Pixel Club: Generalized Laplacians, Ricci curvature and Flow for Images

Speaker:
Eli Appleboim (EE, Technion)
Date:
Tuesday, 15.1.2013, 11:30
Place:
EE Meyer Building 1061

A discrete version of the Ricci flow, applicable to images, is introduced and applied for some image processing tasks such as denoising and non-linear interpolation. This flow is unique among the geometric flows that have been applied in image processing, in the sense that it is the only flow wherein the metric of an image evolves, rather than the image itself, as is the case in other geometric flows. Our curvature and flow represent an adaptation of the combinatorial Ricci curvature defined by Robin Forman in the context of cell complexes. Forman's definition, in its turn, is based on the Bochner-Weitzenbock identity: A fundamental identity in Riemannian Geometry that couples the Laplace-Beltrami operator, the Bochner Laplacian and a curvature term. It is shown that the Ricci flow preserves image structure better than other state-of-the-art image enhancement schemes. The implementation of the Ricci flow is applicable also to general surfaces, such as required in computer graphics and other applications.

Joint work with Yehoshua Y. Zeevi and Emil Saucan.

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