Results 1  10
of
112
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 ..."
Abstract

Cited by 233 (14 self)
 Add to MetaCart
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...
View morphing
 In Computer Graphics (SIGGRAPH’96
, 1996
"... Image morphing techniques can generate compelling 2D transitions between images. However, differences in object pose or viewpoint often cause unnatural distortions in image morphs that are difficult to correct manually. Using basic principles of projective geometry, this paper introduces a simple ex ..."
Abstract

Cited by 233 (20 self)
 Add to MetaCart
Image morphing techniques can generate compelling 2D transitions between images. However, differences in object pose or viewpoint often cause unnatural distortions in image morphs that are difficult to correct manually. Using basic principles of projective geometry, this paper introduces a simple extension to image morphing that correctly handles 3D projective camera and scene transformations. The technique, called view morphing, works by prewarping two images prior to computing a morph and then postwarping the interpolated images. Because no knowledge of 3D shape is required, the technique may be applied to photographs and drawings, as well as rendered scenes. The ability to synthesize changes both in viewpoint and image structure affords a wide variety of interesting 3D effects via simple image transformations.
Euclidean reconstruction from uncalibrated views
 Applications of Invariance in Computer Vision
, 1993
"... The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalen ..."
Abstract

Cited by 233 (14 self)
 Add to MetaCart
The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalently, Euclidean structurefrommotion from an uncalibrated camera. No tractable algorithm for implementing their methods for more than three images have been previously reported. This paper gives a practical algorithm for Euclidean reconstruction from several views with the same camera. The algorithm is demonstrated on synthetic and real data and is shown to behave very robustly in the presence of noise giving excellent calibration and reconstruction results. 1
Autocalibration and the absolute quadric
 in Proc. IEEE Conf. Computer Vision, Pattern Recognition
, 1997
"... We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structu ..."
Abstract

Cited by 210 (7 self)
 Add to MetaCart
We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric — the singular dual 3D quadric ( rank 3 matrix) giving the Euclidean dotproduct between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from images, or quasilinearly from. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasilinear one. It is based on a general constrained optimization technique — sequential quadratic programming — that may well be useful in other vision problems.
Algebraic Functions For Recognition
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1994
"... In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment  yielding a direct reprojection method that cuts through the computations of camera transformation, sce ..."
Abstract

Cited by 147 (29 self)
 Add to MetaCart
In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment  yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks. Keywords Visual Recognition, Al...
Linear Pushbroom Cameras
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1994
"... Modelling th# push broom sensors commonly used in satellite imagery is quite di#cult and computationally intensive due to th# complicated motion ofth# orbiting satellite with respect to th# rotating earth# In addition, th# math#46 tical model is quite complex, involving orbital dynamics, andh#(0k is ..."
Abstract

Cited by 140 (6 self)
 Add to MetaCart
Modelling th# push broom sensors commonly used in satellite imagery is quite di#cult and computationally intensive due to th# complicated motion ofth# orbiting satellite with respect to th# rotating earth# In addition, th# math#46 tical model is quite complex, involving orbital dynamics, andh#(0k is di#cult to analyze. Inth#A paper, a simplified model of apush broom sensor(th# linear push broom model) is introduced. Ith as th e advantage of computational simplicity wh#A9 atth# same time giving very accurate results compared with th# full orbitingpush broom model. Meth# ds are given for solving th# major standardph# togrammetric problems for th e linear push broom sensor. Simple noniterative solutions are given for th# following problems : computation of th# model parameters from groundcontrol points; determination of relative model parameters from image correspondences between two images; scene reconstruction given image correspondences and groundcontrol points. In addition, th# linearpush broom model leads toth#0 retical insigh ts th# t will be approximately valid for th# full model as well.Th# epipolar geometry of linear push broom cameras in investigated and sh own to be totally di#erent from th at of a perspective camera. Neverth eless, a matrix analogous to th e essential matrix of perspective cameras issh own to exist for linear push broom sensors. Fromth#0 it is sh# wn th# t a scene is determined up to an a#ne transformation from two viewswith linearpush broom cameras. Keywords :push broom sensor, satellite image, essential matrixph# togrammetry, camera model The research describ ed in this paper hasb een supportedb y DARPA Contract #MDA97291 C0053 1 Real Push broom sensors are commonly used in satellite cameras, notably th# SPOT satellite forth# generatio...
In Defence of the 8point Algorithm
"... The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the 8point algoritm is a frequent#e cit#3 met#9 d for comput#10 t he fundament al ma t# ix from a set of 8 or more point mat ches. It hast he advant age of simplicit y of implement at ion. The ..."
Abstract

Cited by 133 (3 self)
 Add to MetaCart
The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the 8point algoritm is a frequent#e cit#3 met#9 d for comput#10 t he fundament al ma t# ix from a set of 8 or more point mat ches. It hast he advant age of simplicit y of implement at ion. The prevailing view is, however,t#(9 it isext#3791( suscept#43 t o noise and hence virtually useless for most purposes. This paper challengest#en view, by showing t#ng by precedingt he algorit hm wit h a very simple normalizat ion(t ranslat ion and scaling) oft he coordinat es oft he mat ched point#( result# are obt# ined comparable wit# t he best it## at ive algorit#209 This improved performance is just#690 byt#1082 and verified byext#259( e experiment s on real images.
In Defense of the EightPoint Algorithm
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Abstract—The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eightpoint algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementati ..."
Abstract

Cited by 132 (1 self)
 Add to MetaCart
Abstract—The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eightpoint algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementation. The prevailing view is, however, that it is extremely susceptible to noise and hence virtually useless for most purposes. This paper challenges that view, by showing that by preceding the algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms. This improved performance is justified by theory and verified by extensive experiments on real images. Index Terms—Fundamental matrix, eightpoint algorithm, condition number, epipolar structure, stereo vision.
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 ..."
Abstract

Cited by 99 (2 self)
 Add to MetaCart
. 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 ...
Cooperative Robust Estimation Using Layers of Support
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1991
"... We present an approach to the problem of representing images that contain multiple objects or surfaces. Rather than use an edgebased approach to represent the segmentation of a scene, we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image in ..."
Abstract

Cited by 86 (5 self)
 Add to MetaCart
We present an approach to the problem of representing images that contain multiple objects or surfaces. Rather than use an edgebased approach to represent the segmentation of a scene, we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks. This supportbased approach can represent objects that are split into disjoint regions, or have surfaces that are transparently interleaved. Our framework is based on an extension of robust estimation methods which provide a theoretical basis for supportbased estimation. The Minimum Description Length principle is used to decide how many support maps to use in describing a particular image. We show results applying this framework to heterogeneous interpolation and segmentation tasks on range and motion imagery. 1 Introduction Realworld perceptual systems must deal with complicated and cluttered environments. To succeed in such environments, a system must be able to r...