Heat kernel smoothing using Laplace-Beltrami eigenfunctions.
We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansion avoiding numerical instability and inaccuracy issues. This proposed framework is illustrated with mandible surfaces, and is compared to a widely used iterative kernel smoothing technique in computational anatomy. The MATLAB source code is freely available at http://brainimaging.waisman.wisc.edu/ chung/lb.
Seo
Seongho
S
Department of Brain and Cognitive Sciences Seoul National University, Korea.
Chung
Moo K
MK
Vorperian
Houri K
HK
D000465:Algorithms; D006801:Humans; D008334:Mandible / Q000000981:diagnostic imaging*; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D011861:Radiography, Dental / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*