基于结构张量图像建模方法的滤波性能研究

Research on Filtering Behavior of Structure Tensor Based Image Modeling Approaches

主要研究结构张量驱动的变分偏微分方程(variational Partial Differential Equation;variational PDE)图像建模方法的滤波性能.基于角形强度度量和水平线演化理论,设计了一种具有角点增强性能的角形冲击滤波器,以克服边缘冲击滤波器增强图像的不足.基于边缘和角形冲击滤波器,分析了扩散张量驱动的各向异性PDE的滤波性能.指出,散度型各向异性PDE实质上对应着角点保持的平滑-增强滤波机制;而可计算迹型PDE是散度型各向异性PDE的退化情形,对应的是不具有角点保持性能的平滑滤波机制.在此基础上,给出了结构张量驱动的变分泛函满足角点保持性的条件,同时建立了面向应用的统一正则PDE框架,直观有效地刻画了平坦区域、边缘和角形状结构的滤波性能.单幅图像插值实验结果验证了统一正则PDE框架的有效性.

This paper mainly focuses on the structure tensor based image modeling approaches,including partial differential equations（PDE） and variational functionals.A type of corner shock filter is designated based on measures of corner strength and the theory of level-set evolution to enhance the corner structures.The filtering behavior of structure tensor based anisotropic PDE＇s is subsequently analyzed based on the edge shock filter and our proposed corner shock filter.The analysis comes to the conclusion that,Weickert＇s anisotropic PDE corresponds to a kind of smoothing-enhancing,and corner-preserving filtering mechanism,while Tschumperlè＇s trace-based PDE is the reduced version of Weickert＇s PDE,corresponding to a kind of smoothing filtering scheme but not corner-preserving.With the above conclusion,conditions of corner-preservation are intuitively proposed for structure tensor based variational functionals.Finally,a kind of unified regularization PDE framework is proposed for different image applications.The filtering behavior on homogeneous regions,edge,and corner structures can be described by our unified framework more intuitively and efficiently.Experimental results on image magnification demonstrate the efficiency of the unified PDE framework.