<title>Object recognition using an efficient technique for aligning quadric surfaces</title>

Abstract

Pose and orientation of an object are central issues in 3-D recognition problems. Most of today's available techniques require considerable pre-processing, such as detecting edges or joints, fitting curves or surfaces to segment images, and trying to extract higher order features from the input images. In this paper we present a method based on analytical geometry, whereby all the rotation parameters of any quadric surface are determined and subsequently eliminated. This procedure is iterative in nature and has been found to converge to the desired results in as few as three iterations. The approach enables us to position the quadric surface in a desired coordinate system, then, utilize the presented shape information to explicitly represent and recognize the 3-D surface. Experiments were conducted with simulated data for objects such as hyperboloid of one and two sheets, elliptic and hyperbolic paraboloid, elliptic and hyperbolic cylinders, ellipsoids, and quadric cones. Real data of quadric cones and cylinders were also utilized. Both of these sets yielded excellent results.