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14
Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 1727 (7 self)
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
The Curve Of Least Energy
, 1983
"... Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discus ..."
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Cited by 72 (2 self)
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Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour.
An Active Contour Model For Mapping The Cortex
 IEEE TRANS. ON MEDICAL IMAGING
, 1995
"... A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approac ..."
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Cited by 64 (13 self)
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A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.
A Framework for the Analysis of Error in Global Illumination Algorithms
, 1994
"... In this paper we identify sources of error in global illumination algorithms and derive bounds for each distinct category. Errors arise from three sources: inaccuracies in the boundary data, discretization, and computation. Boundary data consist of surface geometry, reflectance functions, and emissi ..."
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Cited by 62 (3 self)
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In this paper we identify sources of error in global illumination algorithms and derive bounds for each distinct category. Errors arise from three sources: inaccuracies in the boundary data, discretization, and computation. Boundary data consist of surface geometry, reflectance functions, and emission functions, all of which may be perturbed by errors in measurement or simulation, or by simplifications made for computational efficiency. Discretization error is introduced by replacing the continuous radiative transfer equation with a finitedimensional linear system, usually by means of boundaryelements and a corresponding projection method. Finally, computational errors perturb the finitedimensional linear system through imprecise form factors, inner products, visibility, etc., as well as by halting iterative solvers after a finite number of steps. Using the error taxonomy introduced in the paper we examine existing global illumination algorithms and suggest new avenues of research. ...
Optimal deployment of large wireless sensor networks
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—A spatially distributed set of sources is creating data that must be delivered to a spatially distributed set of sinks. A network of wireless nodes is responsible for sensing the data at the sources, transporting them over a wireless channel, and delivering them to the sinks. The problem is ..."
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Cited by 29 (3 self)
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Abstract—A spatially distributed set of sources is creating data that must be delivered to a spatially distributed set of sinks. A network of wireless nodes is responsible for sensing the data at the sources, transporting them over a wireless channel, and delivering them to the sinks. The problem is to find the optimal placement of nodes, so that a minimum number of them is needed. The critical assumption is made that the network is massively dense, i.e., there are so many sources, sinks, and wireless nodes, that it does not make sense to discuss in terms of microscopic parameters, such as their individual placements, but rather in terms of macroscopic parameters, such as their spatial densities. Assuming a particular interferencelimited, capacityachieving physical layer, and specifying that nodes only need to transport the data (and not to sense them at the sources, or deliver them at the sinks once their location is reached), the optimal node placement induces a traffic flow that is identical to the electrostatic field created if the sources and sinks are replaced by a corresponding distribution of positive and negative charges. Assuming a general model for the physical layer, and specifying that nodes must not only transport the data, but also sense them at the sources and deliver them at the sinks, the optimal placement of nodes is given by a scalar nonlinear partial differential equation found by calculus of variations techniques. The proposed formulation and derived equations can help in the design of large wireless sensor networks that are deployed in the most efficient manner, not only avoiding the formation of bottlenecks, but also striking the optimal balance between reducing congestion and having the data packets follow short routes. Index Terms—Capacity, electrostatics, node placement, physical layer, sensor networks, wireless ad hoc networks.
Laser beam resonators
 Proc. IEEE 54
"... AbstractThis paper is a review of the theoryof laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results whi ..."
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Cited by 28 (0 self)
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AbstractThis paper is a review of the theoryof laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results which bear practical significance. 1.
Linear Operators and Integral Equations in Global Illumination
 In SIGGRAPH '93 course notes(course 42
, 1993
"... These notes introduce the basic concepts of integral equations and their application in global illumination. Much of the discussion is expressed in the language of linear operators to simplify the notation and to emphasize the algebraic properties of the integral equations. We start by reviewing som ..."
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Cited by 5 (0 self)
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These notes introduce the basic concepts of integral equations and their application in global illumination. Much of the discussion is expressed in the language of linear operators to simplify the notation and to emphasize the algebraic properties of the integral equations. We start by reviewing some facts about linear operators and examining some of the operators that occur in global illumination. Six general methods of solving operator and integral equations are then discussed: the Neumann series, successive approximations, the Nystrom method, collocation, least squares, and the Galerkin method. Finally, we look at some of the steps involved in applying these techniques in the context of global illumination. 1 Introduction The transfer of energy by radiation has a character fundamentally different from the processes of conduction and convection. One reason for this difference is that the radiant energy passing through a point in space cannot be completely described by a single scala...
Some Bayesian perspectives on statistical modelling
, 1988
"... I would like to thank my supervisor, Professor A. F. M. Smith, for all his advice and encourage ..."
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Cited by 3 (2 self)
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I would like to thank my supervisor, Professor A. F. M. Smith, for all his advice and encourage
A geometric projectionspace reconstruction algorithm
 Linear Algebra and Its Applications, 130:151191
, 1990
"... We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles. The algorithm calculates the maximum a posteriori (MAP) estimate of the full sinogram (which is an image of the 2D Radon transform of the object) from the availa ..."
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Cited by 2 (1 self)
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We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles. The algorithm calculates the maximum a posteriori (MAP) estimate of the full sinogram (which is an image of the 2D Radon transform of the object) from the available data. It is implemented using a primaldual constrained optimization procedure that solves a partial differential equation in the primal phase with an efficient local relaxation algorithm and uses a simple Lagrangemultiplier update in the dual phase. The sinogram prior probability is given by a Markov random field (MRF) that includes information about the mass, center of mass, and convex hul,l of the object, and about the smoothness, fundamental constraints, and periodicity of the 2D Radon transform. The object is reconstructed using convolution backprojection applied to the estimated sinogram. We show several reconstructed objects which are obtained from simulated limited and sparseangle data using the described algorithm, and compare these results with images obtained using convolution backprojection directly. 1.
A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces
, 2006
"... In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for comput ..."
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In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz P, Schwartz D, and Schoen G surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases not equal. Due to the computational cost of the fully, threedimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package. 1.