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<p>Addresses the problems of automatically constructing algebraic surface models from sets of 2D and 3D images and using these models in pose computation, motion and deformation estimation, and object recognition. We propose using a combination of constrained optimization and nonlinear least-squares estimation techniques to minimize the mean-squared geometric distance between a set of points or rays and a parameterized surface. In modeling tasks, the unknown parameters are the surface coefficients, while in pose and deformation estimation tasks they represent the transformation which maps the observer's coordinate system onto the modeled surface's own coordinate system. We have applied this approach to a variety of real range, computerized tomography and video images.</p>
object recognition; solid modelling; algebra; deformation; geometric distance fits; 3D object modeling; 3D object modeling and recognition; algebraic surface models; automatic model construction; pose computation; motion estimation; deformation estimation; constrained optimization; nonlinear least-squares estimation techniques; mean-squared geometric distance minimization; point set; ray set; parameterized surface; unknown parameters; surface coefficients; transformation mapping; coordinate system; range images; computerized tomography images; video images; implicit algebraic surfaces

L. Sandford, S. Sullivan and J. Ponce, "Using Geometric Distance Fits for 3-D Object Modeling and Recognition," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 16, no. , pp. 1183-1196, 1994.
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