Translation invariants of Zernike moments

Moment functions defined using a polar coordinate representation of the image space, such as radial moments and Zernike moments, are used in several recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield translation invariant functions, which are also widely sought after in pattern recognition applications. This paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form. Using a direct application of this framework, translation invariant functions of Zernike moments are derived algebraically from the corresponding central moments. Both derived functions are developed for non-symmetrical as well as symmetrical images. They mitigate the zero-value obtained for odd-order moments of the symmetrical images. Vision applications generally resort to image normalization to achieve translation invariance. The proposed method eliminates this requirement by providing a translation invariance property in a Zernike feature set. The performance of the derived invariant sets is experimentally confirmed using a set of binary Latin and English characters.