An Efficient Algorithm for Topologically Correct Segmentation of the Cortical Sheet in Anatomical MR Volumes

Abstract

Polygon-mesh representations of the cortices of individual subjects are of anatomical interest, aid visualization of functional imaging data and provide important constraints for their statistical analysis. Due to noise and partial volume sampling, however, conventional segmentation methods rarely yield a voxel object whose outer boundary represents the folded cortical sheet without topological errors. These errors, called handles, have particularly deleterious effects when the polygon mesh constructed from the segmented voxel representation is inflated or flattened. So far handles had to be removed by cumbersome manual editing, or the computationally more expensive method of reconstruction by morphing had to be used, incorporating the a priori constraint of simple topology into the polygon-mesh model. Here we describe a linear time complexity algorithm that automatically detects and removes handles in presegmentations of the cortex obtained by conventional methods. The algorithm's modifications reflect the true structure of the cortical sheet. The core component of our method is a region growing process that starts deep inside the object, is prioritized by the distance-to-surface of the voxels considered for inclusion and is selftouching-sensitive, i.e., voxels whose inclusion would add a handle are never included. The result is a binary voxel object identical to the initial object except for “cuts” located in the thinnest part of each handle. By applying the same method to the inverse object, an alternative set of solutions is determined, correcting the errors by addition instead of deletion of voxels. For each handle separately, the solution more consistent with the intensities of the original anatomical MR scan is chosen. The accuracy of the resulting polygon-mesh reconstructions has been validated by visual inspection, by quantitative comparison to an expert's manual corrections, and by crossvalidation between reconstructions from different scans of the same subject's cortex.