Closed-form solutions for physically based shape modeling and recognition

The authors present a closed-form, physically based solution for recovering a three-dimensional (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. The proposed approach is based on the finite element method (FEM) and parametric solid modeling using implicit functions. This approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and, in addition, can provide great accuracy at physical simulation. A physically based object-recognition method that allows simple, closed-form comparisons of recovered 3-D solid models is presented. The performance of these methods is evaluated using both synthetic range data with various signal-to-noise ratios and using laser rangefinder data