Estimation of generalized mixtures and its application in image segmentation

Area of Science:

• Statistical modeling
• Image analysis
• Machine learning

Background:

• Mixture models are widely used in statistical analysis.
• Estimating mixtures with unknown component distributions presents challenges.
• Unsupervised image segmentation requires robust statistical methods.

Purpose of the Study:

• To introduce and develop methods for estimating generalized mixtures.
• To apply these methods to unsupervised statistical image segmentation.
• To adapt existing algorithms for generalized mixture estimation.

Main Methods:

• Adaptation of Expectation-Maximization (EM), Stochastic EM (SEM), and Iterative Conditional Estimation (ICE) algorithms.
• Utilizing skewness and kurtosis for component family recognition within the Pearson system.
• Development of adaptive SEM, EM, and ICE for blind segmentation.
• Adaptation of Gibbsian EM (GEM) and ICE for global segmentation using hidden random Markov fields.

Main Results:

• Demonstrated adaptability of classical mixture estimation algorithms to generalized mixtures.
• Proposed and validated adaptive algorithms for blind and global image segmentation.
• Showcased the effectiveness of the methods through numerical studies and real radar image segmentation.

Conclusions:

• Generalized mixture estimation provides a flexible framework for complex statistical problems.
• The proposed adaptive algorithms enhance unsupervised image segmentation capabilities.
• The methods offer improved performance in segmenting real-world data, such as radar images.