Name
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10915-017-0549-x | J. Sci. Comput. |
Keywords | Field | DocType |
Weighted nonlocal Laplacian, Low dimensional manifold model, Nonlocal methods, Point cloud, 65D05, 65D25, 41A05 | Noise reduction,Discretization,Mathematical optimization,Mathematical analysis,Inpainting,Operator (computer programming),Integral method,Point cloud,Mathematics,Manifold,Laplace operator | Journal |
Volume | Issue | ISSN |
75 | 2 | 0885-7474 |
Citations | PageRank | References |
2 | 0.36 | 22 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zuoqiang Shi | 1 | 121 | 18.35 |
| Stanley Osher | 2 | 7973 | 514.62 |
| Wei Zhu | 3 | 63 | 10.82 |