Character motion in function space

We address the problem of animated character motion representation and approximation by introducing a novel form of motion expression in a function space. For a given set of motions, our method extracts a set of orthonormal basis (ONB) functions. Each motion is then expressed as a vector in the ONB space or approximated by a subset of the ONB functions. Inspired by the static PCA, our approach works with the time-varying functions. The set of ONB functions is extracted from the input motions by using functional principal component analysis and it has an optimal coverage of the input motions for the given input set. We show the applications of the novel compact representation by providing a motion distance metric, motion synthesis algorithm, and a motion level of detail. Not only we can represent a motion by using the ONB; a new motion can be synthesized by optimizing connectivity of reconstructed motion functions, or by interpolating motion vectors. The quality of the approximation of the reconstructed motion can be set by defining a number of ONB functions, and this property is also used to level of detail. Our representation provides compression of the motion. Although we need to store the generated ONB that are unique for each set of input motions, we show that the compression factor of our representation is higher than for commonly used analytic function methods. Moreover, our approach also provides lower distortion rate.