Precision of Geometric Moments in Picture analysis

Abstract

Moments play an important role in picture analysis, pattern recognition, or classification. The presentation of Euclidean sets by digital pictures causes an inherent loss of information. There are infinitely many different preimages with identical corre- sponding digital pictures. The problem we discuss here is how efficiently real geometric moments of planar convex shapes can be reconstructed from their digital pictures in dependency on the applied grid resolution and order of considered moments.