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The two first animations present the tracking of the Dominant Vanishing Point (DVP) in the specific context of urban scenes. I assume (like all authors) that the urban scene contains sets of parallel lines oriented along the three main directions. The algorithm focuses on the DVP which is the projection in the images of the intersection of 3D parallel lines on the plane at infinity. Among the subset of edge-lines converging to the DVP, only those which are detected on the road verify the homography induced by the road plane. Considering the global assumptions, we can then segment the road area in the image in cyan with the 2 extreme painted lanes which are focus with dark green.
At the bottom,  you can see the timing diagram of the DVP coordinates in left red and right green images. Two Kalman filters are used to obtain a prediction of the location of the DVPs and the painted lanes and to smooth the variations of the estimations.

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The third animation shows the same video-sequence with the matching of coplanar feature points detected in the couple of stereo images.
At the top, the feature points are discriminated with their contribution to the Super-Homography estimation :
  • green : verify all the Super-Homography constraints,
  • orange : one projection of the feature point is missing in one view of the current images,
  • red : the both projections of the feature point are missing in the views of the current images,
  • pink : do not verify all the Super-Homography constraints,
  • yellow : only verify the homography between the current stereo views.
At the bottom, the decomposition of the stereo-rig geometry assuming generic matrix of intrinsic parameters for the both cameras and a z-ordinate fixed at 1.2m. Dashed line between the 2 camera means that the relative pose of the right camera in the left camera framework, computed from the stereo homography, is fixed with nominal value. The white vector represents the vertical normal of plane which induces homographies.
On the right, a 2D trajectography of the left camera is computed, assuming the integration of the estimated motion between two consecutive views.

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The methodology is particularly weel-adapted to the typical configuration of urban environments where the localization with GPS is impossible due to the vertical planes which limit the clear view of the horizon. The images are segmented in 3 parts : the road plane in cyan and 2 others in light yellow assumed as vertical planes. A super-homography is computed on each region: the regions in brown represent parts of the scene where the feature points are not coplanar, they contain obstacles. I have now to merge the estimations of the stereo-rig induced by each plane to improve the robustness of the method and make easy the 2.5D reconstruction of the environment.

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The Inverse Perspective Mapping (IPM) transformation can be computed from two parallel lines which are lying on the same plane. Thanks to the tracking of the DVP, computed with the cyan road markers, the IPM transformation can be viewed as a homography, where the four red points, which represent the green foreground of the road plane, will form a parallelogram in the bird-eye view. While the camera calibration is unknown, the warped image is dependant of two scale factors along the u-axis and v-axis. In the animations, we suppose that the road has a constant width, the lateral position and the orientation of the camera can also be estimated with a novel scale-factor uncertainty.

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Thanks to the reliability and the precision of the homography computed with the Super-Homography, an obstacle detection task can be processed. We also consider the homography between the left and right image, induced by the road plane. Only the features which are lying on the plane are correctly reprojected in the other image, according to correlation and spatial criteria. We hence discriminate the green coplanar edges from the red other which represent obstacles. On the right, the IPM view allows a polar map of the free-space in front of the vehicle.

Reconstruction of the road plane

One of the application of the localization of the vehicle with the purposed method is the reconstruction of the road plane. The right image show a bird-eye view of the road followed by the test-vehicle during a sequence recorded in a sloppy street, near the Castel of Versailles. The compound image is made of the superimposure of 312 images of the right camera, joint by the estimated homography, induced by the road plane.
In the middle, some samples of the images used to create the bird-eye viewed image. The field of view is clear along the sequence (< 400 m). The trajectography of the vehicle is a straighted motion during abroad 300 m with a change of lane at the end.

The default of reconstruction at the end of the sequence is mainly due to the lack of feature points extracted in the single lane observed during the change of lane. A car actually obstructs the right lane and the road markers are solid: very few corners are extracted.

The non-straighed shape of the road on the left and right side of the hybrid image is certainly due to the images are not rectified.

All the videos sequences have been recorded thanks to the experimental vehicles of the IMARA and the LIVIC laboratories.