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Closed-Form Solutions for Physically Based Shape Modeling and Recognition
July 1991 (vol. 13 no. 7)
pp. 715-729

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.

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Index Terms:
shape recognition; picture processing; pattern recognition; shape modeling; 3-D surface; rotational symmetries; finite element method; solid modeling; parametric modeling; object-recognition; finite element analysis; pattern recognition; picture processing; solid modelling
A. Pentland, S. Sclaroff, "Closed-Form Solutions for Physically Based Shape Modeling and Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 715-729, July 1991, doi:10.1109/34.85660
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