Computer Vision, IEEE International Conference on (2011)
Nov. 6, 2011 to Nov. 13, 2011
Tsz Wai Wong , University of California, Los Angeles Department of Mathematics, 520 Portola Plaza, Math Science Building 6363, UCLA, 90095, USA
Xianfeng Gu , State University of New York at Stony Brook, Department of Computer Science, Room 2425, Computer Science Building, State University of New York at Stony Brook, 11794-4400, USA
Tony F. Chan , Hong Kong University of Science and Technology, Office of the President, HKUST,, Clear Water Bay, Kowloon, Hong Kong
Lok Ming Lui , The Chinese University of Hong Kong, Department of Mathematics, Room 207, Lady Shaw Building, CUHK, Shatin, Hong Kong
In this paper, we propose novel algorithms for inpainting and refinement of diffeomorphisms. We first represent a diffeomorphism by its Beltrami coefficient. Then it is possible to refine and inpaint the diffeomorphism by processing this Beltrami coefficient. With the inpainted/refined Beltrami coefficient, we construct a new diffeomorphism using the exact Beltrami holomorphic flow algorithm proposed in this paper. We apply our algorithms on several practical applications, which include the inpainting of a highly distorted diffeomorphism, the inpainting of image sequences of deforming shapes, the super-resolution of diffeomorphisms and the global parameterization of cortical surfaces by combining local parameterizations. Experiments show that our algorithm can solve these problems with natural and smooth results. We demonstrate how our proposed method can be widely applied in areas from texture mapping to video processing, and from computer graphics to medical imaging.
T. F. Chan, L. M. Lui, T. W. Wong and X. Gu, "Parallelizable inpainting and refinement of diffeomorphisms using Beltrami holomorphic flow," 2011 IEEE International Conference on Computer Vision (ICCV 2011)(ICCV), Barcelona, 2011, pp. 2383-2390.