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16 December 1988 An Error Analysis For Surface Orientation From Vanishing Points
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There are many cases in which perspective information can be used to derive three-dimensional spatial information about objects from their two-dimensional images. There are established algorithms for estimating the direction of lines and the orientation of surfaces based on their projections onto the image plane. Given two parallel lines on a plane, their projections 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 recover surface orientations via lines extracted from the image, it is necessary to put bounds on the errors while applying these constraints. Our approach involves representing line directions and surface normal vectors as points on a Gaussian sphere and computing the error bounds as regions on the sphere. Multiple constraints are combined by intersecting the corresponding regions. The starting point for computing the error bounds is an estimate of the accuracy of the lines which are extracted from the image. A mathematical analysis of the imaging geometry is used to propagate these errors to vanishing points, vanishing lines, and surface orientations. In addition, constraints based on a priori knowledge can be introduced to improve the accuracy. Some experimental results are presented to illustrate this.
© (1988) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Richard S. Weiss, Hiromasa Nakatani, and Edward M. Riseman "An Error Analysis For Surface Orientation From Vanishing Points", Proc. SPIE 0974, Applications of Digital Image Processing XI, (16 December 1988);


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