9i5SSKrSSKJr SSKJr SrSSjrSSjr Sr S r S r S r S r\R4S jrSrSr\R4SjrSSjrg)N)distance_transform_edt)_supported_float_typecSn[R"USSS9nUSS2SS24USS2SS24- nUSS2SS24USS2SS24- n USS2SS24USS2SS24- S - n USS2SS24USS2SS24- n USS2SS24USS2SS24- n USS2SS24USS2SS24- S - n S [R"XhS--U S--5- nS [R"XiS--U S--5- nS [R"XjS--U S--5- nS [R"XjS--U S--5- nUSS2SS24U-USS2SS24U--USS2SS24U--USS2SS24U--nUS :RUR5n[ UU5unnU*UU- S--X@U- S---nX[ U5-UU-U---nUSX%-[ U5-X-U-U---- $) acReturns the variation of level set 'phi' based on algorithm parameters. This corresponds to equation (22) of the paper by Pascal Getreuer, which computes the next iteration of the level set based on a current level set. A full explanation regarding all the terms is beyond the scope of the present description, but there is one difference of particular import. In the original algorithm, convergence is accelerated, and required memory is reduced, by using a single array. This array, therefore, is a combination of non-updated and updated values. If this were to be implemented in python, this would require a double loop, where the benefits of having fewer iterations would be outweided by massively increasing the time required to perform each individual iteration. A similar approach is used by Rami Cohen, and it is from there that the C1-4 notation is taken. gؗҜ<edgemoderN@?r)nppadsqrtastypedtype_cv_calculate_averages _cv_delta)imagephimulambda1lambda2dtetaPphixpphixnphix0phiypphiynphiy0C1C2C3C4KHphic1c2difference_from_average_termnew_phis _/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/segmentation/_chan_vese.py_cv_calculate_variationr/s$ C sAF#A adABhK!AbD!B$J- 'E adAbDjMAadCRCiL (E qtQRx[1QrT3B3Y< '3 .E ab!B$hK!AbD!B$J- 'E adAbDjMAcrc1R4iL (E qr1R4x[1SbS!B$Y< '3 .E rwwsAX~q01 1B rwwsAX~q01 1B rwwsAX~q01 1B rwwsAX~q01 1B !B$( b1QrT3B3Y<",,qQrT{R/??!CRC2I,QSBSSA !G  EKK (D%eT2HR EBJ1$$w"*1B'BB!)C.(R!V6R-RSSG a"'IcN2bglR6GHH IIcfSSS[R- [R"X- 5---$)zNReturns the result of a regularised heavyside function of the input value(s). ?rr )rpiarctanxepss r. _cv_heavysider85s, #ruu !'(::: ;;r0cXS-US--- $)zJReturns the result of a regularised dirac function of the input value(s). rr5s r.rr<s q&1a4-  r0cUnSU- n[R"U5n[R"U5n[R"X-5n[R"X-5nUS:waXd-nUS:waXu-nXg4$)z2Returns the average values 'inside' and 'outside'.rr)rsum)rr)HHinvHsumHinvsum avg_inside avg_oustides r.rrCsq A 7D 66!9DffTlG "J&&&K qy !|  $$r0c\[X5upESU- nX U- S--U-X0U- S--U--$)znReturns the 'energy' contribution due to the difference from the average value within a region at each point. rr)r)rr) lambda_pos lambda_negr*r+r>s r. _cv_difference_from_average_termrFRsH&e2HR :D ) )D 0:PQ@Q3QTX3X XXr0c[R"USSS9nUSS2SS24USS2SS24- S- nUSS2SS24USS2SS24- S- nU[U5-[R"US-US--5-$) z|Returns the 'energy' contribution due to the length of the edge between regions at each point, multiplied by a factor 'mu'. rrr rNr r r )rrrr)rrrfyfxs r._cv_edge_length_termrJ[s sAF#A AB"H+#2#qt) $ +B AbD!"H+!B$) $ +B # QQ!7 77r0c[U5n[XX45n[X5n[R"U5[R"U5-$)a+Returns the total 'energy' of the current level set function. This corresponds to equation (7) of the paper by Pascal Getreuer, which is the weighted sum of the following: (A) the length of the contour produced by the zero values of the level set, (B) the area of the "foreground" (area of the image where the level set is positive), (C) the variance of the image inside the foreground, (D) the variance of the image outside of the foreground Each value is computed for each pixel, and then summed. The weight of (B) is set to 0 in this implementation. )r8rFrJrr<)rrrrrr= avgenergy lenenergys r. _cv_energyrNesA cA07LI$S-I 66) rvvi0 00r0cU$)zThis is a placeholder function as resetting the level set is not strictly necessary, and has not been done for this implementation. r:)rs r._cv_reset_level_setrPzs  Jr0c[R"USUS9RUSS5n[R"USUS9n[RU- nXE-nX5-n[R"U5[R"U5-$)z|Generates a checkerboard level set function. According to Pascal Getreuer, such a level set function has fast convergence. rrr)rarangereshaper3sin) image_size square_sizeryvxvsfs r._cv_checkerboardr[st :a= . 6 6z!}a HB :a= .B  BHBHB 66":r ""r0c[R"U5n[USS- S- 5n[USS- S- 5nSXU4'[[ X255nU[ U5- U- $)zdGenerates a disk level set function. The disk covers the whole image along its smallest dimension. rrrronesintfloatmindistancerVrescenterYcenterXradiuss r._cv_large_diskrisr ''* C:a=1$)*G:a=1$)*GC 3w( )F Xc] "f ,,r0c[R"U5n[USS- S- 5n[USS- S- 5nSXU4'[[ X255S- nU[ U5- US-- $)zfGenerates a disk level set function. The disk covers half of the image along its smallest dimension. rrrr]r r^rds r._cv_small_diskrls{ ''* C:a=1$)*G:a=1$)*GC 3w( )C /F Xc] "vz 22r0c[U[5(aCUS:Xa[USU5nO1US:Xa [U5nOUS:Xa [ U5nO [ S5eUnUR USS9$)zGGenerates an initial level set function conditional on input arguments. checkerboarddiskz small diskz-Incorrect name for starting level set preset.Fcopy) isinstancestrr[rirl ValueErrorr)init_level_set image_shaperres r._cv_init_level_setrxsm.#&& ^ +";59C v % -C | + -CLM M ::e%: ((r0c 0[UR5S:wa [S5e[UR5n [ XpRU S9n [ U 5[R:wdU RUR:wa [S5eURU SS9nU[R"U5- n[R"U5S:waU[R"U5- nSn [X XU5n /n US-nU S:nX:aX:azU n[X XX65n [U 5n [R"U U- S-R!55nU S:n[X XU5nU R#U 5 Un U S- n X:aX:aMzU(aXU 4$U$) aHChan-Vese segmentation algorithm. Active contour model by evolving a level set. Can be used to segment objects without clearly defined boundaries. Parameters ---------- image : (M, N) ndarray Grayscale image to be segmented. mu : float, optional 'edge length' weight parameter. Higher `mu` values will produce a 'round' edge, while values closer to zero will detect smaller objects. lambda1 : float, optional 'difference from average' weight parameter for the output region with value 'True'. If it is lower than `lambda2`, this region will have a larger range of values than the other. lambda2 : float, optional 'difference from average' weight parameter for the output region with value 'False'. If it is lower than `lambda1`, this region will have a larger range of values than the other. tol : float, positive, optional Level set variation tolerance between iterations. If the L2 norm difference between the level sets of successive iterations normalized by the area of the image is below this value, the algorithm will assume that the solution was reached. max_num_iter : uint, optional Maximum number of iterations allowed before the algorithm interrupts itself. dt : float, optional A multiplication factor applied at calculations for each step, serves to accelerate the algorithm. While higher values may speed up the algorithm, they may also lead to convergence problems. init_level_set : str or (M, N) ndarray, optional Defines the starting level set used by the algorithm. If a string is inputted, a level set that matches the image size will automatically be generated. Alternatively, it is possible to define a custom level set, which should be an array of float values, with the same shape as 'image'. Accepted string values are as follows. 'checkerboard' the starting level set is defined as sin(x/5*pi)*sin(y/5*pi), where x and y are pixel coordinates. This level set has fast convergence, but may fail to detect implicit edges. 'disk' the starting level set is defined as the opposite of the distance from the center of the image minus half of the minimum value between image width and image height. This is somewhat slower, but is more likely to properly detect implicit edges. 'small disk' the starting level set is defined as the opposite of the distance from the center of the image minus a quarter of the minimum value between image width and image height. extended_output : bool, optional If set to True, the return value will be a tuple containing the three return values (see below). If set to False which is the default value, only the 'segmentation' array will be returned. Returns ------- segmentation : (M, N) ndarray, bool Segmentation produced by the algorithm. phi : (M, N) ndarray of floats Final level set computed by the algorithm. energies : list of floats Shows the evolution of the 'energy' for each step of the algorithm. This should allow to check whether the algorithm converged. Notes ----- The Chan-Vese Algorithm is designed to segment objects without clearly defined boundaries. This algorithm is based on level sets that are evolved iteratively to minimize an energy, which is defined by weighted values corresponding to the sum of differences intensity from the average value outside the segmented region, the sum of differences from the average value inside the segmented region, and a term which is dependent on the length of the boundary of the segmented region. This algorithm was first proposed by Tony Chan and Luminita Vese, in a publication entitled "An Active Contour Model Without Edges" [1]_. This implementation of the algorithm is somewhat simplified in the sense that the area factor 'nu' described in the original paper is not implemented, and is only suitable for grayscale images. Typical values for `lambda1` and `lambda2` are 1. If the 'background' is very different from the segmented object in terms of distribution (for example, a uniform black image with figures of varying intensity), then these values should be different from each other. Typical values for mu are between 0 and 1, though higher values can be used when dealing with shapes with very ill-defined contours. The 'energy' which this algorithm tries to minimize is defined as the sum of the differences from the average within the region squared and weighed by the 'lambda' factors to which is added the length of the contour multiplied by the 'mu' factor. Supports 2D grayscale images only, and does not implement the area term described in the original article. References ---------- .. [1] An Active Contour Model without Edges, Tony Chan and Luminita Vese, Scale-Space Theories in Computer Vision, 1999, :DOI:`10.1007/3-540-48236-9_13` .. [2] Chan-Vese Segmentation, Pascal Getreuer Image Processing On Line, 2 (2012), pp. 214-224, :DOI:`10.5201/ipol.2012.g-cv` .. [3] The Chan-Vese Algorithm - Project Report, Rami Cohen, 2011 :arXiv:`1107.2782` rz!Input image should be a 2D array.rRzIThe dimensions of initial level set do not match the dimensions of image.Frqrr)lenshaperurrrxtyperndarrayrrbmaxrNr/rPrmeanappend)rrrrtol max_num_iterrrvextended_output float_dtyperi old_energyenergiesphivar segmentationoldphi new_energys r. chan_vesersN 5;;1<==' 4K ^[[ LC CyBJJ#))u{{": -  LL5L 1E BFF5M !E vve}u % AEW=JH 1WF7L ,1+&e"wK!#&3rs<1+J\<! %Y81*57JJ # - 3;=** )$    !tr0