Covariance shrinking in active shape models with application to gyral labeling of the cerebral cortex

Abstract

Active shape models (ASMs) have been widely used in segmentation tasks in medical image analysis. Complex structures and a limited number of training samples can, however, result in the failure to capture the complete range of shape variations. Various modifications to the point distribution model (PDM) have been proposed to increase the flexibility of the model. Still model parameters are often determined empirically without respect to the underlying data structure. We explore shrinkage covariance estimation in building a PDM by combining the sample covariance matrix with a target covariance matrix estimated from a low-dimensional constrained model. Instead of using a global shrinkage intensity, we apply a spatially varying shrinkage intensity field to better adapt to the spatially varying characteristic of a complex shape. The parameters of the constrained model and the amount of shrinkage are determined in a data-driven fashion, so that the resulting distribution is optimized in representing the underlying data. The PDM, which we call SC-PDM, shows an increased flexibility in fitting new shapes and at the same time, is robust to noise. We demonstrate the effectiveness of using SC-PDM to label gyral regions on the human cerebral cortex.