4D Hyperspherical Harmonic (HyperSPHARM) Representation of Multiple Disconnected Brain Subcortical Structures

Ameer Pasha Hosseinbor¹, Moo K. Chung¹, Stacey M. Schaefer¹, Carien M. van Reekum², Lara Peschke-Schmitz¹, Matt Sutterer¹, Andrew L. Alexander¹, and Richard J. Davidson¹

¹University of Wisconsin-Madison, USA
hosseinbor@wisc.edu

²University of Reading, UK

Abstract. We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can’t represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441.

LNCS 8149, p. 598 ff.

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