Shape from Occluding Contours: a Regularization Method

Abstract

This paper deals with the problem of 3D shape reconstruction from the occluding contours extracted in a set of 2D perspective views acquired by a TV camera. Since the reconstruction implies inverting the perspective equations, the problem is intrinsecally ill-conditioned and therefore very sensitive to errors in the input data. The attention is focused here on the errors coming from imperfect calibration of the extrinsic camera parameters, i.e. viewpoint position and optical axis orientation. Since the shape is recovered by intersecting the generalized cones generated by backprojecting the object silhouettes from each viewpoint, errors on position and orientation of the cones yield wrong intersections and therefore poor reconstruction. The proposed regularization method is based on a simple geometrical constraint concerning the spatial relationship among the cones. It manipulates the six extrinsic parameters of each view to minimize a suitable error function, measured on the projection planes of the views. The technique is described, along with an implementation algorithm, and its performances are illustrated in terms of robustness and quality improvements in both extensive simulation tests and real world reconstructions. A technique to improve the quality of the reconstructed model is also presented, based on the construction of a suitable surface model of the object.