Weighted Nonlocal Total Variation in Image Processing

TL;DR

This paper introduces a weighted nonlocal total variation method that improves semi-supervised image processing tasks by balancing labeled and unlabeled data, demonstrating effectiveness across various applications.

Contribution

The paper proposes a novel weighted nonlocal total variation approach that enhances classical methods by incorporating a weighting scheme for better semi-supervised learning performance.

Findings

Effective in semi-supervised clustering, image inpainting, and colorization.

Outperforms classical nonlocal total variation methods.

Demonstrates efficiency and robustness in multiple image processing tasks.

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 balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpainting and image colorization, we demonstrate that WNTV provides an effective and efficient method in many image processing and machine learning problems.