Applying Kernel Density Estimation of Directional Data to Analyze Head Flatness and Asymmetry

• Activity Number: 319
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Lasse Holmstrom* and Ville Vuollo and Henri Aarnivala and Virpi Harila and Tuomo Heikkinen and Pertti Pirttiniemi and Arja Marita Valkama
• Companies: University of Oulu and University of Oulu and University of Oulu and University of Oulu and University of Oulu and University of Oulu and University of Oulu
• Keywords: 3D shape analysis ; 3D surface imaging ; directional statistics ; head shape ; kernel density estimation ; spherical data

Abstract

Human skull deformation is analyzed using the distribution of head normal vector directions computed from a 3D image. Round head shape corresponds to a uniform distribution of normal vector directions and for a symmetrical head, the distribtion exhibits symmetry across the plane that divides the head into left and right halves. Severity of head flatness and asymmetry can then be quantified by suitable functionals of the kernel estimate of the normal vector direction density. The density estimates can be visualized using a 2D contour plot of an area-preserving projection of the estimate to a planar disk. The numerical integration needed in evaluating the density functionals can be performed efficiently by employing an evenly spaced Fibonacci grid on the unit sphere. Using image data from 99 infants and clinical deformation ratings made by experts, our approach is compared with some recently suggested methods. The results show that the proposed method performs competitively.