On the choice of consistent canonical form during moment normalization

The key issue in normalization with respect to geometric transformation is how to obtain a consistent canonical form which remains unchanged for different geometric transformation related images. Due to ambiguities inherent in the specified normalization methods, more than one canonical form may occur during the normalization procedure. This causes difficulties in obtaining the expected invariant features or the transformation parameters through normalization. This paper aims to provide general schemes to analyze the ambiguity characteristics and to derive the ambiguity matrices through which ambiguities can be eliminated. Three kinds of ambiguities caused by the multi-roots of high-order polynomials, the symmetrical normalization constraints, and the reflection are addressed and solutions are provided to obtain a consistent canonical form for each kind of ambiguities.