An improved algorithm for the piecewise-smooth Mumford and Shah model in image segmentation

Area of Science:

• Computer Vision
• Image Processing
• Computational Mathematics

Background:

• The Mumford and Shah functional is a cornerstone for image segmentation, aiming to partition images into regions with distinct properties.
• Classical algorithms for this functional often suffer from slow convergence, limiting their practical application.
• Previous extensions, such as those by Chan and Vese, and Choi et al., have addressed some limitations but retained certain drawbacks.

Purpose of the Study:

• To present an improved algorithm for solving the piecewise-smooth Mumford and Shah functional.
• To overcome the low convergence problem inherent in classical algorithms.
• To provide a more efficient and robust method for image segmentation tasks.

Main Methods:

• The proposed algorithm replaces extensions of key functions with a novel level set update mechanism.
• This update is based on an artificial image, a composite of the original and diffused image data.
• The method leverages concepts from level set evolution and image diffusion for segmentation.

Main Results:

• The algorithm demonstrates efficient convergence, significantly improving upon classical methods.
• The approach effectively segments images with piecewise-smooth characteristics.
• Demonstrated efficacy across several test cases, validating the algorithm's performance.

Conclusions:

• The developed algorithm offers an efficient solution to the convergence issues in piecewise-smooth Mumford and Shah functional segmentation.
• The novel level set update strategy based on an artificial image proves effective.
• This improved method holds promise for advanced image analysis and computer vision applications.