title: Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.
abstract: We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template.
authors: Department of Biostatistics and Medical Informatics, USA; Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, USA. Electronic address: mkchung@wisc.edu.
authors: Moo K
authors: MK
authors: Chung
authors: Department of Biomedical Engineering, National University of Singapore, Singapore.
authors: Anqi
authors: A
authors: Qiu
authors: Department of Brain and Cognitive Sciences, Seoul National University, Republic of Korea.
authors: Seongho
authors: S
authors: Seo
authors: Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, USA.
authors: Houri K
authors: HK
authors: Vorperian
mesh_terms: D000293:Adolescent; D000375:Aging / Q000502:physiology*; D000465:Algorithms; D002648:Child; D002675:Child, Preschool; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D007223:Infant; D007231:Infant, Newborn; D008297:Male; D008334:Mandible / Q000000981:diagnostic imaging* / Q000254:growth & development*; D010363:Pattern Recognition, Automated / Q000379:methods; D011856:Radiographic Image Enhancement / Q000379:methods; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique; D014057:Tomography, X-Ray Computed / Q000379:methods*; D058067:Wavelet Analysis; D055815:Young Adult
keywords: Diffusion wavelets; Heat kernel regression; Laplace–Beltrami eigenfunctions; Mandible growth; Surface-based morphometry