Abstract

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as pro jection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spa- tiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separa- ble and compact row and column covariances. We relate the marginals of the distribution to the shape, tra jectory, and shape-tra jectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes re- sults in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.