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2009 year, number 6

Model of a Hierarchical System of Invariant Characteristics of Image Description

I. V. Razin
Keywords: gradient image, energetic spectrum, normalized moment, covariational matrix, eigenvector, hodograph of moment, canonical equation, invariant description characteristics
Pages: 3-14


The hodograph of the normalized moment of the energetic spectrum of a gradient image is analyzed. It is shown that transformation of the matrix form of the hodograph equation to diagonal form gives analytical expressions for the invariant characteristics of the image description-the principal spectral moments of gradient images. In this case, rotation of the coordinate system until its axes coincide with the eigenvector directions reduces the hodograph equation to the canonical form. An analysis of the initial equations, in rotation, yields invariant characteristics of the singular points of the hodograph. Subsets of invariant description characteristics for gradient images of different orders constitute a hierarchical system of invariant description characteristics of the initial image.