Segmentation of 3D Objects from MRI Volume Data Using Constrained Elastic Deformations of Flexible Fourier Surface Models

Abstract

This paper describes a new model-based segmentation technique combining desirable properties of physical models (snakes, [2]), shape representation by Fourier parametrization (Fourier snakes, [12]), and modelling of natural shape variability (eigenmodes, [7, 10]). Flexible 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 with respect to a small set of stable landmarks (AC-PC in our application) and explaining the remaining variability among a series of images with the model flexibility. Although straightforward, the extension to 3-D is severely impeded by finding a proper surface parametrization for arbitrary objects with spherical topology. We apply a newly developed surface parametrization [16, 17] which achieves a uniform mapping between object surface and parameter space. The 3D model building and Fourier-snake procedure are demonstrated by segmenting deep structures of the human brain from MR volume data.