9iTSrSSKrSSKJrJr SSKJr SSK J r SSK J r SSK Jr \RR rS r\\Rl\R"5rSS KJr S rSS KJr SSKJrJr SrSrSrSrSr Sr!Sr"\RF"S S9SSSS.Sjj5r$g!\a SrNZf=f!\a S rN_f=f)a Random walker segmentation algorithm from *Random walks for image segmentation*, Leo Grady, IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1768-83. Installing pyamg and using the 'cg_mg' mode of random_walker improves significantly the performance. N)sparsendimage)utils)warn)SCIPY_CG_TOL_PARAM_NAME)umfpackc<[U5 g![a gf=f)N)old_delAttributeError)selfs o/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/segmentation/random_walker_segmentation.pynew_delrs   DM   s  )ruge_stuben_solverTF) img_as_float)cgspsolvec[R"X-U-5RXU45n[R"USSS24R 5USSS24R 545n[R"USS2SS24R 5USS2SS24R 545n[R"USSR 5USSR 545n[R "XEU45nU$)aReturns a list of edges for a 3D image. Parameters ---------- n_x : integer The size of the grid in the x direction. n_y : integer The size of the grid in the y direction n_z : integer The size of the grid in the z direction Returns ------- edges : (2, N) ndarray with the total number of edges:: N = n_x * n_y * (nz - 1) + n_x * (n_y - 1) * nz + (n_x - 1) * n_y * nz Graph edges with each column describing a node-id pair. .N)nparangereshapevstackravelhstack)n_xn_yn_zvertices edges_deep edges_right edges_downedgess r_make_graph_edges_3dr%4s.yyS)113S/BHHS#2#X.446ab8I8O8O8QRSJ))Xa"f-335x127L7L7NOPKHSbM//18AB<3E3E3GHIJ IIz ; A%EV 2.446D#      DJJrN+ NN('zz"~)OBGGDg.R8>>@7;N'     ,5BO,L  2// ff\-.G NG 8O= sE/EE 41E cURSSupVn[XVU5n[XUSUS9n UGb[R"USSS24R 5USS2SS24R 5USSR 5/5n [R"USSS24R 5USS2SS24R 5USSR 5/5n [R "X5n USS2U 4Xp[R"USS9upURUR5nXV-U-nUR 5nUSSS2R 5n[R"X45n[R"UUU44X4S 9nUR[R "URS S 95*5 U$) Ng|=)r4r5r6.rrTreturn_inverser,rr() r,r%r<rrr logical_anduniquerr csr_arraysetdiagsum)r2r3maskr4r6l_xl_yl_zr$r;mask0mask1ind_mask_inv_idxpixel_nb i_indices j_indiceslaps r_build_laplacianrTysJJrNMCc 3 /E! DgLG  #ss(^ ! ! #T!SbS&\%7%7%949??;L M  #qr'] "DABK$5$5$7ab9I J >>%/q({+W->wYYuT:  ,y3H Idd !!#I 99g' (D   D9i"89(AU VCKK#''q'/**+ Jr&c UcUR5nOX$n[R"UR5nUS:nXx)n Xxn [ XXEUS9n XSS24n U SS2U 4n U SS2U 4*n X(n[ R "[R"[SUS-5Vs/sH%n[R"X:H5RPM' sn55nX-nU U4$s snf)zx Build the matrix A and rhs B of the linear system to solve. A and B are two block of the laplacian of the image graph. Nr)rGr4r6r) rrrsizerTr csc_arrayrr. atleast_2dT)r2r3labelsnlabelsrGr4r6indices seeds_maskunlabeled_indices seeds_indices lap_sparserowsBseedslabrhss r_build_linear_systemrfs  |ii $G!J ,'M! D,J * +Da**+J a A  E!! E!Wq[> NN311(F G  66(% & & =  4tT1 1}}T"|Q/H ]]7??6<<88C DFa<>*003G**X.1O D FFr&)multichannel_outputMbP?)prob_tol channel_axisc US;a[US35eUR[R:XaUR [R SS9nUc[R "S5nO_[U5UR:Xa;[U5S:Xa[RUS4n[R"U5nO [S 5eU SLn U (dsURS ;a [S 5eURUR:wa [S 5e[R"[U55S [R4nO{URS;a [S5eURSSUR:wa [S 5e[U5nURS:XaUSS2SS2[RSS24nURn URn U(a[R"U5n[!U5uppnUcbU(aY[R""[R$"U5Vs/sH$nUS:dM [R"UU:H5PM& snSS9$U$['XXXU 5unn[)UUXC5nUR+5U*:dUR-5SU-:a [/S5 UX'UR1U 5nUS:HnSX'U(aJ[R2"U 4U -5n[5[7UU5SS9HununnUUU'SUUU:H'M U$[R8"USS9S-nUR U 5nUUU'U$s snf)aRandom walker algorithm for segmentation from markers. Random walker algorithm is implemented for gray-level or multichannel images. Parameters ---------- data : (M, N[, P][, C]) ndarray Image to be segmented in phases. Gray-level `data` can be two- or three-dimensional; multichannel data can be three- or four- dimensional with `channel_axis` specifying the dimension containing channels. Data spacing is assumed isotropic unless the `spacing` keyword argument is used. labels : (M, N[, P]) array of ints Array of seed markers labeled with different positive integers for different phases. Zero-labeled pixels are unlabeled pixels. Negative labels correspond to inactive pixels that are not taken into account (they are removed from the graph). If labels are not consecutive integers, the labels array will be transformed so that labels are consecutive. In the multichannel case, `labels` should have the same shape as a single channel of `data`, i.e. without the final dimension denoting channels. beta : float, optional Penalization coefficient for the random walker motion (the greater `beta`, the more difficult the diffusion). mode : string, available options {'cg', 'cg_j', 'cg_mg', 'bf'} Mode for solving the linear system in the random walker algorithm. - 'bf' (brute force): an LU factorization of the Laplacian is computed. This is fast for small images (<1024x1024), but very slow and memory-intensive for large images (e.g., 3-D volumes). - 'cg' (conjugate gradient): the linear system is solved iteratively using the Conjugate Gradient method from scipy.sparse.linalg. This is less memory-consuming than the brute force method for large images, but it is quite slow. - 'cg_j' (conjugate gradient with Jacobi preconditionner): the Jacobi preconditionner is applied during the Conjugate gradient method iterations. This may accelerate the convergence of the 'cg' method. - 'cg_mg' (conjugate gradient with multigrid preconditioner): a preconditioner is computed using a multigrid solver, then the solution is computed with the Conjugate Gradient method. This mode requires that the pyamg module is installed. tol : float, optional Tolerance to achieve when solving the linear system using the conjugate gradient based modes ('cg', 'cg_j' and 'cg_mg'). copy : bool, optional If copy is False, the `labels` array will be overwritten with the result of the segmentation. Use copy=False if you want to save on memory. return_full_prob : bool, optional If True, the probability that a pixel belongs to each of the labels will be returned, instead of only the most likely label. spacing : iterable of floats, optional Spacing between voxels in each spatial dimension. If `None`, then the spacing between pixels/voxels in each dimension is assumed 1. prob_tol : float, optional Tolerance on the resulting probability to be in the interval [0, 1]. If the tolerance is not satisfied, a warning is displayed. channel_axis : int or None, optional If None, the image is assumed to be a grayscale (single channel) image. Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- output : ndarray * If `return_full_prob` is False, array of ints of same shape and data type as `labels`, in which each pixel has been labeled according to the marker that reached the pixel first by anisotropic diffusion. * If `return_full_prob` is True, array of floats of shape `(nlabels, labels.shape)`. `output[label_nb, i, j]` is the probability that label `label_nb` reaches the pixel `(i, j)` first. See Also -------- skimage.segmentation.watershed A segmentation algorithm based on mathematical morphology and "flooding" of regions from markers. Notes ----- Multichannel inputs are scaled with all channel data combined. Ensure all channels are separately normalized prior to running this algorithm. The `spacing` argument is specifically for anisotropic datasets, where data points are spaced differently in one or more spatial dimensions. Anisotropic data is commonly encountered in medical imaging. The algorithm was first proposed in [1]_. The algorithm solves the diffusion equation at infinite times for sources placed on markers of each phase in turn. A pixel is labeled with the phase that has the greatest probability to diffuse first to the pixel. The diffusion equation is solved by minimizing x.T L x for each phase, where L is the Laplacian of the weighted graph of the image, and x is the probability that a marker of the given phase arrives first at a pixel by diffusion (x=1 on markers of the phase, x=0 on the other markers, and the other coefficients are looked for). Each pixel is attributed the label for which it has a maximal value of x. The Laplacian L of the image is defined as: - L_ii = d_i, the number of neighbors of pixel i (the degree of i) - L_ij = -w_ij if i and j are adjacent pixels The weight w_ij is a decreasing function of the norm of the local gradient. This ensures that diffusion is easier between pixels of similar values. When the Laplacian is decomposed into blocks of marked and unmarked pixels:: L = M B.T B A with first indices corresponding to marked pixels, and then to unmarked pixels, minimizing x.T L x for one phase amount to solving:: A x = - B x_m where x_m = 1 on markers of the given phase, and 0 on other markers. This linear system is solved in the algorithm using a direct method for small images, and an iterative method for larger images. References ---------- .. [1] Leo Grady, Random walks for image segmentation, IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1768-83. :DOI:`10.1109/TPAMI.2006.233`. Examples -------- >>> rng = np.random.default_rng() >>> a = np.zeros((10, 10)) + 0.2 * rng.random((10, 10)) >>> a[5:8, 5:8] += 1 >>> b = np.zeros_like(a, dtype=np.int32) >>> b[3, 3] = 1 # Marker for first phase >>> b[6, 6] = 2 # Marker for second phase >>> random_walker(a, b) # doctest: +SKIP array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int32) )rirrlrhNzK is not a valid mode. Valid modes are 'cg_mg', 'cg', 'cg_j', 'bf', and Nonesafe)castingNr>rrmz`Input argument `spacing` incorrect, should be an iterable with one number per spatial dimension.)rr>z=For non-multichannel input, data must be of dimension 2 or 3.z$Incompatible data and labels shapes..)r>z9For multichannel input, data must have 3 or 4 dimensions.rrr(rz{The probability range is outside [0, 1] given the tolerance `prob_tol`. Consider decreasing `beta` and/or decreasing `tol`.F)start)rdtyperfloat16rfloat32oneslenndimr_rr,rrnewaxisrrr+rCrfrminrrrzeros enumeratezipargmax)r2rZr4rrrreturn_full_probr3rrr6 labels_shape labels_dtyper[rGrrrdr`rbrout label_probprobs r random_walkerr<s,X 66f+ ,   zzRZZ{{2::v{6''!* W $ w<1 eeGSL)G**W% >   t+L  99F "R  :: %CD D}}\$/0bjjA 99F "N  ::cr?fll *CD DD! 99>1bjj!+,D<>9;69JV9J#cTUg-v}-9JV  ) vLMJ ZC6Auuw(aeegH 4   #2F ^^L )F Q;D %DhhzL01'0S!A'F #C#*d#Jt ()Jv} %(G J IIaa 1 $mmL)D JQWs 9 M M )rhrTFN)%__doc__numpyrscipyrrr_sharedr _shared.utilsr_shared.compatr#scipy.sparse.linalg.dsolve.linsolver rx__del__r r ImportErrorpyamgrrvutilrscipy.sparse.linalgrrr%r<rTrfrr{rchannel_as_last_axisrr&rrs( 4;$$,,G &-G"++-N(J +>#L@@1 h  <G~6   TT7TqNJs$AB3$C3B>=B>C  C