1-Ph'hddlZddlZddlmZddlmZmZddZ ddd d Z d Z d Z dZ dZdS)N)linalg)_ncut_ncut_cyTc|s|}fd|dD}||tj|}t j|dz|j}t|D]%\}}|D]} |j | dD]} ||| <&||S)aCombine 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` c8g|]\}}}|dk||fSweight).0xydthreshs X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/skimage/graph/_graph_cut.py z!cut_threshold..5s1UUUGAq!q{f?T?T!Q?T?T?TTdatardtypelabels) copyedgesremove_edges_fromnxconnected_componentsnparangemaxr enumeratenodes) rragrin_place to_removecomps map_arrayir"nodelabels ` r cut_thresholdr+sR hhjjVUUUsyydy';';UUUI)$$$  #C ( (E  &**,,*&,???Ie$$%%5 % %D42 % %#$ %   % % V rMbP? ?)rngctj|}|s|}|D]}||||t ||||tj|dz|j }|dD]\} } | d|| d<||S)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 rrTr ncut labelr) rrandom default_rngrr"add_edge _ncut_relabelzerosr r) rr#rnum_cutsr$max_edger/r)r'nrs rcut_normalizedr:Fs~ )   $ $C hhjj 22 T4 1111#vx---)>>>I t $$111!"< !H+ V rcfdt|D}fdt|D}||}||}||fS)aRCompute resulting subgraphs from given bi-partition. Parameters ---------- cut : array A array of booleans. Elements set to `True` belong to one set. rag : RAG The Region Adjacency Graph. Returns ------- sub1, sub2 : RAG The two resulting subgraphs from the bi-partition. c*g|]\}}| |Sr r r r(r9cuts rrz$partition_by_cut..s& = = =DAqc!f =a = = =rc*g|]\}}| |Sr r r=s rrz$partition_by_cut..s& A A ADAq#a& Aa A A Ar)r!r"subgraph)r>r#nodes1nodes2sub1sub2s` rpartition_by_cutrEs4> = = =Iciikk22 = = =F A A A AIciikk22 A A AF <<  D <<  D :rc\tj}|}|}tj|t }tj||r||fStj|||dD](}||k} tj | ||} | |kr| }| })||fS)aThreshold an eigenvector evenly, to determine minimum ncut. Parameters ---------- ev : array The eigenvector to threshold. d : ndarray The diagonal matrix of the graph. w : ndarray The weight matrix of the graph. num_cuts : int The number of evenly spaced thresholds to check for. Returns ------- mask : array The array of booleans which denotes the bi-partition. mcut : float The value of the minimum ncut. rF)endpoint) rinfminr zeros_likeboolallcloselinspacer ncut_cost) evrwr7mcutmnmxmin_masktmaskcosts r get_min_ncutrXs* 6D B B }Rt,,,H {2r~[RE : : :AvtQ** $;;HD T>rct|}|j|dd}|dD] \}}|||< dS)aqAssign a unique integer to the given attribute in the RAG. This function assumes that all labels in `rag` are unique. It picks up a random label from them and assigns it to the `attr_name` attribute of all the nodes. rag : RAG The Region Adjacency Graph. attr_name : string The attribute to which a unique integer is assigned. rrTrN)rIr")r# attr_namer) new_labelr9rs r _label_allr\sd syy{{  D $)!,I t $$!!1 ) !!rc &tj|\}}|jd}|dkrU||kjdkrE|}t jt j|j|j|j|_|||z z|z}| |jd} tj |d| td|dz \} } t j | t j | } } tj| } | dd| f} t!| |||\}}||kr9t#||\}}t%||||t%||||dSt'|ddS) 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)whichv0kNr1)r DW_matricesshapennzrr reciprocalsqrtrr2reigshrIrealrargmin2rXrEr5r\)r#rr7random_generatorrrPmd2Arcvalsvectorsindex2rOcut_maskrQrCrDs rr5r5s(  S ! !DAq  A AAFrys;;;;B     M MMMMM`   F)))X!!!$C"C"C"C"C"r