This code belongs to the papers [1] and [2]. Please cite the paper if you use this code.
They are available at
https://doi.org/10.1093/imaiai/iaz033 and https://doi.org/10.1007/978-3-030-22368-7_15
Further an Arxiv-preprint of [1] can be found at
https://arxiv.org/abs/1903.04873
The code in this repository reproduces the examples from the paper [1]. Note that we use in the directory MexNonlocal some functions from the implementation of [3]. For questions and bug reports, please contact Johannes Hertrich (j.hertrich(at)math.tu-berlin.de).
All examples were tested using Matlab 2019a. Each example reproduces the images for one of the figures in the paper. Some of the examples have a very long runtime! The code is highly experimental and far from optimized (especially the building methods for the nonlocal graphs), so use it with care. Probably, the mex files have to be recompiled for executing Example_Singapur.m. Necessary parameter changes for reproducing all images are indicated at the top of each script.
[1] M. Bačák, J. Hertrich, S. Neumayer and G. Steidl.
Minimal Lipschitz and ∞-Harmonic Extensions of Vector-Valued Functions on Finite Graphs.
Information and Inference: A Journal of the IMA, vol 9, pp. 935–959, 2020.
[2] J. Hertrich, M. Bačák, S. Neumayer, G. Steidl.
Minimal Lipschitz extensions for vector-valued functions on finite graphs.
M. Burger, J. Lellmann and J. Modersitzki (eds.)
Scale Space and Variational Methods in Computer Vision.
Lecture Notes in Computer Science, 11603, 183-195, 2019.
[3] F. Laus, F. Pierre, and G. Steidl.
Nonlocal myriad filters for Cauchy noise removal.
Journal of Mathematical Imaging and Vision 60.8 (2018): 1324-1354.