Generalized surface flows for mesh processing

Geometric flows are ubiquitous in mesh processing. Curve and surface evolutions based on functional minimization have been used in the context of surface diffusion, denoising, shape optimization, minimal surfaces, and geodesic paths to mention a few. Such gradient flows are nearly always, yet often implicitly, based on the canonical L2 inner product of vector fields. In this paper, we point out that changing this inner product provides a simple, powerful, and untapped approach to extend current flows. We demonstrate the value of such a norm alteration for regularization and volume-preservation purposes and in the context of shape matching, where deformation priors (ranging from rigid motion to articulated motion) can be incorporated into a gradient flow to drastically improve results. Implementation details, including a differentiable approximation of the Hausdorff distance between irregular meshes, are presented.

• Type: Conference
• Year: 2007
• Where: SGP
• Authors: Ilya Eckstein, Jean-Philippe Pons, Yiying Tong, C. C. Jay Kuo, Mathieu Desbrun
• Keywords: Computer Graphics, Gradient Flow, Inner Product, SGP 2007, Such Gradient Flows