摘要
图像修复模型根据已知区域信息自动修复目标区域,且保证修复后的图像满足人眼视觉系统的要求,目标区域轮廓自然.理论分析证明,流体力学中无粘亥姆霍兹涡量方程可以实现图像修复.根据曲线和曲面运动方程,使用曲率驱动亥姆霍兹修复模型中的等照度线传输方向.曲率是图像几何特征作用的结果,所以新模型可以很好地保持图像中的线性特征.图像中涡量为平滑程度的度量,二维图像域中涡量具有扩散性,对涡量方程的结果做各向异性扩散,使等照度线间的图像信息交互.亥姆霍兹涡量方程修复模型中的各个参数及扩散过程是涡量扩散性和耗散性以及图像几何特征作用的结果,扩散后的修复模型稳定且不存在错误的传输方向.理论和实验证明了曲率驱动的亥姆霍兹涡量方程模型在图像修复中的有效性.
Image inpainting restores the target region according to the known information of image automatically, and the processed image conforms to human＇s vision system; the contour of target region is smooth and it is not clear to recognize. Based on theoretical analysis, inviscid Helmholtz vorticity equation is used to inpaint image. Helmholtz vorticity equation is an equation in fluid mechanics; the equivalence between it and the inpainting model is proved in this paper. Learning from curve and surface kinetic equation, curvature is used to drive the isophote diffusion transporting directions in the inviscid Helmholtz vorticity equation inpainting model. Curvature is determined by geometric structure in image, so the new model preserves linear structure well. Vorticity is the image smoothness measure; in two dimensional （2-D） image domain, vorticity has diffusion property. Diffusing the result of Helmholtz vorticity equation makes the information between isophotes affect each other. The coefficients and diffusion procedure in Helmholtz equation are determined by the diffusion and dissipation property of vorticity. Helmholtz equation processes image based on geometry property. The diffused inpainting model is stable and do not have erroneous transport directions. Both theoretical analysis and experiments have verified the validity of the curvature-driven Helmholtz vorticity image inpainting model proposed in the paper.
出处
《计算机研究与发展》
EI
CSCD
北大核心
2007年第5期860-866,共7页
Journal of Computer Research and Development
基金
国家"九七三"高技术研究发展规划基金项目(2004CB318005)
国家自然科学基金项目(60472033
60672062)
北京交通大学优秀博士生科技创新基金项目(48026)~~
关键词
图像修复
亥姆霍兹涡量方程
曲率
各向异性扩散
偏微分方程
image inpainting
Helmholtz vorticity equation
curvature
anisotropic diffusion
partial differential equation
