Surface reconstruction using robust backpropagation

Abstract

Conventional surface reconstruction methods often either require segmenting data into regions corresponding to piecewise smooth surface patches prior to reconstruction, or have difficulties in preserving discontinuities as well as removing severe noise effects such as outliers. The authors propose a new surface reconstruction method using multilayer feedforward neural networks. The parametric form represented by multilayer neural networks can model piecewise smooth surfaces in a way that is more general and flexible than many of the classical methods. The new approximation method is based upon a robust backpropagation (BP) algorithm, which is resistant to the noise effects and is capable of rejecting gross errors during the approximation process. The spirit of this algorithm comes from the pioneering work in robust statistics by Huber and Hampel. The authors' work is different from that of M-estimators in two aspects: (1) the shape of the objective function changes with the iteration time. (2) The parametric form of the functional approximator is no longer linear. In contrast to the conventional BP algorithm, three advantages of the robust BP algorithm are: (1) it approximates an underlying mapping rather than interpolating training samples; (2) it is robust against gross errors; and (3) its rate of convergence is improved since the influence of incorrect samples is gracefully suppressed. >