Pranav Bhagirath

54 Chapter 3 Implementation: In this work, three separate models were considered: Rician, Rician– Gaussian and Gaussian models. Each model was fitted to the myocardium intensity distribution in the unseen image. The model with the least mean fitting error was chosen. To achieve an optimal fit, the Expectation-Maximization (EM) algorithm was used. Two classes corresponding to healthy and scar were chosen to initialize the EM fit. A threshold was then derived from the mixture distribution obtained from the EM- fitting process. This is the higher of the two means in the two-class mixture model. Using Euclidean distance in 3D and endocardial voxels computed from the myocardium segmentation, voxels with intensity higher than the threshold and closer to the endocardium were chosen as seeds for the watershed process. These seeds were used to define the basins and the watershed transformation determined the extent of each basin. The basins determined each location to be labeled as scar. An ensuing connected- components analysis step removed small noisy structures. Algorithm 5: KCL - Graph-cuts with EM-algorithm (KCL) Background: The background of the method used in this work is in some ways similar to the method proposed by MCG in Section 2.4 except that it employs a non-conditional MRF solved using graph-cuts. The image to be segmented is modeled as a graph with paths or links between neighboring pixels. For each pixel there is also a link to two special nodes also known as source and sink nodes that correspond to scar and healthy myocardium. Each link is assigned a weight based on its intensity. The graph- cuts approach computes a partitioning to divide the graph into two sub-graphs, one containing the source node and the other the sink node. This partitioning assigns a label (source or sink) to each pixel solving the segmentation as an optimization problem. It searches for a globally-optimal solution. Implementation: In the graph-cuts approach implemented in this work, each pixel in the myocardium was modeled as a node in the graph with links to source and sink nodes. These links were assigned weights representing the affinity to healthy (i.e. source) and scar (i.e. sink) nodes. The weights were derived from statistical distribution models developed from training images. There were separate intensity distribution models for healthy and scar tissue, both of which were derived from the training images. For scar, the ratio of delayed enhancement intensity to mean blood pool was modeled using a Gaussian distribution. For healthy tissue, a Gaussian mixture was used. The number of mixtures in the model was fixed at three. The standard EM-algorithm computed mean and variance for each mixture from the training images. In the graph-cuts framework there are also links between adjacent pixels and these were derived from a measure of intensity similarity of two pixels. Adjacent pixels with similar intensities attained a high