Heat kernel smoothing via Laplace-Beltrami eigenfunctions and its application to subcortical structure modeling

Kim, S.-G., Chung, M. K., Seo, S., Schaefer, S. M., Van Reekum, C. ORCID: https://orcid.org/0000-0002-1516-1101 and Davidson, R. J. (2012) Heat kernel smoothing via Laplace-Beltrami eigenfunctions and its application to subcortical structure modeling. In: Advances in Image and Video Technology. Lecture Notes in Computer Science (7087). Springer, pp. 36-47. ISBN 9783642253669 doi: 10.1007/978-3-642-25367-6_4

Abstract/Summary

We present a new subcortical structure shape modeling framework using heat kernel smoothing constructed with the Laplace-Beltrami eigenfunctions. The cotan discretization is used to numerically obtain the eigenfunctions of the Laplace-Beltrami operator along the surface of subcortical structures of the brain. The eigenfunctions are then used to construct the heat kernel and used in smoothing out measurements noise along the surface. The proposed framework is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shape. We detected a significant age effect on hippocampus in accordance with the previous studies. In addition, we also detected a significant gender effect on amygdala. Since we did not find any such differences in the traditional volumetric methods, our results demonstrate the benefit of the current framework over traditional volumetric methods.