A Curvature-Driven Image Inpainting Model Based on Helmholtz Vorticity Equation

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.