9i'lSSKrSSKrSSKJr SSKJrJr S Sjr S SS.Sjjr Sr S r S r S rg)N)linalg)_ncut_ncut_cycU(dUR5nURSS9VVVs/sHupEofSU:dMXE4PM nnnnURU5 [R"U5n[ R "UR5S-URS9n [U5H+upU H n URU SHn XU 'M M" M- X$s snnnf)a-Combine regions separated by weight less than threshold. Given an image's labels and its RAG, output new labels by combining regions whose nodes are separated by a weight less than the given threshold. Parameters ---------- labels : ndarray The array of labels. rag : RAG The region adjacency graph. thresh : float The threshold. Regions connected by edges with smaller weights are combined. in_place : bool If set, modifies `rag` in place. The function will remove the edges with weights less that `thresh`. If set to `False` the function makes a copy of `rag` before proceeding. Returns ------- out : ndarray The new labelled array. Examples -------- >>> from skimage import data, segmentation, graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels) >>> new_labels = graph.cut_threshold(labels, rag, 10) References ---------- .. [1] Alain Tremeau and Philippe Colantoni "Regions Adjacency Graph Applied To Color Image Segmentation" :DOI:`10.1109/83.841950` Tdataweightrdtypelabels) copyedgesremove_edges_fromnxconnected_componentsnparangemaxr enumeratenodes)r ragthreshin_placexyd to_removecomps map_arrayirnodelabels X/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/graph/_graph_cut.py cut_thresholdr%sR hhj(+yydy';U';GA!{f?T!';IU)$  # #C (E  &**,*&,,?Ie$D42#$% 3%  Vs CC)rngc[RRU5nU(dUR5nUR 5HnUR XwUS9 M [ XX65 [R"UR5S-URS9nUR SS9HupU SXS'M X$)aPerform Normalized Graph cut on the Region Adjacency Graph. Given an image's labels and its similarity RAG, recursively perform a 2-way normalized cut on it. All nodes belonging to a subgraph that cannot be cut further are assigned a unique label in the output. Parameters ---------- labels : ndarray The array of labels. rag : RAG The region adjacency graph. thresh : float The threshold. A subgraph won't be further subdivided if the value of the N-cut exceeds `thresh`. num_cuts : int The number or N-cuts to perform before determining the optimal one. in_place : bool If set, modifies `rag` in place. For each node `n` the function will set a new attribute ``rag.nodes[n]['ncut label']``. max_edge : float, optional The maximum possible value of an edge in the RAG. This corresponds to an edge between identical regions. This is used to put self edges in the RAG. rng : {`numpy.random.Generator`, int}, optional Pseudo-random number generator. By default, a PCG64 generator is used (see :func:`numpy.random.default_rng`). If `rng` is an int, it is used to seed the generator. The `rng` is used to determine the starting point of `scipy.sparse.linalg.eigsh`. Returns ------- out : ndarray The new labeled array. Examples -------- >>> from skimage import data, segmentation, graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels, mode='similarity') >>> new_labels = graph.cut_normalized(labels, rag) References ---------- .. [1] Shi, J.; Malik, J., "Normalized cuts and image segmentation", Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 22, no. 8, pp. 888-905, August 2000. )r rr Tr ncut labelr ) rrandom default_rngrradd_edge _ncut_relabelzerosrr ) r rrnum_cutsrmax_edger&r"r nrs r$cut_normalizedr1Fs~ ))   $C hhj  T 1#x-)>I t $!"< H+%  cD[UR55VVs/sHup#X(dMUPM nnn[UR55VVs/sHup#X(aMUPM nnnURU5nURU5nXg4$s snnfs snnf)a"Compute resulting subgraphs from given bi-partition. Parameters ---------- cut : array A array of booleans. Elements set to `True` belong to one set. rag : RAG The Region Adjacency Graph. Returns ------- sub1, sub2 : RAG The two resulting subgraphs from the bi-partition. )rrsubgraph)cutrr!r0nodes1nodes2sub1sub2s r$partition_by_cutr:s~4&ciik2 =2DAcfa2F =%ciik2 A2DA#&a2F A << D << D : > AsBBB(Bc\[RnUR5nUR5n[R"U[ S9n[R "XV5(aXt4$[R"XVUSS9H)nX:n [R"XU5n X:dM%U nU nM+ Xt4$)aThreshold an eigenvector evenly, to determine minimum ncut. Parameters ---------- ev : array The eigenvector to threshold. d : ndarray The diagonal matrix of the graph. w : ndarray The weight matrix of the graph. num_cuts : int The number of evenly spaced thresholds to check for. Returns ------- mask : array The array of booleans which denotes the bi-partition. mcut : float The value of the minimum ncut. r F)endpoint) rinfminr zeros_likeboolallcloselinspacer ncut_cost) evrwr.mcutmnmxmin_masktmaskcosts r$ get_min_ncutrMs* 66D B B }}Rt,H {{2~[[E :vt* ;HD ; >r2c[UR55nURUSSnURSS9H upEX5U'M g)aQAssign a unique integer to the given attribute in the RAG. This function assumes that all labels in `rag` are unique. It picks up a random label from them and assigns it to the `attr_name` attribute of all the nodes. rag : RAG The Region Adjacency Graph. attr_name : string The attribute to which a unique integer is assigned. r rTrN)r>r)r attr_namer" new_labelr0rs r$ _label_allrQsI syy{ D $)!,I t $ ) %r2c [R"U5upEURSnUS:GaBXE:gRS:Ga/UR 5n[ R "[ R"URURS9URS9UlXtU- -U-nURURS5n [R"USU [SUS- 5S9up[ R"U 5[ R"U 5p[R"U 5n U SS2U 4n [!XXR5upX:a)[#X5unn[%UXU5 [%UXU5 g['US5 g) aPerform Normalized Graph cut on the Region Adjacency Graph. Recursively partition the graph into 2, until further subdivision yields a cut greater than `thresh` or such a cut cannot be computed. For such a subgraph, indices to labels of all its nodes map to a single unique value. Parameters ---------- rag : RAG The region adjacency graph. thresh : float The threshold. A subgraph won't be further subdivided if the value of the N-cut exceeds `thresh`. num_cuts : int The number or N-cuts to perform before determining the optimal one. random_generator : `numpy.random.Generator` Provides initial values for eigenvalue solver. r)outSMd)whichv0kNr()r DW_matricesshapennzrr reciprocalsqrtr r)reigshr>realrargmin2rMr:r,rQ)rrr.random_generatorrrEmd2ArXvalsvectorsindex2rDcut_maskrFr8r9s r$r,r,s=(   S !DA  A AAF<rpsN;B     M M` F)X!$C"r2