HMRF-GMM-EM Segmentation

Image segmentation using the Expectation-Maximization (EM) algorithm that relies on a Gaussian Mixture Model (GMM) for the intensities and a Markov Random Field (MRF) model on the labels.
This is based on "Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm" (Zhang, Y et al., 2001)

Usage:

See code/main.mlx and run it cell by cell.

Documentation:

• code/main.mlx: The main script/driver program
• code/EM.m: Implements the EM algorithm
• code/G.m: Returns the Gaussian PDF's value at the given point
• code/ICM.m: Finds the optimal labelling using a modified Iterated Conditional Modes (ICM) algorithm
• code/KMeans.m: Returns the initial segmentation using the standard K-means algorithm
• code/logPosterior.m: Computes the log of the posterior probability for the labels (up to a constant)
• code/priorPenalty.m: The prior penalty for the given pixel using a 4 neighbourhood system, without wrap-around (uses the Potts Model)
• code/showSegmented.m: Plots the segmented image using a custom colormap

(This was done as a course assignment for CS736: Medical Image Computing, Spring 2021, IIT Bombay)