<title>Recognition of free-form shapes using spherical SOFMs</title>

Abstract

Recognition of free-form objects is a difficult task in a variety of engineering applications such as reverse engineering and product inspection. Most recognition systems can handle polyhedral objects that are defined by a set of primitives such as vertices, edges, or planar faces. However, free-form shapes have curved surfaces and often lack identifiable markers such as corners or sharp discontinuities. This paper presents a novel approach to creating structured representations of free-form surfaces that can be used for object recognition. The proposed method maps the three-dimensional coordinate data acquired by a range sensor onto a spherical self-organizing feature map (SOFM). The adaptation algorithm of the SOFm develops a topological order to the measured coordinate data such that connected nodes on the spherical map represent neighboring points on the object surface. Features are then extracted at each node of the SOFM. The feature vector is computed using a simple function that relates the node's positional vector to each of its neighboring nodes, within a circular are of one unit radius, in the SOFM. The feature vectors are used to establish a correspondence between the spherical map generated by an unknown free-form shape and maps of all the reference models. Any two free-form shapes can be matched for recognition purposes by registering the spherical SOFMs and determining the minimum registration error. This approach enables the unknown object to be in an arbitrary orientation. An experimental study is presented in order to demonstrate the effectiveness of this approach. The spatial coordinate data of a human foot and a toy in the shape of a pelican are used for illustrative purposes.