Direct Surface Fitting

In this paper, we propose a new method for estimating the shape of a surface from visual input. Assuming a parametric model of a surface, the parameters best explaining the perspective changes of the surface between different views are estimated. This is in contrast to the usual approach of fitting a model into a 3-D point cloud, generated by some previously calculated local correspondence matching method. The main ingredients of our approach are formulas for a perspective mapping of parametric 3-D surface models between different camera views. Model parameters are estimated using the Hooke-Jeeves optimization method, which works without the derivative of the objective function. We demonstrate our approach with models of a plane, a sphere and a cylinder and show that the parameters are accurately estimated.

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