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.

Key Agreement Protocol (KAP) Based on Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Optimization of Rational Approximations by Continued Fractions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Polynomials of Pellian Type and Continued Fractions

We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex- pansion of √fk (X) is related to that of √C, where √fk (X) = ak*X^2 +bk*X + C. This continues work in [1]–[4].