Robust Student's-t mixture model with spatial constraints and its application in medical image segmentation

Area of Science:

• Computer Vision
• Machine Learning
• Medical Imaging

Background:

• Finite mixture models, particularly Student's-t distributions, offer robust alternatives to Gaussian models for image segmentation due to their heavy tails.
• Existing models often neglect explicit incorporation of spatial relationships between pixels, limiting their performance in complex image structures.

Purpose of the Study:

• To propose a novel finite Student's-t mixture model (SMM) for enhanced image segmentation.
• To address limitations of existing models by incorporating local spatial constraints and simplifying parameter estimation.
• To evaluate the proposed SMM against state-of-the-art methods using simulated and real medical images.

Main Methods:

• The proposed SMM utilizes Dirichlet distribution and Dirichlet law to integrate local spatial constraints within the image.
• Direct estimation of Student's-t distribution parameters is employed, avoiding the complexity of infinite Gaussian mixtures.
• Gradient-based optimization is used to minimize the data negative log-likelihood, replacing the Expectation-Maximization (EM) algorithm.

Main Results:

• The proposed SMM demonstrates successful comparison against current state-of-the-art finite mixture models.
• Numerical experiments show the model's effectiveness on diverse simulated and real medical imaging datasets.
• The model's ability to handle heavy-tailed distributions and spatial information contributes to improved segmentation accuracy.

Conclusions:

• The novel finite Student's-t mixture model offers a robust and computationally efficient approach to image segmentation.
• Incorporating spatial constraints and direct parameter estimation significantly enhances segmentation performance, particularly for medical images.
• The proposed gradient-based optimization method provides an effective alternative to traditional EM algorithms for mixture models.