Image Quotient Set Transforms in Segmentation Problems

Image content interpretation is much dependent on segmentations efficiency. Requirements for the image recognition applications lead to a nessesity to create models of new type, which will provide some adaptation between law-level image processing, when images are segmented into disjoint regions and features are extracted from each region, and high-level analysis, using obtained set of all features for making decisions. Such analysis requires some a priori information, measurable region properties, heuristics, and plausibility of computational inference. Sometimes to produce reliable true conclusion simultaneous processing of several partitions is desired. In this paper a set of operations with obtained image segmentation and a nested partitions metric are introduced.

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12