A Coordinate-Invariant Approach to Multiresolution Motion Analysis

Multiresolution motion analysis has gained great research interest as a unified framework to facilitate a variety of motion editing tasks. In this framework, motion data are represented as a collection of coefficients that form a coarse-to-fine hierarchy. The coefficients at the coarsest level describe the global pattern of a motion signal, while those at fine levels provide different details at successively finer resolutions. Due to the inherent non-linearity of the orientation space, it is challenging to generalize multiresolution representations for motion data that contain orientations as well as positions. Our goal is to develop a multiresolution analysis method which guarantees coordinate-invariance without any singularity. To do so, we employ two novel ideas, that is, hierarchical displacement mapping and motion filtering. The notion of hierarchical displacement mapping provides an elegant formulation to describe positions and orientations in a coherent manner. With the motion filters, we are able to separate motion details level-by-level to build a multiresolution representation in a coordinate-invariant way. Our representation facilitates multiresolution motion editing through level-wise coefficient manipulation to uniformly address issues raised by motion modification, blending, and stitching.