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Activity Number:
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455
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 9, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #306125 |
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Title:
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New Kernel Method on Unit Sphere and Its Application to Brain Imaging
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Author(s):
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Moo Chung*+
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Companies:
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University of Wisconsin-Madison
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Address:
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1300 University Ave., Madison, WI, 53706,
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Keywords:
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spherical harmonics ; Green's function ; unit sphere ; Gauss-Weistrass ; kernel smoothing ; spline
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Abstract:
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Spherical harmonics (SPHARM) have been used as building blocks for spline-smoothing on a unit sphere. We present a new general framework for kernel smoothing on the unit sphere using SPAHRM. The kernel is constructed as the Green's function of a partial differential equation (PDE) that has smooth solution. The data residing in the unit sphere serve as the initial condition of the PDE. Then, we approximate the solution of the PDE via the least squares method in the finite subspace of twice integrable function space. The subspace is constructed as a linear combination of the spherical harmonics. As the dimension of the subspace increases, the approximation converges to the solution of the PDE. As a particular example of this powerful technique, we show the relationship between the Gauss-Weistrass kernel and an isotropic heat flow. This technique has been applied in brain shape analysis.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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