Simultaneous Segmentation and Correspondence Establishment for Statistical Shape Models

Abstract

Statistical Shape Models have been proven to be valuable tools for segmenting anatomical structures of arbitrary topology. Being based on the statistical description of representative shapes, an initial segmentation is required – preferably done by an expert. For this purpose, mostly manual segmentation methods followed by a mesh generation step are employed. A prerequisite for generating the training data based on these segmentations is the establishment of correspondences between all training meshes. While existing approaches decouple the expert segmentation from the correspondence establishment step, we propose in this work a segmentation approach that simultaneously establishes the landmark correspondences needed for the subsequent generation of shape models.

Our approach uses a reference segmentation given as a regular mesh. After an initial placement of this reference mesh, it is manually deformed in order to best match the boundaries of the considered anatomical structure. This deformation is coupled with a real time optimization that preserves point correspondences and thus ensures that a pair of landmark points in two different data sets represents the same anatomical feature.

We applied our new method to different anatomical structures: vertebra of the spinal chord, kidney, and cardiac left ventricle. In order to perform a visual evaluation of the degree of correspondence between different data sets, we have developed well adapted visualization methods. From our tests we conclude that the expected correspondences are established during the manual mesh deformation. Furthermore, our approach considerably speeds up the shape model generation, since there is no need for an independent correspondence establishment step. Finally, it allows the creation of shape models of arbitrary topology and removes potential error sources of landmark and correspondence optimization algorithms needed so far.