ON DIGITAL APPROXIMATION OF MOMENT INVARIANTS.

Abstract

Moment invariants have been used as feature descriptors in a variety of object recognition applications. Moments generated by assuming a continuous image function and using a double-integral formulation are invariant to variations in translation, rotation, and size. However, due to the digital nature of the imagery, the moments computed digitally are not truly invariant. In most applications, the continuous image is approximated by a digital image, and the integrations are approximated by summations. In this study, (1) the undersampling and digitizing effects of a digital image and (2) the quantization effect of intensity levels on moment invariants are presented. Simulated images were used to demonstrate the magnitude of the problems due to the approximations. A better formulation of the moment invariants by numerical integration approaches is also presented.