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Section: New Results

Dimensionality reduction for character animation

Participants : Maxime Tournier, Lionel Reveret.

This work investigates and proposes a mathematical framework to perform statistical analysis and dimensionality reduction on rotational trajectories derived from motion capture data. Motion capture data consists in a set of trajectories in the space of 3D rotations (SO(3)) and as such do not present properties of an Euclidian space. Consequently there is no easy to way to apply standard dimensionality reduction techniques on these data. Using the formalism of exponential maps and Principle Geodesics Analysis (PGA), it has been shown that it is possible to rigorously derive a dimensionality reduction analysis on such data. This reduction can be typically applied for compression of motion capture data and probabilistic implementation of the Inverse Kinematics problem. This approach has shown good properties in the context of physically-based animation with a Lagrangian formulation of rigid body dynamics coupled with geometric integrators. These integrators allow a good preservation of momentum using only first order equations, achieving both real-time and high level of realism. These works were developed through the PhD thesis of Maxime Tournier [4] . Early development of PGA on motion capture data had been published at Eurographics in 2009. Its integration into a GPLVM framework has been published this year in the IEEE CG&A journal [9] . Its extension into the context of physically-based animation is currently under preparation for publication.

Figure 8. Inverse Kinematics and motion synthesis using PGA of motion capture data.