On geometric and orthogonal moments

Moments are widely used in pattern recognition, image processing, computer vision and multiresolution analysis. To clarify and to guide the use of dif ferent types of moments, we present in this paper a study on the different moments and compare their behavior. After an introduction to geometric, Leg endre, Hermite and Gaussian-Hermite moments and their calculation, we analy ze at first their behavior in spatial domain. Our analysis shows orthogonal moment base functions of different orders having different number of zero- crossings and very different shapes, therefore they can better separate ima ge features based on different modes, which is very interesting for pattern analysis and shape classification. Moreover, Gaussian-Hermite moment base functions are much more smoothed, they are thus less sensitive to noise and avoid the artifacts introduced by window function discontinuity. We then a nalyze the spectral behavior of moments in frequency domain. Theoretical an d numerical analyses show that orthogonal Legendre and Gaussian-Hermite mom ents of different orders separate different frequency bands more effectivel y It is also shown that Gaussian-Hermite moments present an approach to con struct orthogonal features from the results of wavelet analysis. The orthog onality equivalence theorem is also presented. Our analysis is confirmed by numerical results, which are then reported.