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27
Separable Nonlinear Least Squares: the Variable Projection Method and its Applications
 Institute of Physics, Inverse Problems
, 2002
"... this paper nonlinear data fitting problems which have as their underlying model a linear combination of nonlinear functions. More generally, one can also consider that there are two sets of unknown parameters, where one set is dependent on the other and can be explicitly eliminated. Models of this t ..."
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Cited by 94 (1 self)
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this paper nonlinear data fitting problems which have as their underlying model a linear combination of nonlinear functions. More generally, one can also consider that there are two sets of unknown parameters, where one set is dependent on the other and can be explicitly eliminated. Models of this type are very common and we will show a variety of applications in different fields. Inasmuch as many inverse problems can be viewed as nonlinear data fitting problems, this material will be of interest to a wide crosssection of researchers and practitioners in parameter, material or system identification, signal analysis, the analysis of spectral data, medical and biological imaging, neural networks, robotics, telecommunications and model order reduction, to name a few
Comparison of Approaches to Egomotion Computation
 In CVPR
, 1996
"... We evaluated six algorithms for computing egomotion from image velocities. We established benchmarks for quantifying bias and sensitivity to noise, and for quantifying the convergence properties of those algorithms that require numerical search. Our simulation results reveal some interesting and sur ..."
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Cited by 85 (0 self)
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We evaluated six algorithms for computing egomotion from image velocities. We established benchmarks for quantifying bias and sensitivity to noise, and for quantifying the convergence properties of those algorithms that require numerical search. Our simulation results reveal some interesting and surprising results. First, it is often written in the literature that the egomotion problem is difficult because translation (e.g., along the Xaxis) and rotation (e.g., about the Yaxis) produce similar image velocities. We found, to the contrary, that the bias and sensitivity of our six algorithms are totally invariant with respect to the axis of rotation. Second, it is also believed by some that fixating helps to make the egomotion problem easier. We found, to the contrary, that fixating does not help when the noise is independent of the image velocities. Fixation does help if the noise is proportional to speed, but this is only for the trivial reason that the speeds are slower under fixatio...
Pictures and trails: a new framework for the computation of shape and motion from perspective image sequences
 In Proc. IEEE Conf. Comp. Vision Patt. Recog
, 1994
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Robust Egomotion Estimation from Affine Motion Parallax
 In European Conference on Computer Vision
, 1994
"... A condensed version of this paper will be presented at ECCV'94 ..."
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Cited by 16 (0 self)
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A condensed version of this paper will be presented at ECCV'94
Motion without Structure
"... We propose a new paradigm, motion without structure, for determining the egomotion between two frames. It is best suited for cases where reliable feature point correspondence is difficult, or for cases where the expected camera motion is large. The problem is posed as a fivedimensional search over ..."
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Cited by 14 (0 self)
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We propose a new paradigm, motion without structure, for determining the egomotion between two frames. It is best suited for cases where reliable feature point correspondence is difficult, or for cases where the expected camera motion is large. The problem is posed as a fivedimensional search over the space of possible motions during which the structural information present in the two views is neither implicitly or explicitly used or estimated. To accomplish this search, a cost function is devised that measures the relative likelihood of each hypothesized motion. This cost function is invariant to the structure present in the scene. An analysis of the global scene statistics present in an image, together with the geometry of epipolar misalignment, suggests a measure based on the sum of squared differences between pixels in the first image and their corresponding epipolar line segments in the second image. The measure relies on a simple statistical characteristic of neighboring image ...
A review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot
, 2003
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VisuallyGuided Navigation by Comparing Edge Images
 Workshop on the Algorithmic Foundations of Robotics
, 1995
"... this paper we describe a method for using twodimensional shape information to determine the location of a mobile robot with respect to some visual landmark in the world. The task is for the robot to navigate to a specified target or landmark in its visual field, possibly in the presence of obstacles ..."
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Cited by 8 (0 self)
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this paper we describe a method for using twodimensional shape information to determine the location of a mobile robot with respect to some visual landmark in the world. The task is for the robot to navigate to a specified target or landmark in its visual field, possibly in the presence of obstacles. The landmark is initially specified either by marking some portion of an image (containing the landmark) or by providing a prior model. The location of the landmark with respect to the robot is recovered from the change in apparent size and position of the landmark in the image, as a function of the motion of the robot. The size and position of the landmark are determined by comparing twodimensional shapes from successive images taken as the robot moves.
Input Redundancy and Output Observability in the Analysis of Visual Motion
, 1993
"... Determining structure and motion from the images produced by a camera on a moving robot is a nonlinear and potentially poorly conditioned computation. A reliable system must use redundant data so that small random errors in the inputs cancel out statistically to produce better outputs. Furthermore, ..."
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Cited by 4 (0 self)
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Determining structure and motion from the images produced by a camera on a moving robot is a nonlinear and potentially poorly conditioned computation. A reliable system must use redundant data so that small random errors in the inputs cancel out statistically to produce better outputs. Furthermore, the output quantities to be computed must be well observable, that is, they should have wellmeasurable effects on the images. I demonstrate the importance of these two principles with three system for the analysis of visual motion: the factorization method for structure and motion under orthography, a system to compute camera motion from narrowly spaced frames, and a global, multiframe, and multifeature method for the reconstruction of structure and motion from sequences taken under perspective.
Angle Independent Bundle Adjustment Refinement
 Proceedings of Third Intâ€™l Symposium on 3D Data Processing, Visualization, and Transmission
, 2006
"... Obtaining a digital model of a realworld 3D scene is a challenging task pursued by computer vision and computer graphics. Given an initial approximate 3D model, a popular refinement process is to perform a bundle adjustment of the estimated camera position, camera orientation, and scene points. Unf ..."
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Obtaining a digital model of a realworld 3D scene is a challenging task pursued by computer vision and computer graphics. Given an initial approximate 3D model, a popular refinement process is to perform a bundle adjustment of the estimated camera position, camera orientation, and scene points. Unfortunately, simultaneously solving for both camera position and camera orientation is an illconditioned problem. To address this issue, we propose an improved, cameraorientation independent cost function that can be used instead of the standard bundle adjustment cost function. This yields a new bundle adjustment formulation which exhibits noticeably better numerical behavior, but at the expense of an increased computational cost. We alleviate the additional cost by automatically partitioning the dataset into smaller subsets. Minimizing our cost function for these subsets still achieves significant error reduction over standard bundle adjustment. We empirically demonstrate our formulation using several different size models and image sequences. 1.
MultiView Structure Computation without Explicitly Estimating Motion
"... Most existing structurefrommotion methods follow a common twostep scheme, where relative camera motions are estimated in the first step and 3D structure is computed afterward in the second step. This paper presents a novel scheme which bypasses the motionestimation step, and goes directly to str ..."
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Cited by 3 (1 self)
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Most existing structurefrommotion methods follow a common twostep scheme, where relative camera motions are estimated in the first step and 3D structure is computed afterward in the second step. This paper presents a novel scheme which bypasses the motionestimation step, and goes directly to structure computation step. By introducing graph rigidity theory to Sfm problems, we demonstrate that such a scheme is not only theoretically possible, but also technically feasible and effective. We also derive a new convex relaxation technique (based on semidefinite programming) which implements the above scheme very efficiently. Our new method provides other benefits as well, such as that it offers a new way to looking at Sfm, and that it is naturally suited for handling sparse largescale Sfm problems. 1.