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Surface Processing

We propose that the generalization of signal processing to surfaces entails filtering normals of the surface, rather than filtering the positions of points on a mesh. Using a variational strategy, penalty functions on the surface geometry can be formulated as penalty functions on the surface normals, which are computed using geometry-based shape metrics and minimized using fourth-order gradient descent partial differential equations (PDE). In this paper, we introduce a two-step approach to implementing geometric processing tools for surfaces: (i) operating on the normal map of a surface, and (ii) manipulating the surface to fit the processed normals. Iterating this two-step process, we can efficiently implement geometric fourth-order flows by solving a set of coupled second-order PDEs. The computational approach uses level set surface models; therefore, the processing does not depend on any underlying parameterization. This paper will demonstrate that the proposed strategy provides for a wide range of surface processing operations, including edge-preserving smoothing and high-boost filtering. Furthermore, the generality of the implementation makes it appropriate for very complex surface models, e.g. those constructed directly from measured data.

Processing results on the MRI head model: (a) original isosurface, (b) isotropic diffusion, and (c) anisotropic diffusion. The small protrusion under the nose is a physical marker used for registration.

• Publications -- Surface Processing
• Image Gallery -- Surface Processing

Principal Researchers:

• Dr. Ross Whitaker
• Tolga Tasdizen