基于Charlier矩的图像分析

Image Analysis by Charlier Moments

摘要: 针对离散正交矩的平移和尺度不变量只能通过图像归一化或者借助几何矩不变量的线性组合间接获取，会带来较大的表示误差，本文基于离散Charlier多项式，提出了一种新的离散正交矩——Charlier矩，并给出了Charlier矩平移与尺度不变量的直接计算方法。实验表明，由Charlier矩直接计算的平移和尺度不变量与现有方法相比，具有较高的表示精度与分类准确率，而且对图像噪声有较强的稳定性，可以应用于图像不变分析与目标识别等应用领域。

Abstract: The existing methods for extracting the translation and scale invariants from the discrete orthogonal moments are via a linear combination of the corresponding invariants of geometric moments or image normalization, which led to calculational errors. In this paper, a novel kind of discrete orthogonal moments named as Charlier moment is proposed based on the discrete Charlier polynomials, and then an approach to directly derive the translation and scale invariants from Charlier moments is also presented. Experimental results show the high classification and representation accuracy of these invariants as a result of direct calculation instead of the image normalization or a linear combination of the corresponding invariants of geometric moments. It is also shown that these invariants are relatively robust in the presence of image noise and are potentially useful as a kind of invariant descriptors in some image analysis and pattern recognition.