Mathematical model for shape description in DCT domain

Abstract

This paper derives a mathematical relationship between the shape information of an object and their discrete cosine transform (DCT) coefficients. Here, each column of the object is put into a matrix. As the lengths of different columns in the object are different, the lengths of the columns of the matrix are reset to the maximum value among these lengths of the columns of the object and the rest elements in the columns of the matrix are set to zero. The mathematical relationship between the shape information of the object and the DCT coefficients is derived. By substituting the DCT coefficients in the derived model, the shape of the object can be obtained directly in the DCT domain. Since most of the images are coded in the DCT domain, the derived result can significantly improve the efficiency for identifying the objects.