On a Generalized Version of the Standard Image Algebra

I.B. Gurevich, I.V. Koryabkina, and Y.I. Zhuravlev (Russia)


Image mining, descriptive image algebras.


The development of an efficient and flexible system for image processing, analysis, and recognition requires, in particular, an adequate language for image description. The principal aim of such a language is an unified representation of objects as the structures convenient for applying algebraic, geometrical, and topological methods. Construction of the language is one of important aspects of the latest trend in image mining - algebraization of image processing, analysis, recognition and understanding. In the framework of Descriptive Theory of Image Analysis is proposed a technique for top-down design of algorithms for image analysis on the base of Zhuravlev’s algebras of algorithms, Grenander’s Pattern Theory and Ritter’s Standard Image Algebras. It allows unified representation both of images and of high-level algorithms of image analysis. Basic blocks for the algebra of algorithms are selected and a method for algebraic representation of images compatible with the algebra of algorithms and the requirements to initial data is developed. The originality of the proposed approach is the combination of the methods for image fusion and algorithm fusion, each of them being able to use the results of the other.

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