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

High-Performance Integrated Window and Façade Solutions for California

The researchers developed a new generation of high-performance façade systems and supporting design and management tools to support industry in meeting California’s greenhouse gas reduction targets, reduce energy consumption, and enable an adaptable response to minimize real-time demands on the electricity grid. The project resulted in five outcomes: (1) The research team developed an R-5, 1-inch thick, triplepane, insulating glass unit with a novel low-conductance aluminum frame. This technology can help significantly reduce residential cooling and heating loads, particularly during the evening. (2) The team developed a prototype of a windowintegrated local ventilation and energy recovery device that provides clean, dry fresh air through the façade with minimal energy requirements. (3) A daylight-redirecting louver system was prototyped to redirect sunlight 15–40 feet from the window. Simulations estimated that lighting energy use could be reduced by 35–54 percent without glare. (4) A control system incorporating physics-based equations and a mathematical solver was prototyped and field tested to demonstrate feasibility. Simulations estimated that total electricity costs could be reduced by 9-28 percent on sunny summer days through adaptive control of operable shading and daylighting components and the thermostat compared to state-of-the-art automatic façade controls in commercial building perimeter zones. (5) Supporting models and tools needed by industry for technology R&D and market transformation activities were validated. Attaining California’s clean energy goals require making a fundamental shift from today’s ad-hoc assemblages of static components to turnkey, intelligent, responsive, integrated building façade systems. These systems offered significant reductions in energy use, peak demand, and operating cost in California

Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt this mathematical field to the discrete differential geometry. All discrete differential geometry terms are explained for triangulated surface meshes. These utilities serve as basis for the feature line methods. We provide the reader with all knowledge to re-implement every feature line method. Furthermore, we summarize the methods and suggest a guideline for which kind of surface which feature line algorithm is best suited. Our work is motivated by, but not restricted to, medical and biological surface models.Comment: 33 page

Single-image RGB Photometric Stereo With Spatially-varying Albedo

We present a single-shot system to recover surface geometry of objects with spatially-varying albedos, from images captured under a calibrated RGB photometric stereo setup---with three light directions multiplexed across different color channels in the observed RGB image. Since the problem is ill-posed point-wise, we assume that the albedo map can be modeled as piece-wise constant with a restricted number of distinct albedo values. We show that under ideal conditions, the shape of a non-degenerate local constant albedo surface patch can theoretically be recovered exactly. Moreover, we present a practical and efficient algorithm that uses this model to robustly recover shape from real images. Our method first reasons about shape locally in a dense set of patches in the observed image, producing shape distributions for every patch. These local distributions are then combined to produce a single consistent surface normal map. We demonstrate the efficacy of the approach through experiments on both synthetic renderings as well as real captured images.Comment: 3DV 2016. Project page at http://www.ttic.edu/chakrabarti/rgbps

A framework for digital sunken relief generation based on 3D geometric models

Sunken relief is a special art form of sculpture whereby the depicted shapes are sunk into a given surface. This is traditionally created by laboriously carving materials such as stone. Sunken reliefs often utilize the engraved lines or strokes to strengthen the impressions of a 3D presence and to highlight the features which otherwise are unrevealed. In other types of reliefs, smooth surfaces and their shadows convey such information in a coherent manner. Existing methods for relief generation are focused on forming a smooth surface with a shallow depth which provides the presence of 3D figures. Such methods unfortunately do not help the art form of sunken reliefs as they omit the presence of feature lines. We propose a framework to produce sunken reliefs from a known 3D geometry, which transforms the 3D objects into three layers of input to incorporate the contour lines seamlessly with the smooth surfaces. The three input layers take the advantages of the geometric information and the visual cues to assist the relief generation. This framework alters existing techniques in line drawings and relief generation, and then combines them organically for this particular purpose

Approaching Visual Search in Photo-Realistic Scenes

Visual search is extended from the domain of polygonal figures presented on a uniform background to scenes in which search is for a photo-realistic object in a dense, naturalistic background. Scene generation for these displays relies on a powerful solid modeling program to define the three dimensional forms, surface properties, relative positions, and illumination of the objects and a rendering program to produce an image. Search in the presented experiments is for a rock with specific properties among other, similar rocks, although the method described can be generalized to other situations. Using this technique we explore the effects of illumination and shadows in aiding search for a rock in front of and closer to the viewer than other rocks in the scene. For these scenes, shadows of two different contrast levels can significantly deet·ease reaction times for displays in which target rocks are similar to distractor rocks. However, when the target rock is itself easily distinguishable from dis tractors on the basis of form, the presence or absence of shadows has no discernible effect. To relate our findings to those for earlier polygonal displays, we simplified the non-shadow displays so that only boundary information remained. For these simpler displays, search slopes (the reaction time as a function of the number of distractors) were significantly faster, indicating that the more complex photo-realistic objects require more time to process for visual search. In contrast with several previous experiments involving polygonal figures, we found no evidence for an effect of illumination direction on search times

Thermal breakage of window glass in room fires conditions - Analysis of some important parameters

In a compartment fire, the breakage and possible fallout of a window glass has a significant impact on the fire dynamics. The thermal breakage of glass depends on various parameters such as glass type, edge shading, edges conditions and constraints on the glass. The purpose of the present study is to investigate some of the key parameters affecting the thermal breakage of window glass in fire conditions using a recently developed and validated computer tool. Fallout is not within the scope of this study. Different boundary conditions of the glass pane (unconstrained and constrained) subjected to fire radiant heat are investigated. The analysis shows that to prevent glass thermal breakage, it is important to provide enough spacing between the frame and glass pane to accommodate the thermal expansion, and constraints on the glass structure should be avoided. The zones where the glass is likely to crack first are shown. The study also quantifies the effects of glass edge conditions on its thermal breakage in fire conditions; such analysis has not been reported in the literature due to its complexity and the statistical nature of edge flaws. The results show that an ordinary float glass mostly used in windows, with the “as-cut” edge condition would break later and is stronger than a ground edge or polished edge glass for the scenarios investigated. The study demonstrates how a predictive tool could be employed for a better understanding of thermal breakage of window glass in fires and for design guidance