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18
Shape Ambiguities in Structure from Motion
 PAMI
, 1996
"... This technical report examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect ..."
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Cited by 54 (4 self)
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This technical report examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape. Our results for orthographic cameras show that the basrelief ambiguity is significant even with many images, unless a large amount of rotation is present. Similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.
Characterization of errors in compositing panoramic images
 in CVPR ’97: Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR ’97
, 1997
"... A panoramic image has 360 horizontal field of view, and it can provide the viewer the impression of being immersed in the scene to a certain extent. A panorama is created by first taking a sequence of images while rotating the camera about a vertical axis. These images are then projected onto a cyl ..."
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Cited by 29 (1 self)
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A panoramic image has 360 horizontal field of view, and it can provide the viewer the impression of being immersed in the scene to a certain extent. A panorama is created by first taking a sequence of images while rotating the camera about a vertical axis. These images are then projected onto a cylindrical surface before being seamlessly composited. The crosssectional circumference of the cylindrical panorama is called the compositing length. This work characterizes the error in compositing panoramic images due to errors in intrinsic camera parameters. The intrinsic camera parameters that are considered are the camera focal length and the radial distortion coefficient. We show that the error in the compositing length is more sensitive to the error in the camera focal length. Especially important is the discovery that the relative error in compositing length is always smaller than the relative error in the focal length. This means that the error in focal length can be corrected by iteratively using the composited length to compute a new and more correct focal length. This compositing approach to camera calibration has the advantages of not requiring both feature detection and separate prior calibration. 1
Perturbative ChernSimons Theory
, 1995
"... We present the perturbation theory of the ChernSimons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a previously unknown integral formula for the Arf invariant of a knot, in complete agreement with ear ..."
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Cited by 22 (1 self)
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We present the perturbation theory of the ChernSimons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a previously unknown integral formula for the Arf invariant of a knot, in complete agreement with earlier nonperturbative results of Witten. We outline our expectations for the behavior of the theory beyond two loops.
Implementation of Parallel Graph Algorithms on a Massively Parallel SIMD Computer with Virtual Processing
, 1995
"... We describe our implementation of several PRAM graph algorithms on the massively parallel computer MasPar MP1 with 16,384 processors. Our implementation incorporated virtual processing and we present extensive test data. In a previous project [13], we reported the implementation of a set of paralle ..."
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Cited by 13 (3 self)
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We describe our implementation of several PRAM graph algorithms on the massively parallel computer MasPar MP1 with 16,384 processors. Our implementation incorporated virtual processing and we present extensive test data. In a previous project [13], we reported the implementation of a set of parallel graph algorithms with the constraint that the maximum input size was restricted to be no more than the physical number of processors on the MasPar. The MasPar language MPL that we used for our code does not support virtual processing. In this paper, we describe a method of simulating virtual processors on the MasPar. We recoded and finetuned our earlier parallel graph algorithms to incorporate the usage of virtual processors. Under the current implementation scheme, there is no limit on the number of virtual processors that one can use in the program as long as there is enough main memory to store all the data required during the computation. We also give two general optimization techniq...
Artificial Boundary Conditions for Computation of Oscillating External Flows
, 1996
"... In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be cau ..."
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Cited by 8 (6 self)
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In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the timeperiodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exteri...
DCEL: A Polyhedral Database And Programming Environment
, 1996
"... In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonst ..."
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Cited by 1 (1 self)
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In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate its use in several applications. Keywords: geometric software, databases, programming environments, polyhedra. 1. Introduction Computational geometry has offered a large amount of algorithms during the last two decades. Software implementation of these algorithms makes them valuable not only for theoreticians but also for practitioners in academia and industry. This is in many cases the appropriate tool for choosing the best algorithm for a specific problem in a given context: hardware platform, operating system, programming language, typical inputs of the application, robustness considerations, etc. The importance of applied computational geometry is now being recognized. 10 Dedicated ...
Stiffness and Strength Tailoring in Uniform SpaceFilling Truss Structures
, 1992
"... This paper presents a deterministic procedure for tailoring the continuum stiffness and strength of uniform spacefilling truss structures through the appropriate selection of truss geometry and member sizes (i.e., flexural and axial stiffnesses and length). The trusses considered herein are generat ..."
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This paper presents a deterministic procedure for tailoring the continuum stiffness and strength of uniform spacefilling truss structures through the appropriate selection of truss geometry and member sizes (i.e., flexural and axial stiffnesses and length). The trusses considered herein are generated by uniform replication of a characteristic truss cell. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using crystallographic techniques. The elastic symmetry associated with each geometric symmetry group is identified to help select an appropriate truss geometry for a given application. Stiffness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum stiffnesses and failure stresses of the truss to the stiffnesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analyt...
Stiffness and Strength Tailoring in Uniform SpaceFilling Truss
, 1992
"... This paper presents a deterministic procedure for tailoring the continuum sti ness and strength of uniform space lling truss structures through the appropriate selection of truss geometry and member sizes (i.e., exural and axial sti nesses and length). The trusses considered herein are generated by ..."
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This paper presents a deterministic procedure for tailoring the continuum sti ness and strength of uniform space lling truss structures through the appropriate selection of truss geometry and member sizes (i.e., exural and axial sti nesses and length). The trusses considered herein are generated by uniform replication of a characteristic truss cell. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using crystallographic techniques. The elastic symmetry associated with each geometric symmetry group is identi ed to help select an appropriate truss geometry for a given application. Sti ness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum sti nesses and failure stresses of the truss to the sti nesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analytical failure theory for trusses. Several examples are presented to illustrate the application of these techniques and to demonstrate the usefulness of the information gained from this analysis.