适用于图像恢复的最优形态滤波设计方法

Design method of optimal morphological filtering for image restoration

针对噪声图像的恢复问题,研究了基于SV形态学理论的最优形态滤波设计方法.通过建立SV形态模式谱解决图像与相关几何结构相似性度量问题;通过引入集差距离函数,解决由形态滤波所产生的几何和拓扑畸变程度的量化问题;通过优化问题的设计,在有效去噪和保持图像基本结构之间寻求一个平衡策略,使得优化问题得以求解.最终从理论上证明了一类SV交替滤波和一类SV交替惯序滤波是SV形态学方法下,适用于图像恢复的最优滤波.

Aiming at the problem of noise image restoration,this paper studies the optimal morphological filtering design method based on SV morphology theory.The similarity measurement problem between image and related geometric structure is solved by establishing SV morphological pattern spectrum,and the quantization problem of geometric and topological distortion caused by morphological filtering is solved by introducing the distance function of set difference.Through the design of the optimization problem,a balance strategy is sought between the effective denoising and preserving the basic structure of the image,and the optimization problem can be solved.Finally,it is proved theoretically that a class of SV alternating filtering and a kind of SV alternating sequence filtering are the optimal filtering for image restoration under the SV morphological method.