Image analysis by modified Legendre moments

摘要

In the paper, a new set of orthogonal moments based on the modified Legendre polynomials is introduced. Three properties of the modified Legendre polynomials, which are orthogonality, orthogonal invariance and the characteristic that an interval on the center of [-1,1] covers more zeros than do that on the edge of [-1,1], are discussed detailedly. The orthogonality of the proposed moments ensures minimal information redundancy in a moment set. The orthogonal invariance of the proposed polynomials makes the proposed moments have the property of translation invariance. And, the third property ensures that the modified Legendre moments have superior feature representation capabilities over Legendre moments in analyzing small images. For small images, the description by the modified Legendre moments is better than that by the Legendre moments and the Chebyshev moments in terms of image-reconstruction errors. Theoretical and experimental measures of performance are carried out to investigate the image-representation capabilities of the proposed moments for images and noisy-images. The computational aspects of the moments using recurrence, integral, symmetry and translation invariance are also discussed. Experimental results are shown.