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397
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 93 (7 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.
A probabilistic framework for space carving
, 2001
"... for the degree of Doctor of Philosophy. ii This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration. This dissertation is not substantially the same as any I have submitted for a degree or diploma or other qualification at any other Unive ..."
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Cited by 90 (3 self)
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for the degree of Doctor of Philosophy. ii This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration. This dissertation is not substantially the same as any I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my dissertation/thesis has already been, or is being concurrently submitted for any such degree, diploma or other qualification. This dissertation contains 78 figures and approximately 46000 words. This dissertation was revised December 2001. This thesis investigates the problem of reconstructing threedimensional objects from image sequences. There are two major contributions in this thesis. The first contribution is an extension to the Space Carving framework that elimi
Interactive construction of 3d models from panoramic mosaics
 IEEE Computer Vision and Pattern Recognition
, 1998
"... This paper presents an interactive modeling system that constructs 3D models from a collection of panoramic image mosaics. A panoramic mosaic consists of a set of images taken around the same viewpoint, and a transformation matrix associated with each input image. Our system first recovers the camer ..."
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Cited by 88 (4 self)
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This paper presents an interactive modeling system that constructs 3D models from a collection of panoramic image mosaics. A panoramic mosaic consists of a set of images taken around the same viewpoint, and a transformation matrix associated with each input image. Our system first recovers the camera pose for each mosaic from known line directions and points, and then constructs the 3D model using all available geometrical constraints. We partition constraints into soft and hard linear constraints so that the modeling process can be formulated as a linearlyconstrained leastsquares problem, which can be solved efficiently using QR factorization. The results of extracting wire frame and texturemapped 3D models from single and multiple panoramas are presented. 1
2 1/2 D Visual servoing with respect to unknown objects through a new estimation scheme of camera displacement
 International Journal of Computer Vision
, 2000
"... Abstract. Classical visual servoing techniques need a strong a priori knowledge of the shape and the dimensions of the observed objects. In this paper, we present how the 2 1/2 D visual servoing scheme we have recently developed, can be used with unknown objects characterized by a set of points. Our ..."
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Cited by 85 (19 self)
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Abstract. Classical visual servoing techniques need a strong a priori knowledge of the shape and the dimensions of the observed objects. In this paper, we present how the 2 1/2 D visual servoing scheme we have recently developed, can be used with unknown objects characterized by a set of points. Our scheme is based on the estimation of the camera displacement from two views, given by the current and desired images. Since visionbased robotics tasks generally necessitate to be performed at video rate, we focus only on linear algorithms. Classical linear methods are based on the computation of the essential matrix. In this paper, we propose a different method, based on the estimation of the homography matrix related to a virtual plane attached to the object. We show that our method provides a more stable estimation when the epipolar geometry degenerates. This is particularly important in visual servoing to obtain a stable control law, especially near the convergence of the system. Finally, experimental results confirm the improvement in the stability, robustness, and behaviour of our scheme with respect to classical methods. Keywords: visual servoing, projective geometry, homography 1.
The dualbootstrap iterative closest point algorithm with application to retinal image registration
 IEEE Trans. Med. Img
, 2003
"... Abstract—Motivated by the problem of retinal image registration, this paper introduces and analyzes a new registration algorithm called DualBootstrap Iterative Closest Point (DualBootstrap ICP). The approach is to start from one or more initial, loworder estimates that are only accurate in small ..."
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Cited by 85 (19 self)
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Abstract—Motivated by the problem of retinal image registration, this paper introduces and analyzes a new registration algorithm called DualBootstrap Iterative Closest Point (DualBootstrap ICP). The approach is to start from one or more initial, loworder estimates that are only accurate in small image regions, called bootstrap regions. In each bootstrap region, the algorithm iteratively: 1) refines the transformation estimate using constraints only from within the bootstrap region; 2) expands the bootstrap region; and 3) tests to see if a higher order transformation model can be used, stopping when the region expands to cover the overlap between images. Steps 1): and 3), the bootstrap steps, are governed by the covariance matrix of the estimated transformation. Estimation refinement [Step 2)] uses a novel robust version of the ICP algorithm. In registering retinal image pairs, DualBootstrap ICP is initialized by automatically matching individual vascular landmarks, and it aligns images based on detected blood vessel centerlines. The resulting quadratic transformations are accurate to less than a pixel. On tests involving approximately 6000 image pairs, it successfully registered 99.5 % of the pairs containing at least one common landmark, and 100 % of the pairs containing at least one common landmark and at least 35 % image overlap. Index Terms—Iterative closest point, medical imaging, registration, retinal imaging, robust estimation.
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 75 (19 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.
Geometrically Constrained Structure from Motion: Points on Planes
 IN EUROPEAN WORKSHOP ON 3D STRUCTURE FROM MULTIPLE IMAGES OF LARGESCALE ENVIRONMENTS (SMILE
, 1998
"... Structure from motion algorithms typically do not use external geometric constraints, e.g., the coplanarity of certain points or known orientations associated with such planes, until a final postprocessing stage. In this paper, we show how such geometric constraints can be incorporated early on ..."
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Cited by 67 (4 self)
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Structure from motion algorithms typically do not use external geometric constraints, e.g., the coplanarity of certain points or known orientations associated with such planes, until a final postprocessing stage. In this paper, we show how such geometric constraints can be incorporated early on in the reconstruction process, thereby improving the quality of the estimates. The approaches we study include hallucinating extra point matches in planar regions, computing fundamental matrices directly from homographies, and applying coplanarity and other geometric constraints as part of the final bundle adjustment stage. Our experimental results indicate that the quality of the reconstruction can be significantly improved by the judicious use of geometric constraints.
Camera network calibration from dynamic silhouettes
 in CVPR
, 2004
"... In this paper we present an automatic method for calibrating a network of cameras from only silhouettes. This is particularly useful for shapefromsilhouette or visualhull systems, as no additional data is needed for calibration. The key novel contribution of this work is an algorithm to robustly ..."
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Cited by 63 (6 self)
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In this paper we present an automatic method for calibrating a network of cameras from only silhouettes. This is particularly useful for shapefromsilhouette or visualhull systems, as no additional data is needed for calibration. The key novel contribution of this work is an algorithm to robustly compute the epipolar geometry from dynamic silhouettes. We use the fundamental matrices computed by this method to determine the projective reconstruction of the complete camera configuration. This is refined into a metric reconstruction using selfcalibration. We validate our approach by calibrating a four camera visualhull system from archive data where the dynamic object is a moving person. Once the calibration parameters have been computed, we use a visualhull algorithm to reconstruct the dynamic object from its silhouettes. 1
Structure and Motion from Silhouettes
, 2001
"... I hereby declare that no part of this thesis has already been or is being submitted for any other degree or qualification. This dissertation is the result of my own original work carried out in the Department of Engineering at the University of Cambridge, except where explicit reference has been mad ..."
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Cited by 62 (13 self)
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I hereby declare that no part of this thesis has already been or is being submitted for any other degree or qualification. This dissertation is the result of my own original work carried out in the Department of Engineering at the University of Cambridge, except where explicit reference has been made to the work of others. This dissertation contains 36,194 words and 91 figures. ii “Cogito, ergo sum. ” (I think, therefore I am.) René Descartes, Le Discours de la Méthode. iv
Quasiconvex optimization for robust geometric reconstruction
 In International Conference on Computer Vision
, 2005
"... Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex fo ..."
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Cited by 61 (1 self)
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Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of smallscale convex programs that are ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing random sampling or local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data. 1