Closed-form solutions for physically-based shape modeling and recognition

We present a closed-form, physically based solution for recovering a 3-D solid model from collections of 3-D surface measurements. Given a sufficient number of independent measurements, the solution is overconstrained and unique except for rotational symmetries. We then present a physically based objectrecognition method that allows simple, closed-form comparisons of recovered 3-D solid models. The performance of these methods is evaluated using both synthetic range data with various signalto-noise ratios and using laser rangefinder data.