SUPPORT VECTOR MACHINE SOLVING FREEFORM CURVE AND SURFACE RECONSTRUCTION PROBLEM

Abstract

Reconstruction of mathematically unknown freeform curve and surface is of paramount importance for reverse engineering. This problem belongs to a regression problem, but there is a particular requirement, namely the curve and surface have to be smooth. Support vector machine (SVM) is a new and powerful method for the regression problem. However, the fitting results of SVM are usually not smooth enough due to its sensitivity to outliers or noises. In this paper, a modified version, called as smooth support vector machine (S-SVM), is proposed. The new version treats the training points differently by constructing their penalty factors based on the smooth degree, so smooth regression curve and surface can be obtained. In order to compare this new version with SVM, numerical experiments on both curve and surface fitting are given, which show clearly the improvements.