Low Dimensional Manifold Model for Image Processing

Prof. Shi,Zuoqiang
Yau Mathematical Sciences Center, Tsinghua University

2017-09-19 ~ 2017-09-19


Science Building No. 1 1479


In this talk, I will introduce a novel low dimensional manifold model for image processing problem. This model is based on the observation that for many natural images, the patch manifold usually has low dimension structure. Then, we use the dimension of the patch manifold as a regularization to recover the original image. Using some formula in diffe- rential geometry, this problem is reduced to solve Laplace-Beltrami equation on manifold.The Laplace-Beltrami equation is solved by the point integral method. Numerical tests show that this method gives very good results in image inpainting and denoising.I will also present an interesting relation between deep residual network (ResNet) and the PDEs on point cloud. This may give some new understanding to the deep learning network.