3D Modeling with Support Vector Machines

Montilla G, Bosnjak A, Palu

Abstract

We developed a new approach based on Support Vector Machines (SVM) to model solids defined by a set of points on their surface. In problems of classification, regression and support of distribution, SVM are focused in the hyper-planes of maximum margin in the feature space. However, the forms that could be described by these surfaces when they return to the input space have not been studied in depth. In this paper, these surfaces are used to model complex objects, connected or non- connected, with a great amount of points, in order of tens of thousands, and with various topologies (hollow, branches, etc.). Two constrains were kept: 1) The use of traditional algorithms of SVM theory; and 2) The design of the appropriate training sets from the object. This combination produced a novel tool and the results obtained illustrated the potential of the proposed method. Therefore, this new application of SVM of Vapnik is capable of creating surfaces of decision and estimation functions, which are well fitted to objects of complex topology.