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Separable Spatiotemporal Priors for Convex Reconstruction of Time-Varying 3D Point Clouds
Tomas Simon1, Jack Valmadre2, 3, Iain Matthews4, 1, and Yaser Sheikh1
1Carnegie Mellon University, USA
tsimon@cs.cmu.edu
yaser@cs.cmu.edu
2Queensland University of Technology, Australia
j.valmadre@qut.edu.au
3Commonwealth Scientific and Industrial Research Organisation, Australia
4Disney Research Pittsburgh, USA
iainm@cs.cmu.edu
Abstract. Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results 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.
Keywords: Matrix normal, trace-norm, spatiotemporal, missing data
LNCS 8691, p. 204 ff.
lncs@springer.com
© Springer International Publishing Switzerland 2014