MORPHOLOGICAL SHAPE AND IMAGE COMPARISON BASED ON SIMPLICITY THEORY AND POINT COVERINGS MODEL
Yu. V. Vizilter, S. A. Brianskiy · Vestnik komp iuternykh i informatsionnykh tekhnologii · 2024
This article is devoted to development of new models and techniques for morphological image analysis and the simplicity theory. A new method for image shape comparison and description via the point coverings model is proposed. It is demonstrated that within the framework of point covering models the concept of projection to mosaic shape and even the concept of mosaic shape are not required for calculation of the morphological correlation coefficients for any morphological models described by the patterns of simplicity distribution on the image frame. Based on these non-strict similarity models, the projective morphology for non-strict shapes is proposed. In the framework of such morpology all shape description tools from original Pyt’ev morphology can be defined: mosaic frame coveraging (analogous to mosaic frame splitting), relational model based on non-strict similarity relations, class of images of the same non-strict shape, morphological operator as a projector to the class of non-strict shapes. The difference between the proposed and original Pyt’ev’s versions of morphological analysis is that the image class is no longer a linear subspace in the image space.