Resuming Shapes with Applications

Many image processing tasks need some kind of average of different shapes. Frequently, different shapes obtained from several images have to be summarized. If these shapes can be considered as different realizations of a given random compact set, then the natural summaries are the different mean sets proposed in the literature. In this paper, new mean sets are defined by using the basic transformations of Mathematical Morphology (dilation, erosion, opening and closing). These new definitions can be considered, under some additional assumptions, as particular cases of the distance average of Baddeley and Molchanov.The use of the former and new mean sets as summary descriptors of shapes is illustrated with two applications: the analysis of human corneal endothelium images and the segmentation of the fovea in a fundus image. The variation of the random compact sets is described by means of confidence sets for the mean and by using set intervals (a generalization of confidence intervals for random sets). Finally, a third application is proposed: a procedure for denoising a single image by using mean sets.

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