A generalization of three approaches to an optimal segmentation of digital image

The paper proposes an analytically justified method for clustering of multisets, called K–method, which in the cluster analysis provides to surpass the conventional K–means method. In the image segmentation domain it solves the problem of optimal image approximating with the sequential numbers of intensity gradations, which is posed in multi–threshold Otsu method, and essentially improves in the total square error the sequence of approximations of the image with connected segments that are treated in the Mumford–Shah model. While the conventional K–means method analyzes the proximity of pixels to the cluster centers, our K–method treats much stronger feature of the optimal partition, namely stability relative to reclassification of pixels from one cluster to another. All other things being equal, K–method turns out more efficient than Otsu method, since in the calculation of the series of the partitions into sequentially increasing cluster number it doesn't face the exponential increase of processing time. In comparison with Mumford–Shah model, the main advantage of K–method consists in the reduction of total square error due to the generation of the sequence of overlapping partitions by means of merge–and–correct, split–and–correct or composite technique.