3-D localization and feature recovering through CAD-based stable pose calculation Shang-Tae Yee, Wenhua Wan, Jose A. Ventura * Department of Industrial and Manufacturing Engineering, 356 Leonhard Building, The Pennsylvania State University, University Park, Pennsylvania, PA 16802, USA Received 10 March 1999; received in revised form 30 August 2000 Abstract CAD-based computer vision methodologies have been used in practice for simplifying the process of geometric inspection. In general, it can be assumed that a three-dimensional (3-D) object lying on a planar surface has a ®nite number of stable poses. These poses precisely determine all feasible positions and orientations of an object, and can be utilized for localization and accurate shape matching. In this paper, procedures are proposed to eciently determine all stable poses of piecewise smooth curved 3-D objects, and to perform 3-D localization and feature recovering. The stable pose determination process is based on a faceted approximation of the associated CAD model built by a CAD solid modeling package. Localization and feature recovering calculations are derived from Lowe's method. Several real 3-D objects are presented to illustrate the proposed methodology. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Stable pose; Faceted approximation; Localization; Feature recovering; Geometric inspection 1. Introduction An object's pose usually represents the rigid body transformation between the object frame (o; x; y ; z) and the world frame O; X ; Y ; Z . Throughout this paper, the world frame represents the frame of a vision system de®ned by the camera and the plane supporting the object. The pose of an object is speci®ed by its position and orienta- tion. Generally, it can be assumed that a three- dimensional (3-D) object has only a ®nite set of stable poses. When an object is in a stable position resting on a supporting plane (e.g., a table top or a belt conveyor), the potential energy of the object becomes a local minimum. Knowing all stable poses of an object is useful for many tasks in machine vision and robotics, including recognition and localization and grasp planning. Camps et al. (1991) used the geometric information of the stable poses of objects with planar surfaces along with the knowledge of the surface re¯ectance proper- ties, light sources, sensors, and image processing operators to symbolically predict the features that will appear on the images of the objects in their object recognition/localization system. Wiegley et al. (1992) presented a method for estimating the distribution of stable poses in a stream of identical polyhedral parts that are randomly dropped under quasi-static conditions. Kriegman (1997) analyzed www.elsevier.nl/locate/patrec Pattern Recognition Letters 22 (2001) 105±121 * Corresponding author. Tel.: +1-814-865-3841; fax: +1-814- 863-4745. E-mail address: jav1@psu.edu (J.A. Ventura). 0167-8655/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 6 5 5 ( 0 0 ) 0 0 0 8 7 - 8