Recovering local shape of a mirror surface from reflection of a regular grid

We present a new technique to recover the shape of an unknown smooth specular surface from a single image. A calibrated camera faces a specular surface reflecting a calibrated scene (for instance a checkerboard or grid pattern). The mapping from the scene pattern to its reflected distorted image in the camera changes the local geometrical structure of the scene pattern. We show that if measurements of both local orientation and scale of the distorted scene in the image plane are available, this mapping can be inverted. Specifically, we prove that surface position and shape up to third order can be derived as a function of such local measurements when two orientations are available at the same point (e.g. a corner). Our results generalize previous work [1, 2] where the mirror surface geometry was recovered only up to first order from at least three intersecting lines. We validate our theoretical results with both numerical simulations and experiments with real surfaces

Properties of a Variable-delay Polarization Modulator

We investigate the polarization modulation properties of a variable-delay polarization modulator (VPM). The VPM modulates polarization via a variable separation between a polarizing grid and a parallel mirror. We find that in the limit where the wavelength is much larger than the diameter of the metal wires that comprise the grid, the phase delay derived from the geometric separation between the mirror and the grid is sufficient to characterize the device. However, outside of this range, additional parameters describing the polarizing grid geometry must be included to fully characterize the modulator response. In this paper, we report test results of a VPM at wavelengths of 350 microns and 3 mm. Electromagnetic simulations of wire grid polarizers were performed and are summarized using a simple circuit model that incorporates the loss and polarization properties of the device.Comment: 25 pages, 10 figures, accepted by Applied Optic

The Evolution of the Accretion Disk around 4U 1820-30 During a Superburst

Accretion from a disk onto a collapsed, relativistic star -- a neutron star or black hole -- is the mechanism widely believed to be responsible for the emission from compact X-ray binaries. Because of the extreme spatial resolution required, it is not yet possible to directly observe the evolution or dynamics of the inner parts of the accretion disk where general relativistic effects are dominant. Here, we use the bright X-ray emission from a superburst on the surface of the neutron star 4U 1820-30 as a spotlight to illuminate the disk surface. The X-rays cause iron atoms in the disk to fluoresce, allowing a determination of the ionization state, covering factor and inner radius of the disk over the course of the burst. The time-resolved spectral fitting shows that the inner region of the disk is disrupted by the burst, possibly being heated into a thicker, more tenuous flow, before recovering its previous form in ~1000 s. This marks the first instance that the evolution of the inner regions of an accretion disk has been observed in real-time.Comment: 5 pages, 2 figures, accepted by ApJ Letter

Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces

The reconstruction of a 3D object or a scene is a classical inverse problem in Computer Vision. In the case of a single image this is called the Shape-from-Shading (SfS) problem and it is known to be ill-posed even in a simplified version like the vertical light source case. A huge number of works deals with the orthographic SfS problem based on the Lambertian reflectance model, the most common and simplest model which leads to an eikonal type equation when the light source is on the vertical axis. In this paper we want to study non-Lambertian models since they are more realistic and suitable whenever one has to deal with different kind of surfaces, rough or specular. We will present a unified mathematical formulation of some popular orthographic non-Lambertian models, considering vertical and oblique light directions as well as different viewer positions. These models lead to more complex stationary nonlinear partial differential equations of Hamilton-Jacobi type which can be regarded as the generalization of the classical eikonal equation corresponding to the Lambertian case. However, all the equations corresponding to the models considered here (Oren-Nayar and Phong) have a similar structure so we can look for weak solutions to this class in the viscosity solution framework. Via this unified approach, we are able to develop a semi-Lagrangian approximation scheme for the Oren-Nayar and the Phong model and to prove a general convergence result. Numerical simulations on synthetic and real images will illustrate the effectiveness of this approach and the main features of the scheme, also comparing the results with previous results in the literature.Comment: Accepted version to Journal of Mathematical Imaging and Vision, 57 page

Separating Reflection and Transmission Images in the Wild

The reflections caused by common semi-reflectors, such as glass windows, can impact the performance of computer vision algorithms. State-of-the-art methods can remove reflections on synthetic data and in controlled scenarios. However, they are based on strong assumptions and do not generalize well to real-world images. Contrary to a common misconception, real-world images are challenging even when polarization information is used. We present a deep learning approach to separate the reflected and the transmitted components of the recorded irradiance, which explicitly uses the polarization properties of light. To train it, we introduce an accurate synthetic data generation pipeline, which simulates realistic reflections, including those generated by curved and non-ideal surfaces, non-static scenes, and high-dynamic-range scenes.Comment: accepted at ECCV 201

Estimation of forest variables using airborne laser scanning

Airborne laser scanning can provide three-dimensional measurements of the forest canopy with high efficiency and precision. There are presently a large number of airborne laser scanning instruments in operation. The aims of the studies reported in this thesis were, to develop and validate methods for estimation of forest variables using laser data, and to investigate the influence of laser system parameters on the estimates. All studies were carried out in hemi-boreal forest at a test area in southwestern Sweden (lat. 58°30’N, long. 13°40’ E). Forest variables were estimated using regression models. On plot level, the Root Mean Square Error (RMSE) for mean tree height estimations ranged between 6% and 11% of the average value for different datasets and methods. The RMSE for stem volume estimations ranged between 19% and 26% of the average value for different datasets and methods. On stand level (area 0.64 ha), the RMSE was 3% and 11% of the average value for mean tree height and stem volume estimations, respectively. A simulation model was used to investigate the effect of different scanning angles on laser measurement of tree height and canopy closure. The effect of different scanning angles was different within different simulated forest types, e.g., different tree species. High resolution laser data were used for detection of individual trees. In total, 71% of the field measurements were detected representing 91% of the total stem volume. Height and crown diameter of the detected trees could be estimated with a RMSE of 0.63 m and 0.61 m, respectively. The magnitude of the height estimation errors was similar to what is usually achieved using field inventory. Using different laser footprint diameters (0.26 to 3.68 m) gave similar estimation accuracies. The tree species Norway spruce (Picea abies L. Karst.) and Scots pine (Pinus sylvestris L.) were discriminated at individual tree level with an accuracy of 95%. The results in this thesis show that airborne laser scanners are useful as forest inventory tools. Forest variables can be estimated on tree level, plot level and stand level with similar accuracies as traditional field inventories