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On the convergence of EM-like algorithms for image segmentation using Markov random fields.

Alexis Roche¹, Delphine Ribes, Meritxell Bach-Cuadra

¹CIBM-Siemens, Ecole Polytechnique Fédérale (EPFL), CH-1015 Lausanne, Switzerland. alexis.roche@epfl.ch

Medical Image Analysis

|May 31, 2011

Summary

This study compares Expectation-Maximization (EM)-like algorithms for Markov random field image segmentation. An asynchronous voxel updating method offers faster convergence and comparable segmentation accuracy for medical imaging applications.

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Area of Science:

Medical image analysis
Computational imaging
Pattern recognition

Background:

Markov random field (MRF) models are crucial for image segmentation.
Expectation-Maximization (EM) algorithms are commonly adapted for MRF inference.
Existing EM adaptations can be numerically unstable and lack theoretical convergence guarantees.

Purpose of the Study:

To review and compare EM-like variants for MRF image segmentation.
To analyze the theoretical and practical convergence properties of these algorithms.
To propose and validate a numerically stable and efficient updating scheme.

Main Methods:

Theoretical analysis of convergence properties for three EM-like variants.
Implementation and comparison of algorithms on synthetic and real-world data.

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Focus on an asynchronous voxel updating scheme for MRF segmentation.

Main Results:

The asynchronous voxel updating scheme demonstrates general convergence properties.
This method achieves significantly faster convergence compared to other tested variants.
Segmentation results are comparable to existing methods, particularly in brain tissue classification.

Conclusions:

Asynchronous voxel updating provides a stable and efficient approach for MRF image segmentation.
This method offers a practical advantage in terms of speed without compromising segmentation quality.
The findings are particularly relevant for accelerating medical image analysis tasks like MRI brain segmentation.