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<p>An abstraction-based paradigm that makes explicit the process of imposing assumptions on data is discussed. The units of abstraction are models in which levels of abstraction are determined by the degree of assumption necessary for their application. A general-to-specific refinement process provides a mechanism to proceed gracefully through the abstraction hierarchy. This strategy was applied to the recognition and pose determination of objects comprising simple and compound cylindrical and planar surfaces in dense range data. A method of computing reliable Gaussian and mean curvature sign-map descriptors from the polynomial approximations of surfaces is demonstrated. A means for determining the pose of constructed geometric forms whose algebraic surface descriptions are nonlinear in terms of their orienting parameters is developed. It is shown that biquadratic surfaces are suitable companion-linear forms for cylinder approximation and parameter estimation. The estimates provide the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data.</p>
image recognition; cylindrical surfaces; Gaussian curvature sign-map descriptors; 3-D pose determination; range images; abstraction-based paradigm; planar surfaces; mean curvature sign-map descriptors; polynomial approximations; algebraic surface descriptions; biquadratic surfaces; cylinder approximation; parameter estimation; nonlinear regression; approximation theory; image recognition; parameter estimation
R. Jain, T.E. Weymouth, F. Quek, "An Abstraction-Based Approach to 3-D Pose Determination from Range Images", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 722-736, July 1993, doi:10.1109/34.221172
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