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137
The Fundamental matrix: theory, algorithms, and stability analysis
 International Journal of Computer Vision
, 1995
"... In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of th ..."
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Cited by 232 (14 self)
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In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by LonguetHiggins [40]. This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...
The development and comparison of robust methods for estimating the fundamental matrix
 International Journal of Computer Vision
, 1997
"... Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibrationfree representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, Mest ..."
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Cited by 219 (9 self)
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Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibrationfree representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, Mestimators and random sampling, and the paper develops the theory required to apply them to nonlinear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practitioner to guess at their value. The second goal is therefore to compare and judge the methods. Comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth. A variety of error measures are examined. The experiments allow a statistically satisfying and quasioptimal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined. The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers.
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...
SelfCalibration of a Moving Camera From Point Correspondences and Fundamental Matrices
, 1997
"... . We address the problem of estimating threedimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orien ..."
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Cited by 99 (2 self)
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. We address the problem of estimating threedimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orientation of the camera (its calibration), the motion parameters, and to compute coherent perspective projection matrices which enable us to reconstruct 3D structure up to a similarity. In contrast with other methods, no calibration object with a known 3D shape is needed, and no limitations are put upon the unknown motions to be performed or the parameters to be recovered, as long as they define a projective camera. The theory of the method, which is based on the constraint that the observed points are part of a static scene, thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic, is first detailed. Several algorithms are then presented, and their ...
Photometric Stereo with General, Unknown Lighting
 In IEEE Conference on Computer Vision and Pattern Recognition
, 2001
"... Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on the presence of a single point source of light in each image. In this paper we ..."
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Cited by 93 (8 self)
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Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on the presence of a single point source of light in each image. In this paper we show how to perform photometric stereo assuming that all lights in a scene are isotropic and distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and arbitrary combination of diffuse, point and extended sources. Our work is based on recent results showing that for Lambertian objects, general lighting conditions can be represented using low order spherical harmonics. Using this representation we can recover shape by performing a simple optimization in a lowdimensional space. We also analyze the shape ambiguities that arise in such a representation. 1.
Video Compass
 In Proc. ECCV
, 2002
"... Abstract. In this paper we describe a flexible approach for determining the relative orientation of the camera with respect to the scene. The main premise of the approach is the fact that in manmade environments, the majority of lines is aligned with the principal orthogonal directions of the world ..."
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Cited by 80 (6 self)
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Abstract. In this paper we describe a flexible approach for determining the relative orientation of the camera with respect to the scene. The main premise of the approach is the fact that in manmade environments, the majority of lines is aligned with the principal orthogonal directions of the world coordinate frame. We exploit this observation towards efficient detection and estimation of vanishing points, which provide strong constraints on camera parameters and relative orientation of the camera with respect to the scene. By combining efficient image processing techniques in the line detection and initialization stage we demonstrate that simultaneous grouping and estimation of vanishing directions can be achieved in the absence of internal parameters of the camera. Constraints between vanishing points are then used for partial calibration and relative rotation estimation. The algorithm has been tested in a variety of indoors and outdoors scenes and its efficiency and automation makes it amenable for implementation on robotic platforms. Key words: Vanishing point estimation, relative orientation, calibration using vanishing points, vision guided mobile and aerial robots. 1
Understanding noise sensitivity in structure from motion

, 1996
"... Solutions to the structure from motion problem have been shown to be very sensitive to measurement noise and the respective motion and geometry configuration. Statistical error analysis has become an invaluable tool in analyzing the sensitivity phenomenon. This paper presents a unifying approach to ..."
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Cited by 54 (5 self)
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Solutions to the structure from motion problem have been shown to be very sensitive to measurement noise and the respective motion and geometry configuration. Statistical error analysis has become an invaluable tool in analyzing the sensitivity phenomenon. This paper presents a unifying approach to the problems of statistical bias, correlated noise, choice of error metrics, geometric instabilities and information fusion exploring several assumptions commonly used in motion estimation and reviews several promising techniques for motion estimation. The techniques are based on a small number of principles of statistics and perturbation theory. The analyticity of the approach enables the design of alternatives overcoming the observed instabilities.
Conic Reconstruction and Correspondence from Two Views
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the cor ..."
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Cited by 48 (3 self)
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Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. These two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics. A unified closedform solution is also developed for both projective reconstruction of conics in space from two views for uncalibrated cameras and metric reconstruction from calibrated cameras. Experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images. Keywords conic, stereo correspondence, reconstruction. I. Introduction In...
Determining the egomotion of an uncalibrated camera from instantaneous optical flow
 Journal of the Optical Society of America A
, 1997
"... Abstract. The main result of this paper is a procedure for selfcalibration of a moving camera from instantaneous optical ow. Under certain assumptions, this procedure allows the egomotion and some intrinsic parameters of the camera to be determined solely from the instantaneous positions and veloc ..."
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Cited by 44 (24 self)
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Abstract. The main result of this paper is a procedure for selfcalibration of a moving camera from instantaneous optical ow. Under certain assumptions, this procedure allows the egomotion and some intrinsic parameters of the camera to be determined solely from the instantaneous positions and velocities of a set of image features. The proposed method relies upon the use of a di erential epipolar equation that relates optical ow to the egomotion and internal geometry of the camera. The paper presents a detailed derivation of this equation. This aspect of the work may be seen as a recasting into an analytical framework of the pivotal research ofVieville and Faugeras. 1 The information about the camera's egomotion and internal geometry enters the di erential epipolar equation via two matrices. It emerges that the optical ow determines the composite ratio of some of the entries of the two matrices. It is shown that a camera with unknown focal length undergoing arbitrary motion can be selfcalibrated via closedform expressions in the composite ratio. The corresponding formulae specify ve egomotion parameters, as well as the focal length and its derivative. An accompanying procedure is presented for reconstructing the viewed scene, up to scale, from the derived selfcalibration data and the optical ow data. Experimental results are given to demonstrate the correctness of the approach. 1.
Robust Motion and Correspondence of Noisy 3D Point Sets with Missing Data
, 1999
"... We describe RICP, a robust algorithm for registering and finding correspondences in sets of 3D points with significant percentages of missing data, and therefore useful for both motion analysis and reverse engineering. RICP exploits LMedS robust estimation to withstand the effect of outliers. Our e ..."
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Cited by 42 (8 self)
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We describe RICP, a robust algorithm for registering and finding correspondences in sets of 3D points with significant percentages of missing data, and therefore useful for both motion analysis and reverse engineering. RICP exploits LMedS robust estimation to withstand the effect of outliers. Our extensive experimental comparison of RICP with ICP shows RICP's superior robustness and reliability. Key words: ICP, Registration, CADbased Vision, Motion Estimation, Reverse Engineering 1 Introduction This paper addresses the registration of noisy sets of 3D points, a percentage of which is present in one set but not in the other, and in the absence of correspondence information. This problem has been considered mainly in two applicative domains, motion analysis and reverse engineering. Apart from the differences in emphasis discussed below, algorithms from both domains solve basically the same two problems: estimating the 3D motion (rotation matrix and translation vector) aligning th...