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270
MLESAC: A New Robust Estimator with Application to Estimating Image Geometry
 Computer Vision and Image Understanding
, 2000
"... A new method is presented for robustly estimating multiple view relations from point correspondences. The method comprises two parts. The first is a new robust estimator MLESAC which is a generalization of the RANSAC estimator. It adopts the same sampling strategy as RANSAC to generate putative solu ..."
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Cited by 335 (10 self)
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A new method is presented for robustly estimating multiple view relations from point correspondences. The method comprises two parts. The first is a new robust estimator MLESAC which is a generalization of the RANSAC estimator. It adopts the same sampling strategy as RANSAC to generate putative solutions, but chooses the solution that maximizes the likelihood rather than just the number of inliers. The second part of the algorithm is a general purpose method for automatically parameterizing these relations, using the output of MLESAC. A difficulty with multiview image relations is that there are often nonlinear constraints between the parameters, making optimization a difficult task. The parameterization method overcomes the difficulty of nonlinear constraints and conducts a constrained optimization. The method is general and its use is illustrated for the estimation of fundamental matrices, image–image homographies, and quadratic transformations. Results are given for both synthetic and real images. It is demonstrated that the method gives results equal or superior to those of previous approaches. c ○ 2000 Academic Press 1.
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 253 (10 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.
Zisserman A.: Metric rectification for perspective images of planes
 In Proc. of International Conference of Computer Vision and Pattern Recognition
, 1998
"... We describe the geometry, constraints and algorithmic implementation for metric rectification of planes. The rectification allows metric properties, such as angles and length ratios, to be measured on the world plane from a perspective image. The novel contributions are: first, that in a stratified ..."
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Cited by 162 (9 self)
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We describe the geometry, constraints and algorithmic implementation for metric rectification of planes. The rectification allows metric properties, such as angles and length ratios, to be measured on the world plane from a perspective image. The novel contributions are: first, that in a stratified context the various forms of providing metric information, which include a known angle, two equal though unknown angles, and a known length ratio; can all be represented as circular constraints on the parameters of an affine transformation of the plane — this provides a simple and uniform framework for integrating constraints; second, direct rectification from right angles in the plane; third, it is shown that metric rectification enables calibration of the internal camera parameters; fourth, vanishing points are estimated using a Maximum Likelihood estimator; fifth, an algorithm for automatic rectification. Examples are given for a number of images, and applications demonstrated for texture map acquisition and metric measurements. 1
Autocalibration from planar scenes
 European Conference on Computer Vision
, 1998
"... This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal par ..."
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Cited by 143 (2 self)
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This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal parameters remain constant during the motion. This work extends the various existing methods for nonplanar autocalibration to a practically common situation in which it is not possible to bootstrap the calibration from an intermediate projective reconstruction. It also extends Hartley’s method for the internal calibration of a rotating camera, to allow camera translation and to provide 3D as well as calibration information. The basic constraint is that the projections of orthogonal direction vectors (points at infinity) in the plane must be orthogonal in the calibrated camera frame of each image. Abstractly, since the two circular points of the 3D plane (representing its Euclidean structure) lie on the 3D absolute conic, their projections into each image must lie on the absolute conic’s image (representing the camera calibration). The resulting numerical algorithm optimizes this constraint over all circular points and projective calibration parameters, using the interimage homographies as a projective scene representation.
Motion Segmentation by Subspace Separation and Model Selection
 Proc. 8th Int. Conf. Comput. Vision
, 2001
"... Reformulating the CosteiraKanade algorithm as a pure mathematical theorem independent of the TomasiKanade factorization, we present a robust segmentation algorithm by incorporating such techniques as dimension correction, model selection using the geometric AIC, and leastmedian fitting. Doing num ..."
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Cited by 135 (18 self)
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Reformulating the CosteiraKanade algorithm as a pure mathematical theorem independent of the TomasiKanade factorization, we present a robust segmentation algorithm by incorporating such techniques as dimension correction, model selection using the geometric AIC, and leastmedian fitting. Doing numerical simulations, we demonstrate that our algorithm dramatically outperforms existing methods. It does not involve any parameters which need to be adjusted empirically. 1.
Geometric Motion Segmentation and Model Selection
 Phil. Trans. Royal Society of London A
, 1998
"... this paper we place the three problems into a common statistical framework; investigating the use of information criteria and robust mixture models as a principled way for motion segmentation of images. The final result is a general fully automatic algorithm for clustering that works in the presence ..."
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Cited by 125 (2 self)
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this paper we place the three problems into a common statistical framework; investigating the use of information criteria and robust mixture models as a principled way for motion segmentation of images. The final result is a general fully automatic algorithm for clustering that works in the presence of noise and outliers. 1. Introduction
Multiscale EMICP: A Fast and Robust Approach for Surface Registration
 European Conference on Computer Vision (ECCV 2002), volume 2353 of LNCS
, 2002
"... We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general MaximumLikelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to t ..."
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Cited by 95 (7 self)
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We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general MaximumLikelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to the Iterative Closest Point algorithm (ICP) with the Mahalanobis distance.
A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each Ndimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there ar ..."
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Cited by 89 (18 self)
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We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each Ndimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for nearperiodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis.
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
 International Journal of Computer Vision
"... We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix. ..."
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Cited by 83 (6 self)
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We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix.
On the fitting of surfaces to data with covariances
 IEEE Trans. Patt. Anal. Mach. Intell
, 2000
"... AbstractÐWe consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanie ..."
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Cited by 71 (17 self)
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AbstractÐWe consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximumlikelihood formulation and applying certain necessary approximations that render the problem tractable. A novel, Newtonlike iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.