Automatic extraction of CAD descriptions which are ultimately intended for human manipulation requires the accurate inference of geometric and topological information. We present a system which applies segmentation techniques from computer vision to automatically extract CAD models from range images of parts with curved surfaces. The segmentation process is an improvement upon Besl and Jain's variable-order surface fitting (IEEE PAMI, 1988, 10(2), 167-192), extracting general quadric surfaces and planes from the data, with a postprocessing stage to identify surface intersections and to extract a B-rep from the segmented image. We present results on a variety of machined objects, which illustrate the high-level nature of the acquired models, and discuss the numerical accuracy (feature sizes and separations) and the correctness of structural inferences of the system. (C) 1997 Elsevier Science Ltd.