Methods and Applications of Analysis
Volume 26 (2019)
Special Issue in Honor of Roland Glowinski (Part 2 of 2)
Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)
Weighted nonlocal total variation in image processing
Pages: 235 – 248
In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to keep balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpaiting and image colorization, we demonstrate that WNTV provides an effective and efficient method in many image processing and machine learning problems.
total variation, nonlocal method, point cloud, nonlocal Laplacian
2010 Mathematics Subject Classification
41A05, 65D05, 65D25
Research supported by NSFC Grant 11671005.
Received 30 January 2018
Accepted 12 April 2019
Published 2 April 2020