Shape Analysis on Lie Groups with Applications in Computer Animation

Abstract

Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher dimensional curves, surfaces, activities, character motions and many other objects. In this paper, we develop a framework for shape analysis of curves in Lie groups for problems of computer animations. In particular, we will use these methods to find cyclic approximations of non-cyclic character animations and interpolate between existing animations to generate new ones.

37 pages, 7 figures, v4: Major revision, corrected typos, simplified and clarified arguments, main results remain unchanged

References in corpus (4)

• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance
• Precise Matching of PL Curves in $R^N$ in the Square Root Velocity Framework
• Fundamentals of submersions and immersions between infinite-dimensional manifolds

Cited by in corpus (14)

• Geomstats: A Python Package for Riemannian Geometry in Machine Learning
• Sobolev metrics on spaces of manifold valued curves
• Shape analysis on homogeneous spaces: a generalised SRVT framework
• Shape analysis on Lie groups and homogeneous spaces
• Completeness of Length-Weighted Sobolev Metrics on the Space of Curves
• Representation and Characterization of Non-Stationary Processes by Dilation Operators and Induced Shape Space Manifolds
• Currents and finite elements as tools for shape space
• Deep neural networks on diffeomorphism groups for optimal shape reparameterization
• Signatures in Shape Analysis: an Efficient Approach to Motion Identification
• Manifolds of absolutely continuous curves and the square root velocity framework
• Macroscopic Single-Qubit Operation for Coherent Photons
• Comparing Curves in Homogeneous Spaces
• Shape Analysis of Surfaces Using General Elastic Metrics
• Riemannian geometry on spaces of submanifolds induced by the diffeomorphism group