<title>3D range image surface description via least squares surface fitting</title>

Abstract

Geometrical description of object surface for 3D range image provides useful invariant features if the necessary first- and second-order partial derivatives are accurately estimated. Two main methods are used in this study to approximate the partial derivatives. One method uses convolutions between derivative operators and range data. The other method is based on local least squares surface fitting. In this report a least squares surface fitting method based on a set of orthogonal polynomials is introduced to extract the desired 3D surface geometrical features. Given a point and its adjacent points, a local least squares surface model using discrete orthogonal polynomials is obtained. The partial derivatives along with the curvatures of the local surface are then computed according to the polynomial functions. The polynomial parameters are also used as the 3D features to describe the local surface. The experiments show that all of the partial derivatives and the polynomial parameters can be used as surface description features for classification and recognition of 3D objects in range images.