Image analysis by modified krawtchouk moments

Abstract

In the paper, a set of modified Krawtchouk moments with high accuracy and computational speed is introduced. Three computational aspects of Krawtchouk moments, which are weighted and normalized Krawtchouk polynomials, symmetry and recurrence relation, are discussed respectively. Firstly, by normalizing the Krawtchouk polynomials with the weight functions and norms, the values of the polynomials are limited to a smaller range than those of the classical polynomials. Secondly, three symmetrical properties are used to simplify the computational complexities of the high-order moments by reducing the modified polynomials by a factor of eight and lower the highest order of the calculated polynomials from N to N/2∈-∈1. Thirdly, the classical recursive relations are modified to calculate the normalized polynomials when the order N goes larger. Finally, the paper demonstrates the effectiveness of the proposed moments by using the method of image reconstruction. © 2009 Springer Berlin Heidelberg.