9iPQSrSSKrSSKJr SSKJrJrJr SSK J r J r SSK J r S rS rSS jrSS jrSS jrSSjrg)aextrema.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. N)warn) dtype_limitsinvertcrop)grayreconstruct_util) _local_maximac^[USS9up#XU- :a [S5eX-nX4XU- :'U$)zDAdd constant to the image while handling overflow issues gracefully.F clip_negativez=The added constant is not compatiblewith the image data type.r ValueErrorimage const_value min_dtype max_dtyperesults Z/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/morphology/extrema.py_add_constant_cliprsK'UCI)+, N   F.75{* *+ Mc^[USS9up#XU- :a [S5eX- nX$XU-:'U$)z=Subtract constant from image while handling underflow issues.Fr zBThe subtracted constant is not compatiblewith the image data type.rrs r_subtract_constant_clipr#sK'UCI)+, S   F095)+ ,- MrcU[R"U5:a-[R"UR[RS9$[R "[ U5[R5(ax[R "UR[R5(aDUS-S:wa [SSS9 UR[5nOURR U5nUS:Xa [S5e[R "UR[R5(aLS[R"UR5R-[R "U5-nX- U- nO [#X5n[$R&"X@SUS 9nX- nXa:R[R5$) a>Determine all maxima of the image with height >= h. The local maxima are defined as connected sets of pixels with equal gray level strictly greater than the gray 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 an equal or higher local 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 to an equal or higher local maximum for which the minimal value is greater. The global maxima of the image are also found by this function. Parameters ---------- image : ndarray The input image for which the maxima are to be calculated. h : unsigned integer The minimal height of all extracted maxima. footprint : 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 local maxima of height >= h and the global maxima. The resulting image is a binary image, where pixels belonging to the determined maxima take value 1, the others take value 0. See Also -------- skimage.morphology.h_minima skimage.morphology.local_maxima skimage.morphology.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 >>> 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(int) We can calculate all maxima with a height of at least 40: >>> maxima = extrema.h_maxima(f, 40) The resulting image will contain 3 local maxima. dtyperr|possible precision loss converting image to floating point. To silence this warning, ensure image and h have same data type.r stacklevelz/h = 0 is ambiguous, use local_maxima() instead?dilationmethod footprint)npptpzerosshapeuint8 issubdtypetypefloatingrintegerrastypefloatrfinfo resolutionabsrr reconstructionrhr%r2 shifted_imgrec_img residue_imgs rh_maximar:1sHJ 266%=xx 28844$ }}T!Wbkk**r}}U[["**/U/U Ea< :   LL'E   #AAvMNN }}U[["++..%++.999BFF5MI i*, -e7 ,,:G/K   $ $RXX ..rcU[R"U5:a-[R"UR[RS9$[R "[ U5[R5(ax[R "UR[R5(aDUS-S:wa [SSS9 UR[5nOURR U5nUS:Xa [S5e[R "UR[R5(aLS[R"UR5R-[R "U5-nX-U-nO [#X5n[$R&"X@SUS 9nXP- nXa:R[R5$) a:Determine all minima of the image with depth >= h. The local minima are defined as connected sets of pixels with equal gray level strictly smaller than the gray 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 an equal or lower local 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 to an equal or lower local minimum for which the maximal value is smaller. The global minima of the image are also found by this function. Parameters ---------- image : ndarray The input image for which the minima are to be calculated. h : unsigned integer The minimal depth of all extracted minima. footprint : 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 local minima of depth >= h and the global minima. The resulting image is a binary image, where pixels belonging to the determined minima take value 1, the others take value 0. See Also -------- skimage.morphology.h_maxima skimage.morphology.local_maxima skimage.morphology.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 >>> 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(int) We can calculate all minima with a depth of at least 40: >>> minima = extrema.h_minima(f, 40) The resulting image will contain 3 local minima. rrrrrr z/h = 0 is ambiguous, use local_minima() instead?erosionr#)r&r'r(r)r*r+r,r-rr.rr/r0rr1r2r3rr r4r5s rh_minimar=sDD 266%=xx 28844 }}T!Wbkk**r}}U[["**/U/U Ea< :   LL'E   #AAvMNN }}U[["++..%++.999BFF5MI i*, (2 ,,9 G/K   $ $RXX ..rc[R"USS9nURS:Xa@U(a[R"U5$[R"UR [ S9$U(a%[R"USSUR5S9n[R"UR [RS9n[R"USS 9 [S UR 55(a [S SS 9 Ox[R"XUR5n[R "UR US UR-S9n[#UR%5UR%5U5 U(a [-US5nO[R"USS 9 U(a[R"U5$UR/[ 5$![&a+ UR([R*:Xa ['S5eef=f)aJFind 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. footprint : ndarray, optional The footprint (structuring element) used to determine the neighborhood of each evaluated pixel (``True`` denotes a connected pixel). It must be a boolean array and have the same number of dimensions as `image`. If neither `footprint` nor `connectivity` are 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 less than or equal to `connectivity` are considered neighbors. Ignored if `footprint` 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 a boolean array 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, a boolean array with the same shape as `image` is returned with ``True`` indicating the position of local maxima (``False`` 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([[False, False, False, False, False, False, False], [False, True, True, False, False, False, False], [False, True, True, False, False, False, False], [ True, False, False, False, False, False, True]]) >>> 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([[False, False, False, False, False, False, False], [False, True, True, False, True, True, False], [False, True, True, False, True, True, False], [ True, False, False, False, False, False, True]]) and exclude maxima that border the image edge: >>> local_maxima(image, connectivity=1, allow_borders=False) array([[False, False, False, False, False, False, False], [False, True, True, False, True, True, False], [False, True, True, False, True, True, False], [False, False, False, False, False, False, False]]) C)orderrrrconstant)modeconstant_values)valuec3*# UH oS:v M g7f)rDN).0ss r local_maxima..s &+Qq5+szVmaxima can't exist for an image with any dimension smaller 3 if borders aren't allowedr )r)centerzLdtype of `image` is float16 which is not supported, try upcasting to float32)r&asarraysizenonzeror(r)boolpadminr*r _set_border_valuesanyr_resolve_neighborhoodndim_offsets_to_raveled_neighborsr ravel TypeErrorrfloat16rview)rr% connectivityindices allow_bordersflagsneighbor_offsetss r local_maximarasX JJuC (E zzQ ::e$ $88EKKt4 4uaj%))+N HHU[[ 1E U!, &%++ &&&  ( // T  >> KKD5::,=   %++-8H IUA   a0zz%  zz$) {{bjj(:  s )G5Hc,[[USS9UUUUS9$)aFind 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. footprint : ndarray, optional The footprint (structuring element) used to determine the neighborhood of each evaluated pixel (``True`` denotes a connected pixel). It must be a boolean array and have the same number of dimensions as `image`. If neither `footprint` nor `connectivity` are 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 less than or equal to `connectivity` are considered neighbors. Ignored if `footprint` 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 a boolean array 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, a boolean array with the same shape as `image` is returned with ``True`` indicating the position of local minima (``False`` 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([[False, False, False, False, False, False, False], [False, True, True, False, False, False, False], [False, True, True, False, False, False, False], [ True, False, False, False, False, False, True]]) >>> 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([[False, False, False, False, False, False, False], [False, True, True, False, True, True, False], [False, True, True, False, True, True, False], [ True, False, False, False, False, False, True]]) and exclude minima that border the image edge: >>> local_minima(image, connectivity=1, allow_borders=False) array([[False, False, False, False, False, False, False], [False, True, True, False, True, True, False], [False, True, True, False, True, True, False], [False, False, False, False, False, False, False]]) T) signed_floatrr%r\r]r^)rarrds r local_minimares(L U.!#  r)N)NNFT)__doc__numpyr& _shared.utilsrutilrrrr r _extrema_cyr rrr:r=rarerGrrrlsQ  --$&  ~/B^/DLPc NLPlr