A robust and accurate algorithm for estimating the complexity of the cortical surface

A fractal dimension (FD) gives a highly compact description of the shape characteristics of the human brain and has been employed in many studies on brain morphology. The accuracy of FD estimation depends on the precision of the input shape description. Facilitated by automatic cerebral cortical surface reconstruction algorithms, the shape of the cerebral cortex can be more precisely modeled using Magnetic Resonance (MR) imaging. Since the reconstructed cortical surface is represented by triangles, rather than by points, as is typical of models that use voxels, the voxel-based FD estimation algorithms that have been used in previous studies do not work when using the cortical surface as the input. Thus, designing a new algorithm that is able to estimate the FD from a surface representation becomes of particular interest. In this paper, a robust and accurate FD estimation algorithm is proposed. The algorithm is based on a box-triangle intersection checking strategy, which is used for the first time in brain analyses, and a box-counting method, which has been widely used in FD computations of the human brain and other natural objects. These two features endowed the algorithm with robustness. The accuracy of the algorithm was validated via several experiments using both manually generated datasets and real MR images. As a result of these features, the algorithm is also suitable for estimating the FD of fractals in addition to that of the cerebral cortex.