Computing 3d Road Shape From Images For A Challenge To An ill-posed Problem

A new algorithm is presented for reconstructing the 3D road shape from camera images for the purpose of navigating auto- nomous land vehicles (ALVs). The approximation that the road sur- face is locally flat enables us to determine a one-to-one correspon- dence between the two road boundaries, which in tum determines the 3D road shape. In order to cope with inaccuracy of image data, a least-square curve fitting technique is proposed with error behaviors taken into account. Examples based on real images are shown, and the role of heuristics is discussed. et al. (15) proposed a parametric fitting approach by preparing several prototypes of the 3D road shape. Kanatani, et al. 181 proposed a differential approach, describing the constraints that ideal roads should satisfy in terms of differential equations and reconstructing the 3D road shape by numerically integrating them. The solution is very robust to noise even in the distant part of the road. The discrete approach of DeMenthon (3) and the differential approach of Kanatani, et al. (8) both suffer the same problem: Computational error grows rapidly in the course of reconstruc- tion due to inaccuracy of the original image data and approxi- mations involved in the scheme. Recently, DeMenthon 141 pro- posed a new scheme based on the assumption that the road is locally Jrat and showed that the solution can be determined point-wise. As a result, one part of the solution is not affected by the error involved in other parts of the solution. At the same time, however, this local determination destroys the global consistency of the solution; locally constructed solutions can be inconsistent with each other. DeMenthon (6) proposed the use of dynamic programming to search for a globally consistent solution, but there is no guarantee that such a solution exists. In this paper, we incorporate the viewpoint of projective