亥姆霍兹涡量方程与偏微分方程耦合修复模型  

Helmholtz vorticity equation and third order PDE coupled image inpainting model

作　　者：仵冀颖[1] 阮秋琦[1] 

机构地区：[1]北京交通大学信息科学研究所,北京100044

出　　处：《光电子．激光》2008年第8期1104-1107,共4页Journal of Optoelectronics·Laser

基　　金：国家"973"资助项目(2004CB318005);国家自然科学基金资助项目(60472033;60672062);北京交通大学优秀博士生科技创新基金资助项目(48026)

摘　　要：提出一种基于图像几何特征的形态学不变的耦合修复模型。耦合模型使用流体力学中无粘度亥姆霍兹涡量方程平滑的修复图像缺失信息区域。本文证明了亥姆霍兹涡量方程与传输平滑度信息的图像修复模型的等价性。曲率是图像几何特征作用的结果,本文提出沿等照度线方向传输曲率信息的三阶形态学不变偏微分方程,并将抑制涡量的无粘亥姆霍兹方程和正向传输曲率信息的三阶偏微分方程耦合。耦合模型平滑的修复图像并保持图像中的线性特征。理论和实验证明了本文提出的耦合模型在图像修复中的有效性。In this paper a novel morphological invariant coupled image inpainting model which restores image based on geometry property is proposed. The coupled model smoothly inpaints the target region by using inviscid Helmholtz vortMty equa tion in fluid mechanics. The equivalence between Helmholtz equation and smoothness transportation inpainting model is proved. Curvature is the result of geometric structure in image; a new third order partial differential equation（PDE） is pro posed which transports curvature information along isophotes. The third order PDE is morphologically invariant. Helmholtz vorticity equation which annihilates vorticity and third order PDE which forward transports curvature information are coupled to be a new model. The novel coupled model restores image smoothly and it preserves linear structure well. Both theoretical analysis and experiments have verified the validity of the new coupled model proposed in this paper.

关 键 词：图像修复 亥姆霍兹涡量方程 曲率 耦合 形态学不变性 

分 类 号：TN911.73[电子电信—通信与信息系统]