A framework for the merging of pre-existing and correspondenceless 3D statistical shape models

The construction of statistical shape models (SSMs) that are rich, i.e., that represent well the natural and complex variability of anatomical structures, is an important research topic in medical imaging. To this end, existing works have addressed the limited availability of training data by decomposing the shape variability hierarchically or by combining statistical and synthetic models built using artificially created modes of variation. In this paper, we present instead a method that merges multiple statistical models of 3D shapes into a single integrated model, thus effectively encoding extra variability that is anatomically meaningful, without the need for the original or new real datasets. The proposed framework has great flexibility due to its ability to merge multiple statistical models with unknown point correspondences. The approach is beneficial in order to re-use and complement pre-existing SSMs when the original raw data cannot be exchanged due to ethical, legal, or practical reasons. To this end, this paper describes two main stages, i.e., (1) statistical model normalization and (2) statistical model integration. The normalization algorithm uses surface-based registration to bring the input models into a common shape parameterization with point correspondence established across eigenspaces. This allows the model fusion algorithm to be applied in a coherent manner across models, with the aim to obtain a single unified statistical model of shape with improved generalization ability. The framework is validated with statistical models of the left and right cardiac ventricles, the L1 vertebra, and the caudate nucleus, constructed at distinct research centers based on different imaging modalities (CT and MRI) and point correspondences. The results demonstrate that the model integration is statistically and anatomically meaningful, with potential value for merging pre-existing multi-modality statistical models of 3D shapes.