Learning Deep Features for Automated Placement of Correspondence Points on Ensembles of Complex Shapes

Correspondence-based shape models are an enabling technology for various medical imaging applications that rely on statistical analysis of populations of anatomical shape. One strategy for automatic correspondence placement is to simultaneously learn a compact representation of the underlying anatomical variation in the shape space while capturing the geometric characteristics of individual shapes. The inherent geometric complexity and population-level shape variation in anatomical structures introduce significant challenges in finding optimal shape correspondence models. Existing approaches adopt iterative optimization schemes with objective functions derived from probabilistic modeling of shape space, e.g. entropy of Gaussian-distributed shape space, to find useful sets of dense correspondence on shape ensembles. Nonetheless, anatomical shape distributions can be far more complex than this Gaussian assumption, which entails linear shape variation. Recent works address this limitation by adopting an application-specific notion of correspondence through lifting positional data to a higher-dimensional feature space (e.g. sulcal depth, brain connectivity, and geodesic distance to anatomical landmarks), with the goal of simplifying the optimization problem. However, this typically requires a careful selection of hand-crafted features and their success heavily rely on expertise in finding such features consistently. This paper proposes an automated feature learning approach using deep convolutional neural networks for optimization of dense point correspondence on shape ensembles. The proposed method endows anatomical shapes with learned features that enhance the shape correspondence objective function to deal with complex objects and populations. Results demonstrate that deep learning based features perform better than methods that rely on position and compete favorably with hand-crafted features.