Let X be a projective scheme over a field. We show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the Frobenius morphism. We also compare various definitions of ample locally free sheaf and show that the vanishing given by the Frobenius morphism is, in a certain sense, the strongest possible. Our work can be viewed as various...

Inversion of the perspective mapping in acquired images enables an autonomous vehicle to perform vision-based navigation tasks, such as obstacle detection. We present work on affine rectification that restores the parallel property of a traffic lane, using the vanishing point of equally spaced parallel lane boundaries. Experimental results demonstrate the potential of our new algorithm.

In [16], Córdoba, Córdoba, and Fontelos proved that for some initial data, the following nonlocaldrift variant of the 1D Burgers equation does not have global classical solutions ∂tθ + u ∂xθ = 0, u = Hθ, where H is the Hilbert transform. We provide four essentially different proofs of this fact. Moreover, we study possible Hölder regularization effects of this equation and its consequences to t...

We consider compactifications of (Pn)3\ ⋃ ∆ij , the space of triples of distinct points in projective space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson; and a third is the triangle space of Schubert and Semple. We compute the sections of line bundles on these spaces, and show that they are equal as ...

Linear perspective is widely used in landscape photography to create the impression of depth on a 2D photo. Automated understanding of the use of linear perspective in landscape photography has a number of real-world applications, including aesthetics assessment, image retrieval, and on-site feedback for photo composition. We address this problem by detecting vanishing points and the associated...

In this paper, we give a new vanishing point detection algorithm, called the normalized unit sphere. By normalizing homogeneous coordinates in the original image space, we transform image points onto a normalized unit sphere. Further, we transform straight lines in image space into circles on normalized unit sphere. As a result, the vanishing point detection is implemented by searching the inte...

4 Captions Table 1. Angular displacements of a camera which is rotated of a xed amount around an axis orthogonal to the image plane between consecutive frames: the rst row reports angular displacements as measured with a goniome-ter, whilst the second row refers to computed values from vanishing points. Fig. 1. Extraction of vanishing points. a) A corridor at IRST; b) edges approximated by stra...