Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models

This paper describes a new model-based segmentation technique combining desirable properties or physical models (snakes), shape representation by Fourier parametrization, and modelling of natural shape variability. Flexible parametric shape models are represented by a parameter vector describing the mean contour and by a set of eigenmodes of the parameters characterizing the shape variation. Usually the segmentation process is divided into an initial placement of the mean model and an elastic deformation restricted to the model variability. This, however, leads to a separation of biological variation due to a global similarity transform from small-scale shape changes originating from elastic deformations of the normalized model contours only. The performance can he considerably improved by building shape models normalised with respect to a small set of stable landmarks (AC-PC in our application) and by explaining the remaining variability among a series of images with the model flexibility. This way the image interpretation is solved by a new coarse-to-fine segmentation procedure based on the set of deformation eigenmodes, making a separate initialization step unnecessary. Although straightforward, the extension to 3-D is severely impeded by difficulties arising during the generation of a proper surface parametrization for arbitrary objects with spherical topology. We apply a newly developed surface parametrization which achieves a uniform mapping between object surface and parameter space. The 3-D procedure is demonstrated by segmenting deep structures of the human brain from MR volume data.