Geodesic distances to landmarks for dense correspondence on ensembles of complex shapes

Abstract

Establishing correspondence points across a set of biomedical shapes is an important technology for a variety of applications that rely on statistical analysis of individual subjects and populations. The inherent complexity (e.g. cortical surface shapes) and variability (e.g. cardiac chambers) evident in many biomedical shapes introduce significant challenges in finding a useful set of dense correspondences. Application specific strategies, such as registration of simplified (e.g. inflated or smoothed) surfaces or relying on manually placed landmarks, provide some improvement but suffer from limitations including increased computational complexity and ambiguity in landmark placement. This paper proposes a method for dense point correspondence on shape ensembles using geodesic distances to a priori landmarks as features. A novel set of numerical techniques for fast computation of geodesic distances to point sets is used to extract these features. The proposed method minimizes the ensemble entropy based on these features, resulting in isometry invariant correspondences in a very general, flexible framework.

Fig. 1

Mean shapes from: (a) particle based automatic correspondence [4] , (b) including fixed landmarks, and (c) and proposed method using geodesic distance features

Fig. 2

Two views of the mean shape of the ensemble of left hemisphere cortical surfaces

Fig. 3

Alignment of cortical curves in the mean space using the geodesic distance method (a) and the CIVET pipeline (b). Note that the two surface templates are different: mean template from geodesic distance method (a), MNI template (b).

Fig. 4

Reconstructed median shapes for the pre-ablation (a) and post-ablation (c) groups, highlighting a particular correspondence. Overlay of the two median shapes, showing the high degree of variability (b).