Bernstein basis function (BBF) network for surface reconstruction

George K. Knopf; Xiao-Gang Guo

doi:10.1117/12.269772

Abstract

Reverse engineering is the process of generating accurate three-dimensional CAD models from measured surface data. The coordinate data is segmented and then approximated by numerous parametric surface patches for an economized CAD representation. Most parametric surface fitting techniques manipulate large non-square matrices in order to interpolate all points. Furthermore, the interpolation process often generates high-order polynomials that produce undesirable oscillations on the reconstructed surface. The Bernstein basis function (BBF) network is an adaptive approach to surface approximation that enables a Bezier surface to be reconstructed from measured data with a pre-determined degree of accuracy. The BBF network is a two-layer architecture that performs a weighted summation of Bernstein polynomial basis functions. Modifying the number of basis neurons is equivalent to changing the degree of the Bernstein polynomials. An increase in the number of neurons will improve surface approximation, however, too many neurons will greatly diminish the network's ability to correctly interpolate the surface between the measured points. The weights of the network represent the control points of the defining polygon net used to generate the desired Bezier surface. The location of the weights are determined by a least-mean square (LMS) learning algorithm. Once the learning phase is complete, the weights can be used as control points for surface reconstruction by any CAD/CAM system that utilizes parametric modeling techniques.

Citation Download Citation

George K. Knopf, George K. Knopf, Xiao-Gang Guo, Xiao-Gang Guo, } "Bernstein basis function (BBF) network for surface reconstruction", Proc. SPIE 3030, Applications of Artificial Neural Networks in Image Processing II, (1 April 1997); doi: 10.1117/12.269772; https://doi.org/10.1117/12.269772

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