ó  ‰\c@sdZddlZddlmZddlmZddlm Z m Z d„Z d „Z d „Z dddd ed „ZdS( swatershed.py - watershed algorithm This module implements a watershed algorithm that apportions pixels into marked basins. The algorithm uses a priority queue to hold the pixels with the metric for the priority queue being pixel value, then the time of entry into the queue - this settles ties in favor of the closest marker. Some ideas taken from Soille, "Automated Basin Delineation from Digital Elevation Models Using Mathematical Morphology", Signal Processing 20 (1990) 171-182. The most important insight in the paper is that entry time onto the queue solves two problems: a pixel should be assigned to the neighbor with the largest gradient or, if there is no gradient, pixels on a plateau should be split between markers on opposite sides. Originally part of CellProfiler, code licensed under both GPL and BSD licenses. Website: http://www.cellprofiler.org Copyright (c) 2003-2009 Massachusetts Institute of Technology Copyright (c) 2009-2011 Broad Institute All rights reserved. Original author: Lee Kamentsky iÿÿÿÿN(tndimagei(t _watershedi(tcropt regular_seedscCsåt|tjttfƒs0t|j|ƒ}n3|j|jkrctdj|j|jƒƒ‚n|dk r|j|jkrtdƒ‚n|dkr´tj |jt ƒ}n|j tj ƒ|j tjƒ|j tjƒfS(s|Ensure that all inputs to watershed have matching shapes and types. Parameters ---------- image : array The input image. markers : int or array of int The marker image. mask : array, or None A boolean mask, True where we want to compute the watershed. Returns ------- image, markers, mask : arrays The validated and formatted arrays. Image will have dtype float64, markers int32, and mask int8. If ``None`` was given for the mask, it is a volume of all 1s. Raises ------ ValueError If the shapes of the given arrays don't match. s?`markers` (shape {}) must have same shape as `image` (shape {})s&`mask` must have same shape as `image`N(t isinstancetnptndarraytlistttupleRtshapet ValueErrortformattNonetonestbooltastypetfloat64tint32tint8(timagetmarkerstmask((s;lib/python2.7/site-packages/skimage/morphology/watershed.pyt_validate_inputs"s  cCsÓ|dkrd}ntj|ƒr9tj||ƒ}n0tj|tƒ}|j|kritdƒ‚n|dkrÉt g|j D]}|ddk^q‚ƒr°tdƒ‚ntj|j ƒd}n||fS(s$Convert any valid connectivity to a structuring element and offset. Parameters ---------- image_dim : int The number of dimensions of the input image. connectivity : int, array, or None The neighborhood connectivity. An integer is interpreted as in ``scipy.ndimage.generate_binary_structure``, as the maximum number of orthogonal steps to reach a neighbor. An array is directly interpreted as a structuring element and its shape is validated against the input image shape. ``None`` is interpreted as a connectivity of 1. offset : tuple of int, or None The coordinates of the center of the structuring element. Returns ------- c_connectivity : array of bool The structuring element corresponding to the input `connectivity`. offset : array of int The offset corresponding to the center of the structuring element. Raises ------ ValueError: If the image dimension and the connectivity or offset dimensions don't match. is,Connectivity dimension must be same as imageiis2Connectivity array must have an unambiguous centerN( R Rtisscalartnditgenerate_binary_structuretarrayRtndimR tanyR (t image_dimt connectivitytoffsettc_connectivitytx((s;lib/python2.7/site-packages/skimage/morphology/watershed.pyt_validate_connectivityJs   ,cCs‡|jƒ}d|t|ƒ>> _offsets_to_raveled_neighbors((4, 5), np.ones((4, 3)), (1, 1)) array([-5, -1, 1, 5, -6, -4, 4, 6, 10, 9, 11]) iitaxisi( tcopyRRt transposetnonzerotravel_multi_indextTtsumtargsort(t image_shapet structuretcentertconnection_indicestoffsetstsquared_distances((s;lib/python2.7/site-packages/skimage/morphology/watershed.pyt_offsets_to_raveled_neighbors{s ic Cs3t|||ƒ\}}}t|j||ƒ\}}g|D]}||f^q=}tj||ddƒ}tj||ddƒjƒ}tj||ddƒ} t|j|d|ƒ} tj| ƒ} tj |j dtj ƒ|j } t j|jƒ| | || || jƒ|ƒt| |dtƒ} | S(s™Find watershed basins in `image` flooded from given `markers`. Parameters ---------- image: ndarray (2-D, 3-D, ...) of integers Data array where the lowest value points are labeled first. markers: int, or ndarray of int, same shape as `image` The desired number of markers, or an array marking the basins with the values to be assigned in the label matrix. Zero means not a marker. connectivity: ndarray, optional An array with the same number of dimensions as `image` whose non-zero elements indicate neighbors for connection. Following the scipy convention, default is a one-connected array of the dimension of the image. offset: array_like of shape image.ndim, optional offset of the connectivity (one offset per dimension) mask: ndarray of bools or 0s and 1s, optional Array of same shape as `image`. Only points at which mask == True will be labeled. compactness : float, optional Use compact watershed [3]_ with given compactness parameter. Higher values result in more regularly-shaped watershed basins. watershed_line : bool, optional If watershed_line is True, a one-pixel wide line separates the regions obtained by the watershed algorithm. The line has the label 0. Returns ------- out: ndarray A labeled matrix of the same type and shape as markers See also -------- skimage.segmentation.random_walker: random walker segmentation A segmentation algorithm based on anisotropic diffusion, usually slower than the watershed but with good results on noisy data and boundaries with holes. Notes ----- This function implements a watershed algorithm [1]_ [2]_ that apportions pixels into marked basins. The algorithm uses a priority queue to hold the pixels with the metric for the priority queue being pixel value, then the time of entry into the queue - this settles ties in favor of the closest marker. Some ideas taken from Soille, "Automated Basin Delineation from Digital Elevation Models Using Mathematical Morphology", Signal Processing 20 (1990) 171-182 The most important insight in the paper is that entry time onto the queue solves two problems: a pixel should be assigned to the neighbor with the largest gradient or, if there is no gradient, pixels on a plateau should be split between markers on opposite sides. This implementation converts all arguments to specific, lowest common denominator types, then passes these to a C algorithm. Markers can be determined manually, or automatically using for example the local minima of the gradient of the image, or the local maxima of the distance function to the background for separating overlapping objects (see example). References ---------- .. [1] http://en.wikipedia.org/wiki/Watershed_%28image_processing%29 .. [2] http://cmm.ensmp.fr/~beucher/wtshed.html .. [3] Peer Neubert & Peter Protzel (2014). Compact Watershed and Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation Algorithms. ICPR 2014, pp 996-1001. DOI:10.1109/ICPR.2014.181 https://www.tu-chemnitz.de/etit/proaut/forschung/rsrc/cws_pSLIC_ICPR.pdf Examples -------- The watershed algorithm is useful to separate overlapping objects. We first generate an initial image with two overlapping circles: >>> x, y = np.indices((80, 80)) >>> x1, y1, x2, y2 = 28, 28, 44, 52 >>> r1, r2 = 16, 20 >>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2 >>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2 >>> image = np.logical_or(mask_circle1, mask_circle2) Next, we want to separate the two circles. We generate markers at the maxima of the distance to the background: >>> from scipy import ndimage as ndi >>> distance = ndi.distance_transform_edt(image) >>> from skimage.feature import peak_local_max >>> local_maxi = peak_local_max(distance, labels=image, ... footprint=np.ones((3, 3)), ... indices=False) >>> markers = ndi.label(local_maxi)[0] Finally, we run the watershed on the image and markers: >>> labels = watershed(-distance, markers, mask=image) The algorithm works also for 3-D images, and can be used for example to separate overlapping spheres. tmodetconstantR-tdtypeR$(RR"RRtpadtravelR1R t flatnonzeroRtstridestintptitemsizeRtwatershed_raveledRtTrue( RRRRRt compactnesstwatershed_linetpt pad_widthtoutputtflat_neighborhoodtmarker_locationst image_strides((s;lib/python2.7/site-packages/skimage/morphology/watershed.pyt watershedœs$k "  (t__doc__tnumpyRtscipyRRtRtutilRRRR"R1R tFalseRE(((s;lib/python2.7/site-packages/skimage/morphology/watershed.pyts  ( 1 !