Fast segmentation and flattening methods of cerebral cortex for visualization of fMRI

Abstract

3D surface-based visualization of cerebral cortex is very valuable to localize and visualize the neuronal activation area with the functional study. However, the intrinsic complex shape of the cerebral cortex makes it difficult to visualize whole surface. Inflation and flattening are the widely used visualization methods to resolve the impediment. There are some obstacles in the flattening process, such as overlap between triangles of the 3D surface, large computation amount, and geometric distortions. Many algorithms have been developed to solve the problems. This thesis proposes methods to map a 3D surface of the cerebral cortex onto a sphere and a plane without overlap between triangles, with reduced computation amount and minimized geometric distortions. The inflated surface is mapped onto a sphere by two steps and onto a plane by three steps. As the first step, surface is projected onto a sphere without overlap between triangles. To project surface to a plane, the projected surface onto a sphere is again projected onto a plane and deforms until there is no overlap between triangles. Each projected surface onto a sphere and a plane deforms for its geometric distortions to be minimized. Vertices deform in 2D (x, y)-spherical coordinates for a spherical map and 2D (x,y)-Cartesian coordinates for a flat map. Computation amount is reduced largely just by examining the sign of normal vectors of triangles instead of examining overlap of triangles. This thesis also proposes a segmentation algorithm that is required for pre-processing of the cerebral cortex visualization. The proposed segmentation method extracts only cerebrum using snakes algorithm and segments it into white matter, gray matter, and cerebrospinal fluid. It is named the hierarchical fuzzy c-means algorithm, which is robust to nonuniformity of the radio frequency signal and requires small computation amount. The experimental results show the efficiency and performance of the proposed visualizat...