ó  ‰\c@@sdZddlmZddlZddlmZddlm Z m Z m Z ddl m Z dd lmZdd lmZdd lmZd „Zd „Zdd„Zdd„Zd„Zd„Zd„Zddeed„Zddeed„ZdS(sextrema.py - local minima and maxima This module provides functions to find local maxima and minima of an image. Here, local maxima (minima) are defined as connected sets of pixels with equal gray level which is strictly greater (smaller) than the gray level of all pixels in direct neighborhood of the connected set. In addition, the module provides the related functions h-maxima and h-minima. Soille, P. (2003). Morphological Image Analysis: Principles and Applications (2nd ed.), Chapter 6. Springer-Verlag New York, Inc. i(tabsolute_importN(tndimagei(t dtype_limitstinverttcrop(twarni(tgreyreconstruct(t_offsets_to_raveled_neighbors(t _local_maximacC@sYt|dtƒ\}}|||kr7tdƒ‚n||}|||||k<|S(sIAdd constant to the image while handling overflow issues gracefully. t clip_negatives=The added constant is not compatiblewith the image data type.(RtFalset ValueError(timaget const_valuet min_dtypet max_dtypetresult((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt_add_constant_clips  cC@sYt|dtƒ\}}|||kr7tdƒ‚n||}|||||k<|S(sBSubtract constant from image while handling underflow issues. R sBThe subtracted constant is not compatiblewith the image data type.(RR R (R R RRR((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt_subtract_constant_clip's  c C@sÍtj|jtjƒradtj|jƒj}||krF|}n||d}||}nt||ƒ}|}tj||ddd|ƒ}||}tj |j dtj ƒ}d|||k<|S(s…Determine all maxima of the image with height >= h. The local maxima are defined as connected sets of pixels with equal grey level strictly greater than the grey level of all pixels in direct neighborhood of the set. A local maximum M of height h is a local maximum for which there is at least one path joining M with a higher maximum on which the minimal value is f(M) - h (i.e. the values along the path are not decreasing by more than h with respect to the maximum's value) and no path for which the minimal value is greater. Parameters ---------- image : ndarray The input image for which the maxima are to be calculated. h : unsigned integer The minimal height of all extracted maxima. selem : ndarray, optional The neighborhood expressed as an n-D array of 1's and 0's. Default is the ball of radius 1 according to the maximum norm (i.e. a 3x3 square for 2D images, a 3x3x3 cube for 3D images, etc.) Returns ------- h_max : ndarray The maxima of height >= h. The result image is a binary image, where pixels belonging to the selected maxima take value 1, the others take value 0. See also -------- skimage.morphology.extrema.h_minima skimage.morphology.extrema.local_maxima skimage.morphology.extrema.local_minima References ---------- .. [1] Soille, P., "Morphological Image Analysis: Principles and Applications" (Chapter 6), 2nd edition (2003), ISBN 3540429883. Examples -------- >>> import numpy as np >>> from skimage.morphology import extrema We create an image (quadratic function with a maximum in the center and 4 additional constant maxima. The heights of the maxima are: 1, 21, 41, 61, 81, 101 >>> w = 10 >>> x, y = np.mgrid[0:w,0:w] >>> f = 20 - 0.2*((x - w/2)**2 + (y-w/2)**2) >>> f[2:4,2:4] = 40; f[2:4,7:9] = 60; f[7:9,2:4] = 80; f[7:9,7:9] = 100 >>> f = f.astype(np.int) We can calculate all maxima with a height of at least 40: >>> maxima = extrema.h_maxima(f, 40) The resulting image will contain 4 local maxima. ig@tmethodtdilationtselemtdtypei( tnpt issubdtypeRtfloatingtfinfot resolutionRRtreconstructiontzerostshapetuint8( R thRRt h_correctedt shifted_imgtrec_imgt residue_imgth_max((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyth_maxima5s?    c C@sÍtj|jtjƒradtj|jƒj}||krF|}n||d}||}nt||ƒ}|}tj||ddd|ƒ}||}tj |j dtj ƒ}d|||k<|S(s‰Determine all minima of the image with depth >= h. The local minima are defined as connected sets of pixels with equal grey level strictly smaller than the grey levels of all pixels in direct neighborhood of the set. A local minimum M of depth h is a local minimum for which there is at least one path joining M with a deeper minimum on which the maximal value is f(M) + h (i.e. the values along the path are not increasing by more than h with respect to the minimum's value) and no path for which the maximal value is smaller. Parameters ---------- image : ndarray The input image for which the minima are to be calculated. h : unsigned integer The minimal depth of all extracted minima. selem : ndarray, optional The neighborhood expressed as an n-D array of 1's and 0's. Default is the ball of radius 1 according to the maximum norm (i.e. a 3x3 square for 2D images, a 3x3x3 cube for 3D images, etc.) Returns ------- h_min : ndarray The minima of depth >= h. The result image is a binary image, where pixels belonging to the selected minima take value 1, the other pixels take value 0. See also -------- skimage.morphology.extrema.h_maxima skimage.morphology.extrema.local_maxima skimage.morphology.extrema.local_minima References ---------- .. [1] Soille, P., "Morphological Image Analysis: Principles and Applications" (Chapter 6), 2nd edition (2003), ISBN 3540429883. Examples -------- >>> import numpy as np >>> from skimage.morphology import extrema We create an image (quadratic function with a minimum in the center and 4 additional constant maxima. The depth of the minima are: 1, 21, 41, 61, 81, 101 >>> w = 10 >>> x, y = np.mgrid[0:w,0:w] >>> f = 180 + 0.2*((x - w/2)**2 + (y-w/2)**2) >>> f[2:4,2:4] = 160; f[2:4,7:9] = 140; f[7:9,2:4] = 120; f[7:9,7:9] = 100 >>> f = f.astype(np.int) We can calculate all minima with a depth of at least 40: >>> minima = extrema.h_minima(f, 40) The resulting image will contain 4 local minima. ig@RterosionRRi( RRRRRRRRRRRR( R R RRR!R"R#R$th_min((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyth_minima†s?    cC@s\xUt|jƒD]D}tdƒg|j}d||<|||>> image = np.zeros((4, 5), dtype=int) >>> _set_edge_values_inplace(image, 1) >>> image array([[1, 1, 1, 1, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 1, 1, 1, 1]]) iiÿÿÿÿN(trangetndimtslicetNone(R tvaluetaxistsl((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt_set_edge_values_inplace×s    cC@sntj|jƒd}tj|d|jddƒ}td„t|jƒDƒƒ}|||>> _fast_pad(np.zeros((2, 3), dtype=int), 4) array([[4, 4, 4, 4, 4], [4, 0, 0, 0, 4], [4, 0, 0, 0, 4], [4, 4, 4, 4, 4]]) iRtordertCcs@s|]}tddƒVqdS(iiÿÿÿÿN(R,(t.0t_((s9lib/python2.7/site-packages/skimage/morphology/extrema.pys s( RtarrayRtemptyRttupleR*R+R1(R R.t new_shapet new_imagetoriginal_slice((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt _fast_padõs !  cC@s•|dkr6|dkr!|}ntj||ƒ}n[tj|dtƒ}|j|kritdƒ‚ntd„|j Dƒƒr‘tdƒ‚n|S(sValidate or create structuring element for use in `local_maxima`. Depending on the values of `connectivity` and `selem` this function either creates a new structuring element (`selem` is None) using `connectivity` or validates the given structuring element (`selem` is not None). Parameters ---------- selem : array-like or None The structuring element to validate. See same argument in `local_maxima`. connectivity : int or None A number used to determine the neighborhood of each evaluated pixel. See same argument in `local_maxima`. ndim : int Number of dimensions `selem` ought to have. Returns ------- selem : ndarray Validated or new structuring element specifying the neighborhood. RsEstructuring element and image must have the same number of dimensionscs@s|]}|dkVqdS(iN((R4ts((s9lib/python2.7/site-packages/skimage/morphology/extrema.pys Hss.dimension size in structuring element is not 3N( R-tnditgenerate_binary_structureRtasarraytboolR+R tanyR(Rt connectivityR+((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt_resolve_neighborhood"s    cC@s—tj|ddƒ}|jdkrS|r7tj|ƒStj|jdtjƒSn|rqt||jƒƒ}ntj|jdtjƒ}t |ddƒt d„|jDƒƒrÈt dd dƒnŒt |||j ƒ}t|j|d d|j ƒ}y t|jƒ|jƒ|ƒWn5tk rS|jtjkrMtd ƒ‚qT‚nX|rlt|d ƒ}nt |ddƒ|rtj|ƒS|Sd S(sFind local maxima of n-dimensional array. The local maxima are defined as connected sets of pixels with equal gray level (plateaus) strictly greater than the gray levels of all pixels in the neighborhood. Parameters ---------- image : ndarray An n-dimensional array. selem : ndarray, optional A structuring element used to determine the neighborhood of each evaluated pixel. It must contain only 1's and 0's, have the same number of dimensions as `image`. If not given, all adjacent pixels are considered as part of the neighborhood. connectivity : int, optional A number used to determine the neighborhood of each evaluated pixel. Adjacent pixels whose squared distance from the center is larger or equal to `connectivity` are considered neighbors. Ignored if `selem` is not None. indices : bool, optional If True, the output will be a tuple of one-dimensional arrays representing the indices of local maxima in each dimension. If False, the output will be an array of 0's and 1's with the same shape as `image`. allow_borders : bool, optional If true, plateaus that touch the image border are valid maxima. Returns ------- maxima : ndarray or tuple[ndarray] If `indices` is false, an array with the same shape as `image` is returned with 1's indicating the position of local maxima (0 otherwise). If `indices` is true, a tuple of one-dimensional arrays containing the coordinates (indices) of all found maxima. Warns ----- UserWarning If `allow_borders` is false and any dimension of the given `image` is shorter than 3 samples, maxima can't exist and a warning is shown. See Also -------- skimage.morphology.local_minima skimage.morphology.h_maxima skimage.morphology.h_minima Notes ----- This function operates on the following ideas: 1. Make a first pass over the image's last dimension and flag candidates for local maxima by comparing pixels in only one direction. If the pixels aren't connected in the last dimension all pixels are flagged as candidates instead. For each candidate: 2. Perform a flood-fill to find all connected pixels that have the same gray value and are part of the plateau. 3. Consider the connected neighborhood of a plateau: if no bordering sample has a higher gray level, mark the plateau as a definite local maximum. Examples -------- >>> from skimage.morphology import local_maxima >>> image = np.zeros((4, 7), dtype=int) >>> image[1:3, 1:3] = 1 >>> image[3, 0] = 1 >>> image[1:3, 4:6] = 2 >>> image[3, 6] = 3 >>> image array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 2, 2, 0], [0, 1, 1, 0, 2, 2, 0], [1, 0, 0, 0, 0, 0, 3]]) Find local maxima by comparing to all neighboring pixels (maximal connectivity): >>> local_maxima(image) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1]], dtype=uint8) >>> local_maxima(image, indices=True) (array([1, 1, 2, 2, 3, 3]), array([1, 2, 1, 2, 0, 6])) Find local maxima without comparing to diagonal pixels (connectivity 1): >>> local_maxima(image, connectivity=1) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 1]], dtype=uint8) and exclude maxima that border the image edge: >>> local_maxima(image, connectivity=1, allow_borders=False) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]], dtype=uint8) R2R3iRR.ics@s|]}|dkVqdS(iN((R4R=((s9lib/python2.7/site-packages/skimage/morphology/extrema.pys ÌssVmaxima can't exist for an image with any dimension smaller 3 if borders aren't allowedt stackleveltcenterisLdtype of `image` is float16 which is not supported, try upcasting to float32N(i(RR@tsizetnonzeroRRRR<tminR1RBRRDR+RRtravelt TypeErrorRtfloat16R(R RRCtindicest allow_borderstflagstneighbor_offsets((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt local_maximaNs8k     c C@s+tdt|ƒd|d|d|d|ƒS(svFind local minima of n-dimensional array. The local minima are defined as connected sets of pixels with equal gray level (plateaus) strictly smaller than the gray levels of all pixels in the neighborhood. Parameters ---------- image : ndarray An n-dimensional array. selem : ndarray, optional A structuring element used to determine the neighborhood of each evaluated pixel. It must contain only 1's and 0's, have the same number of dimensions as `image`. If not given, all adjacent pixels are considered as part of the neighborhood. connectivity : int, optional A number used to determine the neighborhood of each evaluated pixel. Adjacent pixels whose squared distance from the center is larger or equal to `connectivity` are considered neighbors. Ignored if `selem` is not None. indices : bool, optional If True, the output will be a tuple of one-dimensional arrays representing the indices of local minima in each dimension. If False, the output will be an array of 0's and 1's with the same shape as `image`. allow_borders : bool, optional If true, plateaus that touch the image border are valid minima. Returns ------- minima : ndarray or tuple[ndarray] If `indices` is false, an array with the same shape as `image` is returned with 1's indicating the position of local minima (0 otherwise). If `indices` is true, a tuple of one-dimensional arrays containing the coordinates (indices) of all found minima. See Also -------- skimage.morphology.local_maxima skimage.morphology.h_maxima skimage.morphology.h_minima Notes ----- This function operates on the following ideas: 1. Make a first pass over the image's last dimension and flag candidates for local minima by comparing pixels in only one direction. If the pixels aren't connected in the last dimension all pixels are flagged as candidates instead. For each candidate: 2. Perform a flood-fill to find all connected pixels that have the same gray value and are part of the plateau. 3. Consider the connected neighborhood of a plateau: if no bordering sample has a smaller gray level, mark the plateau as a definite local minimum. Examples -------- >>> from skimage.morphology import local_minima >>> image = np.zeros((4, 7), dtype=int) >>> image[1:3, 1:3] = -1 >>> image[3, 0] = -1 >>> image[1:3, 4:6] = -2 >>> image[3, 6] = -3 >>> image array([[ 0, 0, 0, 0, 0, 0, 0], [ 0, -1, -1, 0, -2, -2, 0], [ 0, -1, -1, 0, -2, -2, 0], [-1, 0, 0, 0, 0, 0, -3]]) Find local minima by comparing to all neighboring pixels (maximal connectivity): >>> local_minima(image) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1]], dtype=uint8) >>> local_minima(image, indices=True) (array([1, 1, 2, 2, 3, 3]), array([1, 2, 1, 2, 0, 6])) Find local minima without comparing to diagonal pixels (connectivity 1): >>> local_minima(image, connectivity=1) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 1]], dtype=uint8) and exclude minima that border the image edge: >>> local_minima(image, connectivity=1, allow_borders=False) array([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]], dtype=uint8) R RRCRMRN(RQR(R RRCRMRN((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt local_minimañs e ( t__doc__t __future__RtnumpyRtscipyRR>tutilRRRt _shared.utilsRtRt watershedRt _extrema_cyRRRR-R&R)R1R<RDR tTrueRQRR(((s9lib/python2.7/site-packages/skimage/morphology/extrema.pyt s&    Q Q  - ,  ¢