np.count_nonzero(image) == 0: warn("Input image is entirely zero, no valid convex hull. " "Returning empty image", UserWarning) return np.zeros(image.shape, dtype=np.bool_) # In 2D, we do an optimisation by choosing only pixels that are # the starting or ending pixel of a row or column. This vastly # limits the number of coordinates to examine for the virtual hull. if ndim == 2: coords = possible_hull(np.ascontiguousarray(image, dtype=np.uint8)) else: coords = np.transpose(np.nonzero(image)) if offset_coordinates: # when offsetting, we multiply number of vertices by 2 * ndim. # therefore, we reduce the number of coordinates by using a # convex hull on the original set, before offsetting. hull0 = ConvexHull(coords) coords = hull0.points[hull0.vertices] # Add a vertex for the middle of each pixel edge if offset_coordinates: offsets = _offsets_diamond(image.ndim) coords = (coords[:, np.newaxis, :] + offsets).reshape(-1, ndim) # repeated coordinates can *sometimes* cause problems in # scipy.spatial.ConvexHull, so we remove them. coords = unique_rows(coords) # Find the convex hull hull = ConvexHull(coords) vertices = hull.points[hull.vertices] # If 2D, use fast Cython function to locate convex hull pixels if ndim == 2: mask = grid_points_in_poly(image.shape, vertices) else: gridcoords = np.reshape(np.mgrid[tuple(map(slice, image.shape))], (ndim, -1)) # A point is in the hull if it satisfies all of the hull's inequalities coords_in_hull = np.all(hull.equations[:, :ndim].dot(gridcoords) + hull.equations[:, ndim:] < tolerance, axis=0) mask = np.reshape(coords_in_hull, image.shape) return mask def convex_hull_object(image, neighbors=None, *, connectivity=None): r"""Compute the convex hull image of individual objects in a binary image. The convex hull is the set of pixels included in the smallest convex polygon that surround all white pixels in the input image. Parameters ---------- image : (M, N) ndarray Binary input image. neighbors : {4, 8}, int, optional Whether to use 4 or 8 adjacent pixels as neighbors. If ``None``, set to 8. **Deprecated, use** ``connectivity`` **instead.** connectivity : {1, 2}, int, optional Determines the neighbors of each pixel. Adjacent elements within a squared distance of ``connectivity`` from pixel center are considered neighbors. If ``None``, set to 2:: 1-connectivity 2-connectivity [ ] [ ] [ ] [ ] | \ | / [ ]--[x]--[ ] [ ]--[x]--[ ] | / | \ [ ] [ ] [ ] [ ] Returns ------- hull : ndarray of bool Binary image with pixels inside convex hull set to ``True``. Notes ----- This function uses ``skimage.morphology.label`` to define unique objects, finds the convex hull of each using ``convex_hull_image``, and combines these regions with logical OR. Be aware the convex hulls of unconnected objects may overlap in the result. If this is suspected, consider using convex_hull_image separately on each object or adjust ``connectivity``. """ if image.ndim > 2: raise ValueError("Input must be a 2D image") if neighbors is None and connectivity is None: connectivity = 2 elif neighbors is not None: # Backward-compatibility if neighbors == 4: connectivity = 1 elif neighbors == 8: connectivity = 2 else: raise ValueError('`neighbors` must be either 4 or 8.') warn("The argument `neighbors` is deprecated and will be removed in " "scikit-image 0.18, use `connectivity` instead. " "For neighbors={neighbors}, use connectivity={connectivity}" "".format(neighbors=neighbors, connectivity=connectivity), stacklevel=2) else: if connectivity not in (1, 2): raise ValueError('`connectivity` must be either 1 or 2.') labeled_im = label(image, connectivity=connectivity, background=0) convex_obj = np.zeros(image.shape, dtype=bool) convex_img = np.zeros(image.shape, dtype=bool) for i in range(1, labeled_im.max() + 1): convex_obj = convex_hull_image(labeled_im == i) convex_img = np.logical_or(convex_img, convex_obj) return convex_img