Volumetric Shapes of Solids of Revolution from a Single-View Range Image

Many man-made objects such as industrial parts are partially constructed of surfaces of revolution, as well as planar surfaces. We have studied the problem of finding and recovering solids of revolution in range data which are potentially useful for modeling and recognizing 3D objects. We propose an approach to the problem which is based on the fact that at least one of two focal surfaces for a surface of revolution degenerates into the axis of rotation. First, by computing the surface normal and principal curvatures, the centers of principal curvature which construct the focal surfaces are obtained for each point in the range image. Then, using the Hough transform, the axes of rotation are detected by finding the centers of principal curvature which lie on straight lines in space. Finally, the solid of revolution is completely determined by estimating the radius function of cross-section along each rotational axis. The proposed method can be used even in situations where occlusion or truncation is a problem because it does not require the visibility of entire surfaces. Experiments have been successfully carried out with real range data obtained from laser rangefinders.