A Family of Principal Component Analyses for Dealing with Outliers

Principal Component Analysis (PCA) has been widely used for dimensionality reduction in shape and appearance modeling. There have been several attempts of making PCA robust against outliers. However, there are cases in which a small subset of samples may appear as outliers and still correspond to plausible data. The example of shapes corresponding to fractures when building a vertebra shape model is addressed in this study. In this case, the modeling of "outliers" is important, and it might be desirable not only not to disregard them, but even to enhance their importance. A variation on PCA that deals naturally with the importance of outliers is presented in this paper. The technique is utilized for building a shape model of a vertebra, aiming at segmenting the spine out of lateral X-ray images. The results show that the algorithm can implement both an outlier-enhancing and a robust PCA. The former improves the segmentation performance in fractured vertebrae, while the latter does so in the unfractured ones.