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147
Flexible camera calibration by viewing a plane from unknown orientations
, 1999
"... We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled ..."
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Cited by 358 (6 self)
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We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closedform solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real world use. The corresponding software is available from the author’s Web page.
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 244 (13 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...
Canonic representations for the geometries of multiple projective views
, 1993
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ObjectCentered Surface Reconstruction: Combining MultiImage Stereo and Shading
 International Journal of Computer Vision
, 1995
"... Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rig ..."
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Cited by 121 (19 self)
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Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and selfocclusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...
Fast and Globally Convergent Pose Estimation From Video Images
, 1998
"... Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effecti ..."
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Cited by 119 (5 self)
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Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers. ChienPing Lu, Silicon Graphics Inc. cplu@engr.sgi.com y Greg Hager, Department of Computer...
Selfcalibration of a moving camera from point correspondences and fundamental matrices
 The International Journal of Computer Vision
, 1997
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On Determining The Fundamental Matrix: Analysis Of Different Methods and . . .
, 1993
"... The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper addresses the important problem of its robust determ ..."
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Cited by 92 (15 self)
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The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper addresses the important problem of its robust determination given a number of image point correspondences. We first define precisely this matrix, and show clearly how it is related to the epipolar geometry and to the Essential matrix introduced earlier by LonguetHiggins. In particular, we show that this matrix, defined up to a scale factor, must be of rank two. Different parametrizations for this matrix are then proposed to take into account these important constraints and linear and nonlinear criteria for its estimation are also considered. We then clearly show that the linear criterion is unable to express the rank and normalization constraints. Using the linear criterion leads definitely to the worst result in the determination of the Fu...
Recent progress in coded structured light as a technique to solve the correspondence problem: a survey
 NCE PROBLEM: A SURVEY, PATTERN RECOGNITION
, 1998
"... We present a survey of the most significant techniques, used in the last few years, concerning the coded structured light methods employed to get 3D information. In fact, depth perception is one of the most important subjects in computer vision. Stereovision is an attractive and widely used method, ..."
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Cited by 84 (17 self)
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We present a survey of the most significant techniques, used in the last few years, concerning the coded structured light methods employed to get 3D information. In fact, depth perception is one of the most important subjects in computer vision. Stereovision is an attractive and widely used method, but, it is rather limited to make 3D surface maps, due to the correspondence problem. The correspondence problem can be improved using a method based on structured light concept, projecting a given pattern on the measuring surfaces. However, some relations between the projected pattern and the reflected one must be solved. This relationship can be directly found codifying the projected light, so that, each imaged region of the projected pattern carries the needed information to solve the correspondence problem.
3D Scene Representation as a Collection of Images and Fundamental Matrices
, 1994
"... : In this report, we address the problem of the prediction of new views of a given scene from existing weakly or fully calibrated views called reference views. Our method does not make use of a threedimensional model of the scene, but of the existing relations between the images. The new views are ..."
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Cited by 77 (0 self)
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: In this report, we address the problem of the prediction of new views of a given scene from existing weakly or fully calibrated views called reference views. Our method does not make use of a threedimensional model of the scene, but of the existing relations between the images. The new views are represented in the reference views by a viewpoint and a retinal plane, i.e. by four points which can be chosen interactively. From this representation and from the constraints between the images, we derive an algorithm to predict the new views. We discuss the advantages of this method compared to the commonly used scheme : 3D reconstructionprojection. We show some experimental results with synthetic and real data. Keywords: 3D scene representation, multiview stereo, image synthesis (R'esum'e : tsvp) This work was partially supported by DRET contract No 91815/DRET/EAR and by the EEC under Esprit project 6448, Viva Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 9...