Advertisement
Published in:
06-09-2017
Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold Model
Published in: Journal of Scientific Computing | Issue 2/2018
Log inActivate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
In this paper we use the idea of the weighted nonlocal Laplacian (Shi et al. in J Sci Comput, 2017) to deal with the constraints in the low dimensional manifold model (Osher et al. in SIAM J Imaging Sci, 2017). In the original LDMM, the constraints are enforced by the point integral method. The point integral method provides a correct way to deal with the constraints, however it is not very efficient due to the fact that the symmetry of the original Laplace–Beltrami operator is destroyed. WNLL provides another way to enforce the constraints in LDMM. In WNLL, the discretized system is symmetric and sparse and hence it can be solved very fast. Our experimental results show that the computational cost is reduced significantly with the help of WNLL. Moreover, the results in image inpainting and denoising are also better than the original LDMM and competitive with state-of-the-art methods.