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Modeling and Rendering Architecture from Photographs
, 1999
"... Contents Thissectionofthecoursenotesisorganizedasfollows: 1.Introductorymaterialforthissection.Thisincludesabriefoverviewofrelatedandcomplimentarymaterialtophotogrammetricmodeling, suchasstructurefrommotion,stereocorrespondence,shapefrom silhouettes,cameracalibration,laserscanning,andimagebasedre ..."
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Cited by 888 (18 self)
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Contents Thissectionofthecoursenotesisorganizedasfollows: 1.Introductorymaterialforthissection.Thisincludesabriefoverviewofrelatedandcomplimentarymaterialtophotogrammetricmodeling, suchasstructurefrommotion,stereocorrespondence,shapefrom silhouettes,cameracalibration,laserscanning,andimagebasedrendering. 2.Abibliographyofrelatedpapers. 3.Areprintof: PaulE.Debevec,CamilloJ.Taylor,andJitendraMalik.ModelingandRenderingArchitecturefrom Photographs.InSIGGRAPH96,August1996,pp.1120. 4.NotesonphotogrammetricrecoveryofarchesandsurfacesofrevolutionwrittenbyGeorgeBorshukov. 5.Copiesoftheslidesusedforthepresentation. Moreinformationcanbefoundin[10],[5],and[13],availableat: http://www.cs.berkeley.edu/debevec/Thesis 1 Introduction Thecreationofthreedimensionalmodelsofexistingarchitecturalsceneswiththeaidofthecomputerhas beencommonplaceforsometime,andtheresultingmodelshavebeenbothentertainingvirtualenvironments aswellasvaluablevisualizationtools.LargescaleeffortshavepushedthecampusesofI
Variational principles, Surface Evolution, PDE's, level set methods and the Stereo Problem
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1999
"... We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equati ..."
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Cited by 194 (21 self)
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We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and vibility are presented on synthetic and real images.
A Theory of Networks for Approximation and Learning
 Laboratory, Massachusetts Institute of Technology
, 1989
"... Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, t ..."
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Cited by 194 (24 self)
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Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nonlinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. Wedevelop a theoretical framework for approximation based on regularization techniques that leads to a class of threelayer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the wellknown Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods suchasParzen windows and potential functions and to several neural network algorithms, suchas Kanerva's associative memory,backpropagation and Kohonen's topology preserving map. They also haveaninteresting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.
A geometrical framework for low level vision
 IEEE Trans. on Image Processing
, 1998
"... Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, an ..."
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Cited by 176 (35 self)
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Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, and 2D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scalespace. I.
Occlusions and Binocular Stereo
, 1995
"... Binocular stereo is the process of obtaining depth information from a pair of cameras. In the past, stereo algorithms have had problems at occlusions and have tended to fail there (though sometimes postprocessing has been added to mitigate the worst effects). We show that, on the contrary, occlusio ..."
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Cited by 129 (5 self)
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Binocular stereo is the process of obtaining depth information from a pair of cameras. In the past, stereo algorithms have had problems at occlusions and have tended to fail there (though sometimes postprocessing has been added to mitigate the worst effects). We show that, on the contrary, occlusions can help stereo computation by providing cues for depth discontinuities. We describe a theory for stereo based on the Bayesian approach, using adaptive windows and a prior weak smoothness constraint, which incorporates occlusion. Our model assumes that a disparity discontinuity, along the epipolar line, in one eye always corresponds to an occluded region in the other eye thus, leading to an occlusion constraint. This constraint restricts the space of possible disparity values, thereby simplifying the computations. An estimation of the disparity at occluded features is also discussed in light of psychophysical experiments. Using dynamic programming we can find the optimal solution to our s...
Complete Dense Stereovision using Level Set Methods
 in Proc. 5th European Conf. on Computer Vision
, 1998
"... We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satised by the surfaces of the objects in the scene and their images. The EulerLagrange equation ..."
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Cited by 106 (1 self)
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We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satised by the surfaces of the objects in the scene and their images. The EulerLagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and vibility are presented on synthetic and real images.
Occlusions, discontinuities, and epipolar lines in stereo
 In European Conference on Computer Vision
, 1998
"... Abstract. Binocular stereo is the process of obtaining depth information from a pair of left and right views of a scene. We present a new approach to compute the disparity map by solving a global optimization problem that models occlusions, discontinuities, and epipolarline interactions. In the mod ..."
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Cited by 92 (8 self)
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Abstract. Binocular stereo is the process of obtaining depth information from a pair of left and right views of a scene. We present a new approach to compute the disparity map by solving a global optimization problem that models occlusions, discontinuities, and epipolarline interactions. In the model, geometric constraints require every disparity discontinuity along the epipolar lineinoneeyetoalways correspond to an occluded region in the other eye, while at the same time encouraging smoothness across epipolar lines. Smoothing coefficients are adjusted according to the edge and junction information. For some welldefined set of optimization functions, we can map the optimization problem to a maximumflow problem on a directed graph in a novel way, which enables us to obtain a global solution in a polynomial time. Experiments confirm the validity of this approach. 1
Optimal perceptual inference
 In CVPR, Washington DC
, 1983
"... When a vision system creates an interpretation of some input datn, it assigns truth values or probabilities to intcrnal hypothcses about the world. We present a nondctcrministic method for assigning truth values that avoids many of the problcms encountered by existing relaxation methods. Instead of ..."
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Cited by 91 (14 self)
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When a vision system creates an interpretation of some input datn, it assigns truth values or probabilities to intcrnal hypothcses about the world. We present a nondctcrministic method for assigning truth values that avoids many of the problcms encountered by existing relaxation methods. Instead of rcprcscnting probabilitics with realnumbers, we usc a more dircct encoding in which thc probability associated with a hypotlmis is rcprcscntcd by the probability hat it is in one of two states, true or false. Wc give a particular nondeterministic operator, based on statistical mechanics, for updating the truth values of hypothcses. The operator ensures that the probability of discovering a particular combination of hypothcscs is a simplc function of how good that combination is. Wc show that thcrc is a simple relationship bctween this operator and Bayesian inference, and we describe a learning rule which allows a parallel system to converge on a set ofweights that optimizes its perccptt~al inferences. lnt roduction One way of interpreting images is to formulate hypotheses about parts or aspects of the imagc and then decide which of these hypotheses are likely to be correct. Thc probability that each hypothesis is correct is determined partly by its fit to the imagc and partly by its fit to other hypothcses (hat are taken to be correct, so the truth'value of an individual hypothesis cannot be decided in isolation. One method of searching for the most plausible combination of hypotheses is to use a rclaxation process in which a probability is associated with each hypothesis, and the probabilities arc then iteratively modified on the basis of the fit to the imagc and the known relationships bctwcen hypotheses. An attractive property of rclaxation methods is that they can be implemented in parallel hardwarc where one computational unit is used for each possible hypothcsis, and the interactions betwcen hypotheses are implemented by dircct hardwarc connections betwcen the units. Many variations of the basic relaxation idea have becn However, all the current methods suffer from one or more of the following problems:
Segmentbased stereo matching
 Computer Vision, Graphics, and Image Processing
, 1985
"... Images are 2dimensional projections of 3dimensional scenes, therefore depth recovery is a crucial problem in image understanding, with applications in passive navigation, cartography, surveillance, and industrial robotics. Stereo analysis provides a more direct quantitative depth evaluation than t ..."
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Cited by 60 (2 self)
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Images are 2dimensional projections of 3dimensional scenes, therefore depth recovery is a crucial problem in image understanding, with applications in passive navigation, cartography, surveillance, and industrial robotics. Stereo analysis provides a more direct quantitative depth evaluation than techniques such as shape from shading, and its being passive makes it more applicable than active range finding imagery by laser or radar. This paper addresses the subproblem of identifying corresponding points in the two images. The primitives we use are groups of collinear connected edge points called segments, and we base the correspondence on the "minimum differential disparity " criterion. The result of this processing is a sparse array disparity map of the analyzed scene. 9 1985 Academic Press, Inc. 1.