Hierarchical isosurface segmentation based on discrete curvature

Abstract

A high-level approach to describe the characteristics of a surface is to segment it into regions of uniform curvature behavior and construct an abstract representation given by a (topology) graph. We propose a surface segmentation method based on discrete mean and Gaussian curvature estimates. The surfaces are obtained from three-dimensional imaging data sets by isosurface extraction after data presmoothing and postprocessing the isosurfaces by a surface-growing algorithm. We generate a hierarchical multiresolution representation of the isosurface. Segmentation and graph generation algorithms can be performed at various levels of detail. At a coarse level of detail, the algorithm detects the main features of the surface. This low-resolution description is used to determine constraints for the segmentation and graph generation at the higher resolutions. We have applied our methods to MRI data sets of human brains. The hierarchical segmentation framework can be used for brain-mapping purposes.