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Academic Commons Search Resultsen-usA First Order Analysis of Lighting, Shading, and Shadows
http://academiccommons.columbia.edu/catalog/ac:110547
Ramamoorthi, Ravi; Mahajan, Dhruv; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29458Wed, 27 Apr 2011 00:00:00 +0000The shading in a scene depends on a combination of many factors---how the lighting varies spatially across a surface, how it varies along different directions, the geometric curvature and reflectance properties of objects, and the locations of soft shadows. In this paper, we conduct a complete first order or gradient analysis of lighting, shading and shadows, showing how each factor separately contributes to scene appearance, and when it is important. Gradients are well suited for analyzing the intricate combination of appearance effects, since each gradient term corresponds directly to variation in a specific factor. First, we show how the spatial {\em and} directional gradients of the light field change, as light interacts with curved objects. This extends the recent frequency analysis of Durand et al.\ to gradients, and has many advantages for operations, like bump-mapping, that are difficult to analyze in the Fourier domain. Second, we consider the individual terms responsible for shading gradients, such as lighting variation, convolution with the surface BRDF, and the object's curvature. This analysis indicates the relative importance of various terms, and shows precisely how they combine in shading. As one practical application, our theoretical framework can be used to adaptively sample images in high-gradient regions for efficient rendering. Third, we understand the effects of soft shadows, computing accurate visibility gradients. We generalize previous work to arbitrary curved occluders, and develop a local framework that is easy to integrate with conventional ray-tracing methods. Our visibility gradients can be directly used in practical gradient interpolation methods for efficient rendering.Computer sciencepb2019Computer ScienceTechnical reportsRigid Formations with Leader-Follower Architecture
http://academiccommons.columbia.edu/catalog/ac:110506
Eren, Tolga; Whiteley, Walter; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29445Tue, 26 Apr 2011 00:00:00 +0000This paper is concerned with information structures used in rigid formations of autonomous agents that have leader-follower architecture. The focus of the paper is on sensor/network topologies to secure control of rigidity. This papers extends the previous rigidity based approaches for formations with symmetric neighbor relations to include formations with leader-follower architecture. We provide necessary and sufficient conditions for rigidity of directed formations, with or without cycles. We present the directed Henneberg constructions as a sequential process for all guide rigid digraphs. We refine those results for acyclic formations, where guide rigid formations had a simple construction. The analysis in this paper confirms that acyclicity is not a necessary condition for stable rigidity. The cycles are not the real problem, but rather the lack of guide freedom is the reason behind why cycles have been seen as a problematic topology. Topologies that have cycles within a larger architecture can be stably rigid, and we conjecture that all guide rigid formations are stably rigid for internal control. We analyze how the external control of guide agents can be integrated into stable rigidity of a larger formation. The analysis in the paper also confirms the inconsistencies that result from noisy measurements in redundantly rigid formations. An algorithm given in the paper establishes a sequential way of determining the directions of links from a given undirected rigid formation so that the necessary and sufficient conditions are fulfilled.Computer sciencepb2019Computer ScienceTechnical reportsUsing Angle of Arrival (Bearing) Information in Network Localization
http://academiccommons.columbia.edu/catalog/ac:110523
Eren, Tolga; Whiteley, Walter; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29450Tue, 26 Apr 2011 00:00:00 +0000In this paper, we consider using angle of arrival information (bearing) for network localization and control in two different fields of multi-agent systems: (i) wireless sensor networks; (ii) robot networks. The essential property we require in this paper is that a node can infer heading information from its neighbors. We address the uniqueness of network localization solutions by the theory of globally rigid graphs. We show that while the parallel rigidity problem for formations with bearings is isomorphic to the distance case, the global rigidity of the formation is simpler (in fact identical to the simpler rigidity case) for a network with bearings, compared to formations with distances. We provide the conditions of localization for networks in which the neighbor relationship is not necessarily symmetric.Computer sciencepb2019Computer ScienceTechnical reportsInformation Structures to Secure Control of Rigid Formations with Leader-Follower Structure
http://academiccommons.columbia.edu/catalog/ac:109832
Eren, Tolga; Whiteley, Walter; Morse, A. Stephen; Anderson, Brian D. O.; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29236Fri, 22 Apr 2011 00:00:00 +0000This paper is concerned with rigid formations of mobile autonomous agents using a leader-follower structure. A formation is a group of agents moving in real 2- or 3- dimensional space. A formation is called rigid if the distance between each pair of agents does not change over time under ideal conditions. Sensing/communication links between agents are used to maintain a rigid formation. Two agents connected by a sensing/communication link are called neighbors. There are two types of neighbor relations in rigid formations. In the first type, the neighbor relation is symmetric. In the second type, the neighbor relation is asymmetric. Rigid formations with a leader-follower structure have the asymmetric neighbor relation. A framework to analyze rigid formations with symmetric neighbor relations is given in our previous work. This paper suggests an approach to analyze rigid formations that have a leader-follower structure.Computer sciencepb2019Computer ScienceTechnical reportsA Theoretical Analysis of the Conditions for Unambiguous Node Localization in Sensor Networks
http://academiccommons.columbia.edu/catalog/ac:109826
Eren, Tolga; Whiteley, Walter; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29234Fri, 22 Apr 2011 00:00:00 +0000In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring distances or bearings to their neighbors. Distance information is the separation between two nodes connected by a sensing/communication link. Bearing is the angle between a sensing/communication link and the x-axis of a node's local coordinate system. We construct grounded graphs to model network localization and apply graph rigidity theory and parallel drawings to test the conditions for unique localizability and to construct uniquely localizable networks. We further investigate partially localizable networks.Computer sciencepb2019Computer ScienceTechnical reportsTime-Varying Textures
http://academiccommons.columbia.edu/catalog/ac:110320
Enrique, Sebastian; Koudelka, Melissa; Belhumeur, Peter N.; Dorsey, Julie; Nayar, Shree K.; Ramamoorthi, Ravihttp://hdl.handle.net/10022/AC:P:29388Fri, 22 Apr 2011 00:00:00 +0000Essentially all computer graphics rendering assumes that the reflectance and texture of surfaces is a static phenomenon. Yet, there is an abundance of materials in nature whose appearance varies dramatically with time, such as cracking paint, growing grass, or ripening banana skins. In this paper, we take a significant step towards addressing this problem, investigating a new class of time-varying textures. We make three contributions. First, we describe the carefully controlled acquisition of datasets of a variety of natural processes including the growth of grass, the accumulation of snow, and the oxidation of copper. Second, we show how to adapt quilting-based methods to time-varying texture synthesis, addressing the important challenges of maintaining temporal coherence, efficient synthesis on large time-varying datasets, and reducing visual artifacts specific to time-varying textures. Finally, we show how simple procedural techniques can be used to control the evolution of the results, such as allowing for a faster growth of grass in well lit (as opposed to shadowed) areas.Computer sciencepb2019, skn3Computer ScienceTechnical reportsRigid Formations with Leader-Follower Architecture
http://academiccommons.columbia.edu/catalog/ac:110497
Eren, Tolga; Whiteley, Walter; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29442Thu, 21 Apr 2011 00:00:00 +0000This paper is concerned with information structures used in rigid formations of autonomous agents that have leader-follower architecture. The focus of this paper is on sensor/network topologies to secure control of rigidity. We extend our previous approach for formations with symmetric neighbor relations to include formations with leader-follower architecture. Necessary and sufficient conditions for stably rigid directed formations are given including both cyclic and acyclic directed formations. Some useful steps for creating topologies of directed rigid formations are developed. An algorithm to determine the directions of links to create stably rigid directed formations from rigid undirected formations is presented. It is shown that k-cycles (k > 2) do not cause inconsistencies when measurements are noisy, while 2-cycles do. Simulation results are presented for (i) a rigid acyclic formation, (i) a flexible formation, and (iii) a rigid formation with cycles.Computer sciencepb2019Computer ScienceTechnical reportsMerging Globally Rigid Formations of Mobile Autonomous Agents
http://academiccommons.columbia.edu/catalog/ac:110041
Eren, Tolga; Anderson, Brian D. O.; Whiteley, Walter; Morse, A. Stephen; Belhumeur, Peter N.http://hdl.handle.net/10022/AC:P:29300Thu, 21 Apr 2011 00:00:00 +0000This paper is concerned with merging globally rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as an integral part of coordination. Network topologies are critically important for autonomous systems involving mobile underwater, ground and air vehicles and for sensor networks. This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to merge globally rigid formations for cooperative tasks. Central to the development of these techniques and strategies will be the use of tools from rigidity theory, and graph theory.Computer sciencepb2019Computer ScienceTechnical reports