Localized maximum entropy shape modelling.

A core part of many medical image segmentation techniques is the point distribution model, i.e., the landmark-based statistical shape model which describes the type of shapes under consideration. To build a proper model, that is flexible and generalizes well, one typically needs a large amount of landmarked training data, which can be hard to obtain. This problem becomes worse with increasing shape complexity and dimensionality. This work presents a novel methodology applicable to principal component-based shape model building and similar techniques. The main idea of the method is to make regular PCA shape modelling more flexible by using merely covariances between neighboring landmarks. The remaining unknown second order moments are determined using the maximum entropy principle based on which the full covariance matrix--as employed in the PCA--is determined using matrix completion. The method presented can be applied in a variety of situations and in conjunction with other technique facilitating model building. The experiments on point distributions demonstrate that improved shape models can be obtained using this localized maximum entropy modelling.