Flexibly regularized mixture models and application to image segmentation.

Area of Science:

• Machine Learning
• Computer Vision
• Statistical Modeling

Background:

• Probabilistic finite mixture models are essential for unsupervised clustering.
• Adapting models to data topology, such as spatial adjacency, can improve clustering performance.
• Existing methods for topological adaptation often involve complex priors or intractable inference.

Purpose of the Study:

• To propose a novel parametrization of the Dirichlet distribution for flexible regularization of mixture model mixing probabilities.
• To enable arbitrary linear update rules for mixing probabilities, including spatial smoothing.
• To extend the flexible design for sharing class information across multiple mixture models.

Main Methods:

• Developed a new Dirichlet distribution parametrization for over-parametrized mixture models.
• Utilized the Expectation-Maximization algorithm for inference.
• Applied the method to artificial and natural image segmentation, and deep convolutional neural networks.

Main Results:

• Demonstrated the ability to define any linear update rule for mixing probabilities, with spatial smoothing as a special case.
• Showcased successful application to image segmentation tasks, comparing Gaussian and Student-t mixtures.
• Extended the approach to propagate class information across deep convolutional neural network layers.

Conclusions:

• The proposed flexible parametrization significantly enhances probabilistic mixture models by adapting to data topology.
• The method offers a more tractable and versatile alternative to existing regularization techniques.
• The approach has broad applicability, including image segmentation and novel interpretations of biological visual systems.