Image Analysis by Modified Krawtchouk Moments

Authors:
Luo Zhu;Jiaping Liao;Xiaoqin Tong;Li Luo;Bo Fu;Guojun Zhang
Affiliations:
School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China 430068;School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China 430068;School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China 430068;School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China 430068;School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China 430068;School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China 430074
Venue:
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Year:
2009

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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.