Super-resolving multiresolution images with band-independant geometry of multispectral pixels

A new resolution enhancement method is presented for multispectral and multi-resolution images, such as these provided by the Sentinel-2 satellites. Starting from the highest resolution bands, band-dependent information (reflectance) is separated from information that is common to all bands (geometry of scene elements). This model is then applied to unmix low-resolution bands, preserving their reflectance, while propagating band-independent information to preserve the sub-pixel details. A reference implementation is provided, with an application example for super-resolving Sentinel-2 data.Comment: Source code with a ready-to-use script for super-resolving Sentinel-2 data is available at http://nicolas.brodu.net/recherche/superres

Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification added, typos corrected, to appear in JHE

Asymptotics of random Betti tables

The purpose of this paper is twofold. First, we present a conjecture to the effect that the ranks of the syzygy modules of a smooth projective variety become normally distributed as the positivity of the embedding line bundle grows. Then, in an attempt to render the conjecture plausible, we prove a result suggesting that this is in any event the typical behavior from a probabilistic point of view. Specifically, we consider a "random" Betti table with a fixed number of rows, sampled according to a uniform choice of Boij-Soderberg coefficients. We compute the asymptotics of the entries as the length of the table goes to infinity, and show that they become normally distributed with high probability

Species and Strings

Based on well-known properties of semi-classical black holes, we show that weakly-coupled string theory can be viewed as a theory of N = 1/g_s^2 particle species. This statement is a string theoretic realization of the fact that the fundamental scale in any consistent D-dimensional theory of gravity is not the Planck length l_D, but rather the species scale L_N = N^1/(D-2) l_D. Using this fact, we derive the bound on semi-classical black hole entropy in any consistent theory of gravity as S > N, which when applied to string theory provides additional evidence for the former relation. This counting also shows that the Bekenstein-Hawking entropy can be viewed as the entanglement entropy, without encountering any puzzle of species. We demonstrate that the counting of species extends to the M-theory limit. The role of the species scale is now played by the eleven-dimensional Planck length, beyond which resolution of distances is gravitationally-impossible. The conclusion is, that string theory is a theory of species and gets replaced by a pure gravitational theory in the limit when species become strongly coupled and decouple.Comment: 20 page

The Right (Angled) Perspective: Improving the Understanding of Road Scenes Using Boosted Inverse Perspective Mapping

Many tasks performed by autonomous vehicles such as road marking detection, object tracking, and path planning are simpler in bird's-eye view. Hence, Inverse Perspective Mapping (IPM) is often applied to remove the perspective effect from a vehicle's front-facing camera and to remap its images into a 2D domain, resulting in a top-down view. Unfortunately, however, this leads to unnatural blurring and stretching of objects at further distance, due to the resolution of the camera, limiting applicability. In this paper, we present an adversarial learning approach for generating a significantly improved IPM from a single camera image in real time. The generated bird's-eye-view images contain sharper features (e.g. road markings) and a more homogeneous illumination, while (dynamic) objects are automatically removed from the scene, thus revealing the underlying road layout in an improved fashion. We demonstrate our framework using real-world data from the Oxford RobotCar Dataset and show that scene understanding tasks directly benefit from our boosted IPM approach.Comment: equal contribution of first two authors, 8 full pages, 6 figures, accepted at IV 201