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34
Determining the Epipolar Geometry and its Uncertainty: A Review
 International Journal of Computer Vision
, 1998
"... Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, an ..."
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Cited by 320 (7 self)
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Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, and its determination is very important in many applications such as scene modeling and vehicle navigation. This paper gives an introduction to the epipolar geometry, and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty. A wellfounded measure is proposed to compare these techniques. Projective reconstruction is also reviewed. The software which we have developed for this review is available on the Internet.
A generalized Gaussian image model for edgepreserving MAP estimation
 IEEE Trans. on Image Processing
, 1993
"... Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distri ..."
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Cited by 238 (34 self)
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Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisifies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the U posteriori loglikeihood function. The GGMRF is demonstrated to be useful for image reconstruction in lowdosage transmission tomography. I.
Matching properties of MOS transistors
 IEEE J. SolidState Circuits
, 1989
"... AbstractThe matching properties of the threshold voltage, substrate factor, and current factor of MOS transistors have been analyzed and measured. Improvements to the existing theory are given, as well as extensions for longdistance matching and rotation of devices. Matching parameters of several ..."
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Cited by 208 (1 self)
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AbstractThe matching properties of the threshold voltage, substrate factor, and current factor of MOS transistors have been analyzed and measured. Improvements to the existing theory are given, as well as extensions for longdistance matching and rotation of devices. Matching parameters of several processes are compared. The matching results have been verified by measurements and calculations on several basic circuits. 1.
Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting
 Image and Vision Computing
, 1997
"... : Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear leastsquares (pseudoinverse and eigen ..."
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Cited by 196 (6 self)
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: Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear leastsquares (pseudoinverse and eigen analysis); orthogonal leastsquares; gradientweighted leastsquares; biascorrected renormalization; Kalman øltering; and robust techniques (clustering, regression diagnostics, Mestimators, least median of squares). Particular attention has been devoted to discussions about the choice of appropriate minimization criteria and the robustness of the dioeerent techniques. Their application to conic øtting is described. Keywords: Parameter estimation, Leastsquares, Bias correction, Kalman øltering, Robust regression (R#sum# : tsvp) Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 93, 06902 SOPHIAANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77  Telecopie : (33) 9...
Measurement and modeling of depth cue combination: in defense of weak fusion
 Vision Research
, 1995
"... Various visual cues provide information about depth and shape in a scene. When several of these cues are simultaneously available in a single location in the scene, the visual system attempts to combine them. In this paper, we discuss three key issues relevant to the experimental analysis of depth c ..."
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Cited by 130 (20 self)
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Various visual cues provide information about depth and shape in a scene. When several of these cues are simultaneously available in a single location in the scene, the visual system attempts to combine them. In this paper, we discuss three key issues relevant to the experimental analysis of depth cue combination in human vision: cue promotion, dynamic weighting of cues, and robustness of cue combination. We review recent psychophysical studies of human depth cue combination in light of these issues. We organize the discussion and review as the development of a model of the depth cue combination process termed modified weak fusion (MWF). We relate the MWF framework to Bayesian theories of cue combination. We argue that the MWF model is consistent with previous experimental results and is a parsimonious summary of these results. While the MWF model is motivated by normative considerations, it is primarily intended to guide experimental analysis of depth cue combination in human vision. We describe experimental methods, analogous to perturbation analysis, that permit us to analyze depth cue combination in novel ways. In particular these methods allow us to investigate the key issues we have raised. We summarize recent experimental tests of the MWF framework that use these methods. Depth Multiple cues Sensor fusion
Layered Motion Segmentation and Depth Ordering by Tracking Edges
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—This paper presents a new Bayesian framework for motion segmentation—dividing a frame from an image sequence into layers representing different moving objects—by tracking edges between frames. Edges are found using the Canny edge detector, and the ExpectationMaximization algorithm is then ..."
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Cited by 33 (0 self)
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Abstract—This paper presents a new Bayesian framework for motion segmentation—dividing a frame from an image sequence into layers representing different moving objects—by tracking edges between frames. Edges are found using the Canny edge detector, and the ExpectationMaximization algorithm is then used to fit motion models to these edges and also to calculate the probabilities of the edges obeying each motion model. The edges are also used to segment the image into regions of similar color. The most likely labeling for these regions is then calculated by using the edge probabilities, in association with a Markov Random Fieldstyle prior. The identification of the relative depth ordering of the different motion layers is also determined, as an integral part of the process. An efficient implementation of this framework is presented for segmenting two motions (foreground and background) using two frames. It is then demonstrated how, by tracking the edges into further frames, the probabilities may be accumulated to provide an even more accurate and robust estimate, and segment an entire sequence. Further extensions are then presented to address the segmentation of more than two motions. Here, a hierarchical method of initializing the ExpectationMaximization algorithm is described, and it is demonstrated that the Minimum Description Length principle may be used to automatically select the best number of motion layers. The results from over 30 sequences (demonstrating both two and three motions) are presented and discussed. Index Terms—Video analysis, motion, segmentation, depth cues. æ 1
A convergent incremental gradient method with constant step size
 SIAM J. OPTIM
, 2004
"... An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits ..."
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Cited by 26 (2 self)
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An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits regions in which the gradient is small infinitely often. Under certain unimodality assumptions, global convergence is established. In the quadratic case, a global linear rate of convergence is shown. The method is applied to distributed optimization problems arising in wireless sensor networks, and numerical experiments compare the new method with the standard incremental gradient method.
Rates of convex approximation in nonHilbert spaces
 Constructive Approximation
, 1997
"... This paper deals with sparse approximations by means of convex combinations of elements from a predetermined \basis " subset S of a function space. Speci cally, the focus is on the rate at which the lowest achievable error can be reduced as larger subsets of S are allowed when constructing an approx ..."
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Cited by 18 (0 self)
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This paper deals with sparse approximations by means of convex combinations of elements from a predetermined \basis " subset S of a function space. Speci cally, the focus is on the rate at which the lowest achievable error can be reduced as larger subsets of S are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron, including in particular a computationally attractive incremental approximation scheme. Bounds are derived for broad classes of Banach spaces; in particular, for Lp spaces with 1 <p<1, the O(n 1=2) bounds of Barron and Jones are recovered when p =2. One motivation for the questions studied here arises from the area of \arti cial neural networks, " where the problem can be stated in terms of the growth in the number of \neurons " (the elements of S) needed in order to achieve a desired error rate. The focus on nonHilbert spaces is due to the desire to understand approximation in the more \robust" (resistant to exemplar noise) Lp, 1 p<2 norms. The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of stochastic processes on function spaces. 1
If at First You Don’t Succeed
 in Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI97
, 1997
"... One quality that makes biological systems appear intelligent is their robustness to difficult circumstances. Robustness is crucial to intelligent behavior and important to AI research. We distinguish between antefailtire and postfcailwe robustness for causal tasks. Antefailure robust systems resis ..."
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Cited by 12 (3 self)
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One quality that makes biological systems appear intelligent is their robustness to difficult circumstances. Robustness is crucial to intelligent behavior and important to AI research. We distinguish between antefailtire and postfcailwe robustness for causal tasks. Antefailure robust systems resist failure, whereas postfailure systems incorporate the ability to recover from failure once it happens. We point out the power of postfailure robustness in AI problems, closely examining one example in visual motion tracking. Finally, we raise theoretical issues and argue for greater effort towards building postfailure robust systems.
Regularized Estimation of Mixed Spectra Using a Circular GibbsMarkov Model
 IEEE Trans. Signal Processing
, 2001
"... Formulated as a linear inverse problem, spectral estimation is particularly underdetermined when only short data sets are available. Regularization by penalization is an appealing nonparametric approach to solve such illposed problems. Following Sacchi et al., we first address line spectra reco ..."
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Cited by 9 (3 self)
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Formulated as a linear inverse problem, spectral estimation is particularly underdetermined when only short data sets are available. Regularization by penalization is an appealing nonparametric approach to solve such illposed problems. Following Sacchi et al., we first address line spectra recovering in this framework. Then, we extend the methodology to situations of increasing difficulty: the case of smooth spectra and the case of mixed spectra, i.e., peaks embedded in smooth spectral contributions.