Research And Applications Of Orthogonal Moment Invariants

In the 19th century, the German mathematician Gordan and Hilbert studied the theory of algebraic invariants. In 1962, Hu proposed his famous seven moment invariants, who firstly introduced moment invariants in pattern recognition. Since then, a large number of theories in image recognition were proposed, including aircraft identification, satellite image positioning, industrial product quality supervision, letter recognition and biometric recognition. The studies include the application of Legendre moments, Zernike moments, pseudo-Zernike moments, Tchebichef moments, Fourier-Melling moments, complex moments, etc. Most of these moments are orthogonal and contain more information and high recognition rate.Rotation, translation, scaling (RST) is the simplest transformations in image recognition. Only the method which is invariant to RST transformations may be applicable for constructing other invariants. Orthogonal moments such as Zernike moments have been successfully used in the field of image analysis. In this paper, a new approach based on Zernike moments is proposed. The method is directly derived from the orthogonal projection transform (OPT) and applicable for constructing the RST invariants. Because that closed curve can be drawn, the proposed descriptors are complete. There is a similar RST invariants based on pseudo-Zernike moments given in this paper. Both of the Zernike moment invariants and the pseudo-Zernike moment invariants are demonstrated high recognition rate and complete.Projective transformation is the basic geometric change in image analysis, but there is no moment invariant for this geometric change. In this paper, the projective invariants of co-moments were proved correct both in theory and experiments.In the past decades, moment theory in biometrics recognition has received more attention. In this paper, Tchebichef moments are introduced into the fingerprint orientation field. The results illustrate that the method is much better than gradient method and FOMFE; the proposed method also has better robustness than the Legendre method.