Methods and Applications of Analysis

Volume 26 (2019)

Number 3

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

DOI: https://dx.doi.org/10.4310/MAA.2019.v26.n3.a2

Authors

Haohan Li (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong)

Zuoqiang Shi (Department of Mathematical Sciences and the Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Xiao-Ping Wang (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong)

Abstract

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.

Keywords

total variation, nonlocal method, point cloud, nonlocal Laplacian

2010 Mathematics Subject Classification

41A05, 65D05, 65D25

Full Text (PDF format)

Research supported by NSFC Grant 11671005.

Received 30 January 2018

Accepted 12 April 2019

Published 2 April 2020