4th order diffusion tensor interpolation with divergence and curl constrained Bézier patches

Authors:
Inas Yassine;Tim McGraw
Affiliations:
Department of Computer Science and Electrical Engineering, West Virginia University;Department of Computer Science and Electrical Engineering, West Virginia University
Venue:
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Year:
2009

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Abstract

We present a tensor field interpolation method based on tensor-valued Bézier patches. The control points of the patch are determined by imposing physical constraints on the interpolated field by constraining the divergence and curl of the tensor field. The method generalizes to Cartesian tensors of all orders. Solving for the control points requires the solution of a sparse linear system. Results are presented for order 2 and 4 tensors and comparisons are made with linear interpolation and a previously proposed subdivision scheme.