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If the inaccuracy of image point due to discrete distribution of pixels is taken into account, the total measuring error is about five millimeters. 2 Projection Model Fig. 2 depicts the full imaging model of a perspective camera with two hyperbolic mirrors. There are three essentially coordinate systems. O c2 Zw ǹ2 M1 O c1 ǹ1 M2 ZC (u1,v1(u ) 2,v2) (u0,v0) Image plane OC Yc XC OW(Fo) Yw Xw P(xp,yp,zp) Figure 2. The projection model of the omnidirectional stereo vision system. There are transformations between the camera coordinate system and the mirror (or world) coordinate system 1.

2006), the provided results could be understood as a piecewise planar approximation, due to the fact that road and camera parameters are continuously computed and updated. Note that since on-board vision system pose is related to the current 3D road plane, camera position and orientation are equivalent to the 3D road plane parameters⎯3D plane parameters are expressed in the camera coordinate system. The proposed technique could be indistinctly used for urban or highway environments, since it is not based on a specific visual traffic feature extraction but on raw 3D data points.

The ζ subset of points gathers all the 3D points mapped onto those cells. 3 RANSAC based plane fitting The outcome of the previous stage is a subset of points, ζ, where most of them belong to the road. In the current stage a RANSAC based technique (Fischler & Bolles, 1981) is used for fitting a plane to those data2, ax+by+cz=1. In order to speed up the process, a predefined threshold value for inliers/outliers detection has been defined (a band of ±5cm was enough for taking into account both 3D data point accuracy and road planarity).

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