General Construction of Time-Domain Filters for Orientation Data

Capturing live motion has gained considerable attention in computer animation as an important motion generation technique. Canned motion data comprise both position and orientation components. Although a great deal of signal processing methods are available for manipulating position data, the majority of these methods cannot be generalized easily to orientation data due to the inherent non-linearity of the orientation space. In this paper, we present a new scheme that enables us to apply a filter mask (or a convolution filter) to orientation data. The key idea is to transform the orientation data into their analogues in a vector space, to apply a filter mask on them, and then to transform the results back to the orientation space. This scheme gives time-domain filters for orientation data that are computationally efficient and satisfy such important properties as coordinate-invariance, time-invariance, and symmetry. Experimental results indicate that our scheme is useful for various purposes including smoothing and sharpening. Keywords— Orientation and Rotation, Unit quaternions, Motion signal processing, LTI filters, Convolution filters, Coordinate-invariance, Timeinvariance.