On discrete moments of unbounded order

Abstract

Moment-based procedures are commonly used in computer vision, image analysis, or pattern recognition. Basic shape features such as size, position, orientation, or elongation are estimated by moments of order ≤ 2. Shape invariants are defined by higher order moments. In contrast to a theory of moments in continuous mathematics, shape moments in imaging have to be estimated from digitized data. Infinitely many different shapes in Euclidean space are represented by an identical digital shape. There is an inherent loss of information, impacting moment estimation. This paper discusses accuracy limitations in moment reconstruction in dependency of order of reconstructed moments and applied resolution of digital pictures. We consider moments of arbitrary order, which is not assumed to be bounded by a constant.