Comparison of the Four models

(WGMMS, WGMMu, WGMMMrf, and WGMMMrf)

A cross-validation approach is used to determine the optimal number of component Gaussians, for each breast type. The determined value of m is then used for all training folds comprising each breast type. To determine the optimal value of m, models with a different number of components are trained and evaluated with a WGMMS strategy, using an independent validations set. Model fitness is quantified by examining the log likelihood resulting from the validation set. Training files are created by taking 200 samples randomly drawn with replacement from each normal and abnormal images for each breast type. For training we use 50 training images per breast type (n = 25 normal, n = 25 abnormal) giving a training size of 10,000 samples per breast type. Repeating the procedure for 50 remaining validation image per breast type, we get 10,000 samples for validation.

In our evaluation procedure the aim is to determine the correct number of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN) in order to plot the ROC curve. A detailed summary of how each segmented region is classed as one of these is detailed in [18]. The results are shown in Table 11.10 grouped on the basis of breast density. It is easily concluded that the supervised strategy with MRF is a clear winner. Interestingly, the performance of this method is superior for denser images compared to fatty ones. A simple explanation for this phenomenon could be based on the model order selection where m = 1 for the abnormal class of the fatty breast types. A more sophisticated approach to determining model order might improve the segmentation of these breast types. Without the hidden MRF model, the supervised strategy is inferior to the unsupervised approach on the denser breasts.

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