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Image segmentation
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== Region-growing methods == [[Region-growing]] methods rely mainly on the assumption that the neighboring pixels within one region have similar values. The common procedure is to compare one pixel with its neighbors. If a similarity criterion is satisfied, the pixel can be set to belong to the same cluster as one or more of its neighbors. The selection of the similarity criterion is significant and the results are influenced by noise in all instances. The method of [[Statistical region merging|Statistical Region Merging]]<ref name="SRM">R. Nock and F. Nielsen, [http://www.academia.edu/download/3433683/Statistical_Region_Merging.pdf Statistical Region Merging]{{dead link|date=July 2022|bot=medic}}{{cbignore|bot=medic}}, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 26, No 11, pp 1452β1458, 2004.</ref> (SRM) starts by building the graph of pixels using 4-connectedness with edges weighted by the absolute value of the intensity difference. Initially each pixel forms a single pixel region. SRM then sorts those edges in a priority queue and decides whether or not to merge the current regions belonging to the edge pixels using a statistical predicate. One [[region-growing]] method is the seeded region growing method. This method takes a set of seeds as input along with the image. The seeds mark each of the objects to be segmented. The regions are iteratively grown by comparison of all unallocated neighboring pixels to the regions. The difference between a pixel's intensity value and the region's mean, <math>\delta</math>, is used as a [[Similarity measure|measure of similarity]]. The pixel with the smallest difference measured in this way is assigned to the respective region. This process continues until all pixels are assigned to a region. Because seeded region growing requires seeds as additional input, the segmentation results are dependent on the choice of seeds, and noise in the image can cause the seeds to be poorly placed. Another [[region-growing]] method is the unseeded region growing method. It is a modified algorithm that does not require explicit seeds. It starts with a single region <math>A_1</math>βthe pixel chosen here does not markedly influence the final segmentation. At each iteration it considers the neighboring pixels in the same way as seeded region growing. It differs from seeded region growing in that if the minimum <math>\delta</math> is less than a predefined threshold <math>T</math> then it is added to the respective region <math>A_j</math>. If not, then the pixel is considered different from all current regions <math>A_i</math> and a new region <math>A_{n+1}</math> is created with this pixel. One variant of this technique, proposed by [[Haralick]] and Shapiro (1985),<ref name="computervision" /> is based on pixel [[Brightness|intensities]]. The [[Arithmetic mean|mean]] and [[Statistical dispersion|scatter]] of the region and the intensity of the candidate pixel are used to compute a test statistic. If the test statistic is sufficiently small, the pixel is added to the region, and the region's mean and scatter are recomputed. Otherwise, the pixel is rejected, and is used to form a new region. A special region-growing method is called <math>\lambda</math>-connected segmentation (see also [[lambda-connectedness]]). It is based on pixel [[Brightness|intensities]] and neighborhood-linking paths. A degree of connectivity (connectedness) is calculated based on a path that is formed by pixels. For a certain value of <math>\lambda</math>, two pixels are called <math>\lambda</math>-connected if there is a path linking those two pixels and the connectedness of this path is at least <math>\lambda</math>. <math>\lambda</math>-connectedness is an equivalence relation.<ref name="lambda-connectedness">L. Chen, H. D. Cheng, and J. Zhang, [https://www.sciencedirect.com/science/article/pii/1069011594900094 Fuzzy subfiber and its application to seismic lithology classification], Information Sciences: Applications, Vol 1, No 2, pp 77β95, 1994.</ref> [[Split and merge segmentation|Split-and-merge segmentation]] is based on a [[quadtree]] partition of an image. It is sometimes called quadtree segmentation. This method starts at the root of the tree that represents the whole image. If it is found non-uniform (not homogeneous), then it is split into four child squares (the splitting process), and so on. If, in contrast, four child squares are homogeneous, they are merged as several connected components (the merging process). The node in the tree is a segmented node. This process continues recursively until no further splits or merges are possible.<ref name="split-and-merge1">S.L. Horowitz and T. Pavlidis, Picture Segmentation by a Directed Split and Merge Procedure, Proc. ICPR, 1974, Denmark, pp. 424β433.</ref><ref name="split-and-merge2">S.L. Horowitz and T. Pavlidis, Picture Segmentation by a Tree Traversal Algorithm, Journal of the ACM, 23 (1976), pp. 368β388.</ref> When a special data structure is involved in the implementation of the algorithm of the method, its time complexity can reach <math>O(n\log n)</math>, an optimal algorithm of the method.<ref name="split-and-merge3">L. Chen, [http://www.spclab.com/research/lambda/lambdaConn91.pdf The lambda-connected segmentation and the optimal algorithm for split-and-merge segmentation] {{Webarchive|url=https://web.archive.org/web/20160310054934/http://www.spclab.com/research/lambda/lambdaConn91.pdf |date=10 March 2016 }}, Chinese J. Computers, 14(1991), pp 321β331</ref>
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