An error analysis for surface orientation from vanishing points

Given two parallel lines in a plane, their images formed by central projection onto the viewing plane intersect at a vanishing point, which provides a constraint on the orientation of the plane. Two such independent constraints define a vanishing line and thereby determine the orientation of the plane uniquely. In order to effectively use this information, an estimate of its accuracy must be incorporated. In the approach suggested, line directions and surface normal vectors are represented as points on a Gaussian sphere, and the error bounds are computed as regions on the sphere. Information from multiple vanishing points and surfaces is combined by intersecting the corresponding regions. In addition, constraints based on real-world knowledge can be introduced to improve the accuracy. Some experimental results on natural images re presented to illustrate this method.<
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