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Nonlocal Mumford-Shah regularizers for color image restoration
Miyoun Jung1, Xavier Bresson, Tony F Chan
1Department of Mathematics, University of California, Los Angeles, CA 90095, USA. jung@ceremade.dauphine.fr
Summary
This study introduces novel nonlocal algorithms for color image restoration, enhancing texture and fine structure details. These advanced methods outperform traditional local approaches in various applications, including denoising and inpainting.
Area of Science:
- Computer Vision
- Image Processing
- Mathematical Modeling
Background:
- Traditional image restoration often relies on local image information, which is insufficient for complex textures.
- The Mumford-Shah (MS) model provides a framework for image segmentation and restoration but local approximations have limitations.
- Nonlocal image information has shown promise in capturing global image properties for better restoration.
Purpose of the Study:
- To develop novel nonlocal formulations of the Mumford-Shah (MS) functional for improved color image restoration.
- To extend existing local Ambrosio-Tortorelli and Shah approximations to nonlocal versions.
- To demonstrate the effectiveness of these nonlocal regularizers across various image processing tasks.
Main Methods:
- Extension of local Ambrosio-Tortorelli and Shah approximations to nonlocal Mumford-Shah (MS) functional.
- Development of a class of restoration algorithms based on nonlocal image information.
- Characterization of minimizers using dual norm formulations.
Main Results:
- The proposed nonlocal MS regularizers yield superior results compared to local methods in color image denoising, deblurring, inpainting, super-resolution, and demosaicing.
- Significant improvements were observed in image inpainting, particularly for large missing regions.
- Nonlocal approaches effectively restore fine structures and textures that are challenging for local methods.
Conclusions:
- Nonlocal image information integrated with the Mumford-Shah model offers a powerful approach for advanced color image restoration.
- The developed algorithms provide enhanced performance across a wide range of image processing applications.
- This work advances the state-of-the-art in image restoration by leveraging nonlocal image properties.
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