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2003 year, number 4

On a system of invariants of energetic spectrum of gradient images of an arbitrary order as applied to texture analysis

I.V.Razin and V.S.Emdin
St. Petersburg
Pages: 78–90


An expression is given for a normalized moment (determined in an arbitrary direction) of an energetic spectrum of a gradient image of an arbitrary order. It is shown that the matrix form of this expression makes it possible to obtain analytical expressions for the main moments of the spectrum and the main values for the mean square frequencies of the gradient image and the corresponding directions. It is demonstrated that the estimates of the characteristics can be obtained in the plane of space variables without performing the direct Fourier transform, which is important in solving the problems of image express analysis. Experimental results on a limited amount of test images are presented.