In conventional methods for detecting vanishing points and vanishing lines, the observed feature points are clustered into collections that represent different lines. The multiple lines are then detected and the vanishing points are detected as points of intersection of the lines. The vanishing line is then detected based on the points of intersection. However, for the purpose of optimization, ...

For any complex reductive connected Lie group G, many of the structure constants of the ordinary cohomology ring H(G/B;Z) vanish in the Schubert basis, and the rest are strictly positive. We present a combinatorial game, the “root game”, which provides some criteria for determining which of the Schubert intersection numbers vanish. The definition of the root game is manifestly invariant under a...

In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short paths during training. To support this observation, we rewrite residual networks as an explicit collection of paths. Unlike traditional models, paths through...

We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to plane. It is shown that affine scene structure may then be determined from the image, without knowl...

The absolute conic is the key for recovering the Euclidean structure in 3-D space. The image of the absolute conic can be parametrized by the set of three vanishing points corresponding to orthogonal directions in space with two independent additional factors. Whereas a single plane to image homography only allows the image to inherit two vanishing points and one of these factors, we describe a...

This paper presents a vehicle occlusion identification system based on the perceptive characters of a roadway. To tracking the vehicles, two stages are devised, initial parameter setting stage and occlusion handling stage. In the initial stage, a background extracting method is adopted to obtain the first clean background. Then, a road detection algorithm is used for finding the vanishing point...