Image analysis via the general theory of moments*

TLDR

The approach is contrasted with the usual method of moments and situates the general problem of two‑ and three‑dimensional pattern recognition within this framework. The study defines two‑dimensional image moments using Zernike polynomials and demonstrates how to construct many independent, algebraic combinations invariant to translation, orientation, and scale. The authors construct a coding scheme for image storage and retrieval based on invariant Zernike moment combinations. The method enables unique reconstruction of images in real or Fourier space from a finite set of moments and is illustrated with several applications.

Abstract

Two-dimensional image moments with respect to Zernike polynomials are defined, and it is shown how to construct an arbitrarily large number of independent, algebraic combinations of Zernike moments that are invariant to image translation, orientation, and size. This approach is contrasted with the usual method of moments. The general problem of two-dimensional pattern recognition and three-dimensional object recognition is discussed within this framework. A unique reconstruction of an image in either real space or Fourier space is given in terms of a finite number of moments. Examples of applications of the method are given. A coding scheme for image storage and retrieval is discussed.