Bayesian Multifractal Image Segmentation

Area of Science:

• Image analysis and computer vision
• Statistical modeling and machine learning
• Texture analysis

Background:

• Multifractal analysis (MFA) characterizes image textures via spatial fluctuations of local regularity.
• Existing MFA methods are effective for homogeneous textures but struggle with natural images composed of multiple textures.
• Natural images often exhibit multifractal properties that vary across different regions.

Purpose of the Study:

• To introduce an unsupervised Bayesian multifractal segmentation method for modeling and segmenting complex image textures.
• To jointly estimate multifractal parameters and pixel-level labels for enhanced texture segmentation.
• To develop a method capable of handling images with diverse and spatially varying multifractal properties.

Main Methods:

• A computationally efficient multifractal parameter estimation model for wavelet leaders was developed.
• A multiscale Potts Markov random field was employed to model spatial and cross-scale correlations between wavelet leader labels.
• A Gibbs sampling methodology was utilized for posterior distribution sampling of model parameters.

Main Results:

• The proposed method successfully segments images based on multifractal properties at the pixel level.
• Numerical experiments on synthetic multifractal images demonstrated the approach's effectiveness.
• The Bayesian method achieved superior performance compared to traditional unsupervised and deep learning-based segmentation techniques.

Conclusions:

• The developed unsupervised Bayesian multifractal segmentation method provides an effective solution for complex texture analysis.
• The approach demonstrates significant advantages over existing segmentation techniques, particularly for images with varying multifractal characteristics.
• This work advances the field of image segmentation by offering a robust method for multifractal texture characterization.