PCA-Based False Positive Reduction

When the algorithm used to detect potential masses has finished, a set suspicious regions (centre of masses and lesion size) have been found, some of them being actually masses whilst the rest represent normal tissue. Thus, a posterior processing step is needed to classify a RoI according to these two classes. For doing such task we adapted, once again, the eigenfaces approach.

The eigenfaces approach assumes that a database of already classified RoIs is available. This contains only two types of RoIs: RoIs containing masses and RoIs of normal tissue^5.1 (this is equivalent to a face recognition system containing two people). Different instances for each class are included in the database. Their intra class variability is mainly due to grey-level and texture differences and to the shape and size of the mass or other structures present in the RoI. Again, a parallelism with face detection can be established related to variations of pose and illumination, respectively.

According to the Karhunen-Loeve transform (Eq. ) the usefulness of the different eigenvectors to characterize the variation among the images is ranked by the value of the corresponding eigenvalue. Note that in this case we should refer them as eigenrois. Thus, the eigenrois span the RoI subspace of the original image space, and each RoI can be transformed into this space by using them. The result of this transformation is a vector of weights describing the contribution of each eigenroi in representing the corresponding input image.

Therefore, a model for each RoI in the database is constructed by using Eq. . When a new RoI has to be tested, it will be classified as belonging to the most similar class. Although in the original algorithm the similarity was calculated using the k-Nearest Neighbour algorithm, here we used the already explained Bayesian combination of this algorithm with the C$4.5$ decision tree (see Section  in Chapter ). With this algorithm we can obtain a degree of membership for each class and hence a ROC analysis can be done obtaining an $A_z$ value.