please see my MIT page for up-to-date information
3D Boundary Reconstruction from Multiple Views
- “Reconstruction of Objects with Jagged Edges through Rao-Blackwellized Fitting of Piecewise Smooth Subdivision Curves” by M. Kaess and F. Dellaert. In Proceedings of the IEEE 1st International Workshop on Higher-Level Knowledge in 3D Modeling and Motion Analysis, (Nice, France), Oct. 2003, pp. 39-47. Details. Download: PDF.
- “MCMC-based Multiview Reconstruction of Piecewise Smooth Subdivision Curves with a Variable Number of Control Points” by M. Kaess, R. Zboinski, and F. Dellaert. In Eur. Conf. on Computer Vision, ECCV, (Prague, Czech Republic), May 2004, pp. 329-341. Acceptance ratio 34.2% (190 of 555). Details. Download: PDF.
Given a set of images of an object we want to fit a 3D curve to the
boundary of the object. The cameras are calibrated using standard
computer vision approaches, based on the calibration pattern partially
visible in the background.
We use subdivision curves as a powerful curve
representation. Depending on an averaging mask, different types of
curves can be generated that range from B-splines to fractals.
Tagging allows easy modeling of non-smooth features by locally using a
different averaging mask.
We use a generative model and define the likelihood function based on
the Chamfer distance, that can efficiently be precalculated.
Because of the huge combined space of continuous 3D control point
locations and discrete taggings, we choose to sample from the
posterior distribution. Rao-Blackwellization makes efficient sampling
possible by integrating out the continuous part of the state space.
We do not know how many control points are needed to represent the
outline sufficiently well, i.e. we are faced with a model selection
problem. A reversible-jump Markov chain Monte Carlo sampler solves
this problem by allowing adding and removing of control points.
No manual interaction is needed in this process, as the object is
automatically segemented from the calibration background by a Markov
Random Field approach.
We visualize the development of the 3D curve by reprojecting it into three
different views (columns). Note that we show the initial guess
(circular configuration of the control points), and the fifth and
250th sample, while the complete set of samples approximates the
posterior distribution and can for example be used to obtain