MCMC-Based Multiview Reconstruction of Piecewise Smooth Subdivision Curves with a Variable Number of Control Points

Abstract

We investigate the automated reconstruction of piecewise smooth 3D curves, using subdivision curves as a simple but flexible curve representation. This representation allows tagging corners to model non- smooth features along otherwise smooth curves. We present a reversible jump Markov chain Monte Carlo approach which obtains an approxi- mate posterior distribution over the number of control points and tags. In a Rao-Blackwellization scheme, we integrate out the control point lo- cations, reducing the variance of the resulting sampler. We apply this general methodology to the reconstruction of piecewise smooth curves from multiple calibrated views, in which the object is segmented from the background using a Markov random field approach. Results are shown for multiple images of two pot shards as would be encountered in archae- ological applications.