Gaussian-Hermite矩旋转不变矩的构建

矩及矩的方程因其较强的表述图像特征的能力在图像处理与模式识别中有着广泛的应用,但目前基于具有正交性质的Gaussian-Hermite矩的研究还比较有限.针对Gaussian-Hermite矩进行深入的研究,将其推广到极坐标下复数空间中,提出Polar-Gaussian-Hermite矩;给出利用升降算符计算矩的方程的方法;并利用极坐标下复数空间中的优势,以及它们之间的一一对应关系,推导Gaussian-Hermite矩的旋转不变矩,并给出其旋转不变矩的独立与完备集.实验结果验证所提出的旋转不变矩的正确性,以及良好的数字稳健性.

Construction of invariants of Gaussian-Hermite moments

Moments and functions of moment are widely used in image processing and pattern recognition due to their strong ability to represent features of an image. However, the researches on Gaussian-Hermite moments with which own orthogonal properties are still relatively less currently. Gaussian-Hermite moments were deeply studied, and correspondently, Polar-Gaussian-Hermite moments were proposed in polar coordinate. The method to compute the functions of both moments using raising and lowering operators were presented. Finally, the rotation invariants of Gaussian-Hermite moments were derived based on the Polar-Gaussian-Hermite moments and an independent and complete set of the invariants were given. The given experiment validates the correctness and good digital stability of the proposed invariants.