Small Sample Size Learning for Shape Analysis of Anatomical Structures

We present a novel approach to statistical shape analysis of anatomical structures based on small sample size learning techniques. The high complexity of shape models used in medical image analysis, combined with a typically small number of training examples, places the problem outside the realm of classical statistics. This difficulty is traditionally overcome by first reducing dimensionality of the shape representation (e.g., using PCA) and then performing training and classification in the reduced space defined by a few principal components. We propose to learn the shape differences between the classes in the original high dimensional parameter space, while controlling the capacity (generalization error) of the classifier. This approach makes significantly fewer assumptions on the properties and the distribution of the underlying data, which can be advantageous in anatomical shape analysis where little is known about the true nature of the input data. Support Vector Machines with Radial Basis Function kernels are used as a training method and the VC dimension is used for the theoretical analysis of the classifier capacity. We demonstrate the method by applying it to shape classification of the hippocampus-amygdala complex in a data set of 15 schizophrenia patients and 15 normal controls. Using our technique, the separation between the classes and the confidence intervals are improved over a volume based analysis (63% to 73%). Thus exploiting techniques from small sample size learning theory provides us with a principled way of utilizing shape information in statistical analysis of the disorder effects on the brain.