“An Introduction to Ricci Flow and Volumetric Approximation with Applications to Shape Modeling” Chaired by
Conference:
Type(s):
Title:
- An Introduction to Ricci Flow and Volumetric Approximation with Applications to Shape Modeling
Presenter(s)/Author(s):
Abstract:
Extending a shape-driven map to the interior of the input shape and to the surrounding volume is a difficult problem since it typically relies on the integration of shape-based and volumetric information, together with smoothness conditions, interpolating constraints, preservation of feature values at both a local and global level. This survey discusses the main volumetric approximation schemes for both 3D shapes and d-dimensional data, and provides a unified discussion on the integration of surface-based and volume-based shape information. Then, it describes the application of shape-based and volumetric techniques to shape modeling through volumetric parameterization and polycube splines; feature-driven approximation through kernels and radial basis functions. We also discuss the Hamilton’s Ricci flow, which is a powerful tool to compute the conformal shape structure and to design Riemannian metrics of manifolds by prescribed curvatures. We conclude the presentation by discussing applications to shape analysis and medicine.
Additional Information:
Level
Advanced
Prerequisites
Knowledge about differential geometry, mesh processing, function approximation.
Intended Audience
The target audience of this tutorial includes graduate students and researchers interested in Riemannian geometry, spectral geometry processing, and implicit modeling.
