Visual pattern recognition by moment invariants

TLDR

The paper develops a theory of two‑dimensional moment invariants for planar geometric figures. The authors derive complete systems of moment invariants under translation, similitude, orthogonal, and general linear transformations, relate them to algebraic invariants, and present theoretical and practical models—including a simulation program—to apply them for visual pattern recognition. The approach enables recognition of geometric patterns and alphabetical characters invariant to position, size, and orientation, and can be extended to parallel projection invariance.

Abstract

In this paper a theory of two-dimensional moment invariants for planar geometric figures is presented. A fundamental theorem is established to relate such moment invariants to the well-known algebraic invariants. Complete systems of moment invariants under translation, similitude and orthogonal transformations are derived. Some moment invariants under general two-dimensional linear transformations are also included. Both theoretical formulation and practical models of visual pattern recognition based upon these moment invariants are discussed. A simple simulation program together with its performance are also presented. It is shown that recognition of geometrical patterns and alphabetical characters independently of position, size and orientation can be accomplished. It is also indicated that generalization is possible to include invariance with parallel projection.