伪Zernike矩不变性分析及其改进研究

Improvement and Invariance Analysis of Pseudo-Zernike Moments

伪 Zernike矩是基于图象整个区域的形状描述算子 ,而基于轮廓的形状描述子 ,例如曲率描述子、傅立叶描述子和链码描述子等是不能正确描述由几个不连接区域组成的形状的 ,因为这些算子只能描述单个的轮廓形状 .同时 ,由于伪 Zernike矩的基是正交径向多项式 ,和 Hu矩相比 ,除了具有旋转不变性、高阶矩和低阶矩能表达不同信息等特征外 ,还具有冗余性小、可以任意构造高阶矩等特点 ,另外 ,伪 Zernike矩还可以用于目标重构 .目前 ,伪 Zernike矩没有得到广泛的应用 ,其中的一个主要原因是 ,它不具备真正意义上的比例不变性 .为了能使伪Zernike矩得到更广泛的应用 ,在详细分析伪 Zernike矩不变性的基础上 ,提出了伪 Zernike矩的改进方法 ,使改进后的伪 Zernike矩在保持旋转不变性的同时 ,还具有真正意义上的比例不变性 ,同时给出了部分的实验分析结果 .实验结果证明 ,该改进后的伪 Zernike矩较改进前的伪 Zernike矩 ,具有更好的旋转和比例不变性 .

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.