A multiscale algorithm for image segmentation by variational method
SIAM Journal on Numerical Analysis
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive dichotomous image segmentation toolkit
Pattern Recognition and Image Analysis
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The Otsu method (1979) and the Mumford-Shah model (1985) for image segmentation described by image approximations by a step (piecewise constant) function are described and developed to formalize automatic object detection. Segmentation here means image preprocessing performed without tuning parameters, assumptions about image content, or training data from the user. A sequence of partitions of image pixels into sets that consist of either pixels of specific intensity ranges or pixels of connected image segments is considered a result of segmentation. The resulting partitions of image pixels need to generate a sequence of optimal approximations of an image averaged over the sets according to intensity with the lowest standard deviation of the approximation from the image. In general, the sequence of optimal approximations of an image is nonhierarchical, and the conventionally used merging of sets is insufficient to calculate it. Therefore, the merging of sets is complemented by a correction operation. The paper presents an analytical validation for correction of sets by reclassification of pixels and discusses the stability of optimal approximations during the reclassification operation of image pixels. Experimental results are demonstrated, and a comparative analysis of image approximations obtained in different algorithms is given. The prospects for improving segmentation with respect to standard deviation are analyzed.