Pseudo-Zernike is a kind of region-based shape descriptor

contour-based shape descriptors

such as curvature descriptors

Fourier descriptors

signature or chain code-based descriptors

are not appropriate for describing shapes consisting of several disjoint regions

since they are often based on a single contour. There is no information redundancy because the bases of pseudo-Zernike moments are orthogonal. The magnitude of pseudo-Zernike moments has rotational invariant property. An image can be better described by a small set of its pseudo-Zernike moments than any other types of moments such as geometric moments

Legendre moments

rotational moments

and complex moments in terms of mean-square error. A relatively small set of pseudo-Zernike moments can characterize the global shape of a pattern effectively. Lower order moments represent the global shape of a pattern and higher order moments represent the detail. Pseudo-Zernike moments do not possess scale invariance. In this paper

we analyze the invariance of pseudo-Zernike moments and present an improved pseudo-Zernike moments that not only have rotation invariance

but also have scale invariance

and the same time

we give part of analysis result. The experimental results show that the improved Zernike moments have better invariant properties than unimproved Zernike moment using as region-based shape descriptor.