\(p\)-Laplace diffusion for distance function estimation, optimal transport approximation, and image enhancement. (English) Zbl 1505.65308
Summary: In this paper, we propose ADMM-based numerical schemes for power-law diffusion equations involving the \(p\)-Laplacian \(\operatorname{div}(|\nabla u|^{p-2} \nabla u)\) with constant (\(p = \text{const}\)) and variable (\(p = p(\boldsymbol{x})\)) exponents. Applications to distance function and optimal transport approximations (\(p\) is large and constant) and image enhancement (\(p\) is small and variable) are considered.
MSC:
| 65N99 | Numerical methods for partial differential equations, boundary value problems |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 49Q22 | Optimal transportation |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
power-law diffusion; \(p\)-Laplacian; distance function estimation; optimal transport approximation; image enhancementReferences:
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