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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 diculty is tradi- tionally overcome by rst reducing dimensionality of the shape represen- tation (e.g., using PCA) and then performing training and classication in the reduced space dened by a few principal components. We propose to learn the shape dierences between the classes in the original high di- mensional parameter space, while controlling the capacity (generalization error) of the classier. This approach makes signicantly fewer assump- tions 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 classier capacity. We demonstrate the method by applying it to shape classication 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 condence 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 eects on the brain.

Small Sample Size Learning for Shape Analysis of Anatomical Structures