扩散PDE彩色图像滤波方法

Color Image Filtering with Diffusion PDEs

研究基于函数极小化、基于散度和基于迹算子的3个不同层次的彩色图像滤波方法,并将它们统一到一个各向异性扩散PDEs(Partial Differential Equation).提出一个新的扩散PDE方法,该方法在实现一致扩散滤波的同时很好地保持了图像的边缘信息,另一方面,由于该方法具有局部几何结构特性,因此通过适当地选择不同的平滑函数即可满足特殊的需求.最后,展示了基于该方法的彩色图像去噪、修补等应用结果.

Color image filtering based on the functional minimization,the divergence-based and trace-based PDE（Partial Differential Equation） are studied. A unifying expression that gathers the majority of these previous framework into a single generic anisotropic diffusion equation. Then,a new diffusion PDE equation witch is coherent with a local vector image geometry is proposed. On one hand,this new scheme is removing image noise while preserve then well edges. On the other hand,it can satisfy special applications by choosing different smoothing function due to its local vector image geometry. Finally,experimental resuits of color image restoration and inpainting handle by proposed anisotropie diffusion equation are presented.