New geometric transform based on stochastic geometry in the context of pattern recognition

Abstract

Application of stochastic geometry methods to pattern recognition is analyzed. The paper is based on Trace-transforms of original images introduced by [1] into images on the Möbius band. The ability of a Trace-transform to solve such structuralistic problems as segmentation, analysis of objects' relative position, and their number evaluation, is established. Feasibility of image nonlinear filtering through Trace-transforms is considered. Based on the new geometric transform, a new approach towards the construction of features, independent of images' motions or their linear transforms, is put forward. A prominent characteristic of the group of features under consideration is that we can represent each of them as a consecutive composition of three functionals. © Springer-Verlag 2003.