Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure

Deep Reflectance Maps

Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring shape, materials and illumination from images only, progress in an unconstrained setting is still limited. We propose a convolutional neural architecture to estimate reflectance maps of specular materials in natural lighting conditions. We achieve this in an end-to-end learning formulation that directly predicts a reflectance map from the image itself. We show how to improve estimates by facilitating additional supervision in an indirect scheme that first predicts surface orientation and afterwards predicts the reflectance map by a learning-based sparse data interpolation. In order to analyze performance on this difficult task, we propose a new challenge of Specular MAterials on SHapes with complex IllumiNation (SMASHINg) using both synthetic and real images. Furthermore, we show the application of our method to a range of image-based editing tasks on real images.Comment: project page: http://homes.esat.kuleuven.be/~krematas/DRM

DeLight-Net: Decomposing Reflectance Maps into Specular Materials and Natural Illumination

In this paper we are extracting surface reflectance and natural environmental illumination from a reflectance map, i.e. from a single 2D image of a sphere of one material under one illumination. This is a notoriously difficult problem, yet key to various re-rendering applications. With the recent advances in estimating reflectance maps from 2D images their further decomposition has become increasingly relevant. To this end, we propose a Convolutional Neural Network (CNN) architecture to reconstruct both material parameters (i.e. Phong) as well as illumination (i.e. high-resolution spherical illumination maps), that is solely trained on synthetic data. We demonstrate that decomposition of synthetic as well as real photographs of reflectance maps, both in High Dynamic Range (HDR), and, for the first time, on Low Dynamic Range (LDR) as well. Results are compared to previous approaches quantitatively as well as qualitatively in terms of re-renderings where illumination, material, view or shape are changed.Comment: Stamatios Georgoulis and Konstantinos Rematas contributed equally to this wor

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

Joint Material and Illumination Estimation from Photo Sets in the Wild

Faithful manipulation of shape, material, and illumination in 2D Internet images would greatly benefit from a reliable factorization of appearance into material (i.e., diffuse and specular) and illumination (i.e., environment maps). On the one hand, current methods that produce very high fidelity results, typically require controlled settings, expensive devices, or significant manual effort. To the other hand, methods that are automatic and work on 'in the wild' Internet images, often extract only low-frequency lighting or diffuse materials. In this work, we propose to make use of a set of photographs in order to jointly estimate the non-diffuse materials and sharp lighting in an uncontrolled setting. Our key observation is that seeing multiple instances of the same material under different illumination (i.e., environment), and different materials under the same illumination provide valuable constraints that can be exploited to yield a high-quality solution (i.e., specular materials and environment illumination) for all the observed materials and environments. Similar constraints also arise when observing multiple materials in a single environment, or a single material across multiple environments. The core of this approach is an optimization procedure that uses two neural networks that are trained on synthetic images to predict good gradients in parametric space given observation of reflected light. We evaluate our method on a range of synthetic and real examples to generate high-quality estimates, qualitatively compare our results against state-of-the-art alternatives via a user study, and demonstrate photo-consistent image manipulation that is otherwise very challenging to achieve