Moment invariants and quantization effects

This paper considers the effect of spatial quantization on several moment invariants. Of particular interest are the affine moment invariants, which have emerged in recent years as a useful tool for image reconstruction, image registration, and recognition of deformed objects. Traditional analysis assumes moments and moment invariants for images that are defined in the continuous domain. In practice, however, the digitization process introduces errors that violate the invariance assumption. This paper presents an analysis of quantization-induced error on (two-dimensional) Hu moment invariants and affine moment invariants, and on invariants derived from (one-dimensional) contour moments. Error bounds are given in several cases.