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A framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross-weighted moments with fractional weights is presented. The fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise. Moreover, it makes it possible to arrive at low order (zero order) affine invariants that are more robust than those derived from higher order regular moments. The affine transformation parameters are recovered from the zero and the first order cross-weighted moments without requiring any feature point correspondence information. The equations used to find the affine transformation parameters are linear algebraic. The sensitivity of the cross-weighted moment invariants to noise, missing data, and perspective effects is shown on real images.
Yang et al. (Fri,) studied this question.