We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown height. The local ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to dielectric objects exhibiting diffuse and specular reflectance, though lighting and albedo must be known. We relax this requirement by showing that either spatially varying albedo or illumination can be estimated from the polarisation image alone using nonlinear methods. In the case of illumination, the estimate can only be made up to a binary ambiguity which we show is a generalised Bas-relief transformation corresponding to the convex/concave ambiguity. We believe that our method is the first passive, monocular shape-from-x technique that enables well-posed height estimation with only a single, uncalibrated illumination condition. We present results on real world data, including in uncontrolled, outdoor illumination.

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations.

Aims.We present a comprehensive analysis of the performance of noise-reduction (denoising) algorithms to determine whether they provide advantages in source detection, mitigating noise on extragalactic survey images.Methods.The methods we analyze here are representative of different algorithmic families: Perona-Malik filtering, bilateral filter, total variation denoising, structure-texture image decomposition, non-local means, wavelets, and block-matching We tested the algorithms on simulated images of extragalactic fields with resolution and depth typical of theHubble,Spitzer, andEuclidSpace Telescopes, and of ground-based instruments. After choosing their best internal parameters configuration, we assessed their performance as a function of resolution, background level, and image type, in addition to testing their ability to preserve the objects fluxes and shapes. Finally, we analyze, in terms of completeness and purity, the catalogs that were extracted after applying denoising algorithms on a simulatedEuclidWide Survey VIS image and on real H160 andK-band (HAWK-I) observations of the CANDELS GOODS-South field.Results.Denoising algorithms often outperform the standard approach of filtering with the point spread function (PSF) of the image. Applying structure-texture image decomposition, Perona-Malik filtering, the total variation method by Chambolle, and bilateral filtering on theEuclid-VIS image, we obtain catalogs that are both more pure and complete by 0.2 magnitude than those based on the standard approach. The same result is achieved with the structure-texture image decomposition algorithm applied on the H160 image. The relative advantage of denoising techniques with respect to PSF filtering rises with increasing depth. Moreover, these techniques better preserve the shape of the detected objects with respect to PSF smoothing.Conclusions.Denoising algorithms provide significant improvements in the detection of faint objects and enhance the scientific return of current and future extragalactic surveys. We identify the most promising denoising algorithms among the 20 techniques considered in this study.

In this paper, we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representatio...