Recognition of the blurred image by complex moment invariants

An important class of radiometric degradations we are faced with often in practice is image blurring. In this paper, special attention is paid to the recognition of the blurred image by complex moment invariant. Some important rules of complex moments for the blurred image are presented and proofed. Based on these rules, a useful subset of complex moment invariants is introduced, that are not affected by the blur, rotation, scale, and translation of the images. Another conclusion is that these complex moment invariants, which are not effected by image blurring, can all be expressed by a set of sub-polynomials, which are invariant to blurring. The graphs of these invariants under the effect of both blurring and image resolution are presented. The experiments have shown that these invariants can be successfully used in recognition of the blurred images.