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266
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 88 (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 78 (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.
Guided sampling and consensus for motion estimation. In
 Proc. European Conference on Computer Vision,
, 2002
"... ..."
A featurebased, robust, hierarchical algorithm for registering pairs of images of the curved human retina
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... AbstractÐThis paper describes a robust hierarchical algorithm for fullyautomatic registration of a pair of images of the curved human retina photographed by a fundus microscope. Accurate registration is essential for mosaic synthesis, change detection, and design of computeraided instrumentation. ..."
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Cited by 68 (18 self)
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AbstractÐThis paper describes a robust hierarchical algorithm for fullyautomatic registration of a pair of images of the curved human retina photographed by a fundus microscope. Accurate registration is essential for mosaic synthesis, change detection, and design of computeraided instrumentation. Central to the newalgorithm is a 12parameter interimage transformation derived by modeling the retina as a rigid quadratic surface with unknown parameters, imaged by an uncalibrated weak perspective camera. The parameters of this model are estimated by matching vascular landmarks extracted by an algorithm that recursively traces the blood vessel structure. The parameter estimation technique, which could be generalized to other applications, is a hierarchy of models and methods: an initial match set is pruned based on a zeroth order transformation estimated as the peak of a similarityweighted histogram; a first order, affine transformation is estimated using the reduced match set and leastmedian of squares; and the final, second order, 12parameter transformation is estimated using an Mestimator initialized from the first order estimate. This hierarchy makes the algorithm robust to unmatchable image features and mismatches between features caused by large interframe motions. Before final convergence of the Mestimator, feature positions are refined and the correspondence set is enhanced using normalized sumofsquared differences matching of regions deformed by the emerging transformation. Experiments involving 3,000 image pairs �1; 024 1; 024 pixels) from 16 different healthy eyes were performed. Starting with as low as 20 percent overlap between images, the algorithm improves its success rate exponentially and has a negligible failure rate above 67 percent overlap. The experiments also quantify the reduction in errors as the model complexities increase. Final registration errors less than a pixel are routinely achieved. The speed, accuracy, and
Estimation of subspace arrangements with applications in modeling and segmenting mixed data
, 2006
"... Abstract. Recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted highdimensional data that have very complicated structures. From both geometric and statistical points of view, such unsorted data are considered mixed as differ ..."
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Cited by 60 (4 self)
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Abstract. Recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted highdimensional data that have very complicated structures. From both geometric and statistical points of view, such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model. In this paper we propose to use subspace arrangements—a union of multiple subspaces—for modeling mixed data: each subspace in the arrangement is used to model just a homogeneous subset of the data. Thus, multiple subspaces together can capture the heterogeneous structures within the data set. In this paper, we give a comprehensive introduction to a new approach for the estimation of subspace arrangements. This is known as generalized principal component analysis (GPCA). In particular, we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust, even when the given data are corrupted by noise or contaminated with outliers. This new method in many ways improves and generalizes extant methods for modeling or clustering mixed data. There have been successful applications of this new method to many realworld problems in computer vision, image processing, and system identification. In this paper, we will examine several of those representative applications. This paper is intended to be expository in nature. However, in order that this may serve as a more complete reference for both theoreticians and practitioners, we take the liberty of filling in several gaps between the theory and the practice in the existing literature.
Impsac: A synthesis of importance sampling and random sample consensus to effect multiscale image matching for small and wide baselines
 In ECCV2000
, 2000
"... The goal of this work is to obtain accurate matches and epipolar geometry between two images of the same scene, where the motion is unlikely to be smooth or known a priori. Once the matches and two view image relation have been recovered, they can be used for image compression, for building 3D model ..."
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Cited by 58 (1 self)
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The goal of this work is to obtain accurate matches and epipolar geometry between two images of the same scene, where the motion is unlikely to be smooth or known a priori. Once the matches and two view image relation have been recovered, they can be used for image compression, for building 3D models [3, 33, 35, 48], for object recognition [19], for extraction of images from databases [31]
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 54 (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...
Reconstruction from uncalibrated sequences with a hierarchy of trifocal tensors
 In ECCV
, 2000
"... This paper considers projective reconstruction with a hierarchical computational structure of trifocal tensors that integrates feature tracking and geometrical validation of the feature tracks. The algorithm was embedded into a system aimed at completely automatic Euclidean reconstruction from uncal ..."
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Cited by 54 (5 self)
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This paper considers projective reconstruction with a hierarchical computational structure of trifocal tensors that integrates feature tracking and geometrical validation of the feature tracks. The algorithm was embedded into a system aimed at completely automatic Euclidean reconstruction from uncalibrated handheld amateur video sequences. The algorithm was tested as part of this system on a number of sequences grabbed directly from a lowend video camera without editing. The proposed approach can be considered a generalisation of a scheme of [Fitzgibbon and Zisserman, ECCV ‘98]. The proposed scheme tries to adapt itself to the motion and frame rate in the sequence by finding good triplets of views from which accurate and unique trifocal tensors can be calculated. This is in contrast to the assumption that three consecutive views in the video sequence are a good choice. Using trifocal tensors with a wider span suppresses error accumulation and makes the scheme less reliant on bundle adjustment. The proposed computational structure may also be used with fundamental matrices as the basic building block. 1
The Geometry and Matching of Lines and Curves Over Multiple Views
"... This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography in ..."
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Cited by 52 (1 self)
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This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography induced by this plane for transfer from one image to another. It is shown that given the fundamental matrix between two views, and images of the curve in each view, then the plane of a conic may be determined up to a two fold ambiguity, but local curvature of a curve uniquely determines the plane. It is then shown that given the trifocal tensor between three views, this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third. Simple expressions are developed for the plane and homography in each case.
Match Propagation for ImageBased Modeling and Rendering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... This paper presents a quasidense matching algorithm between images based on match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best rst strategy, and produces a quasidense disparity map. The quasidense matching ..."
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Cited by 50 (6 self)
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This paper presents a quasidense matching algorithm between images based on match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best rst strategy, and produces a quasidense disparity map. The quasidense matching aims at broad modeling and visualization applications which rely heavily on matching information. Our algorithm is robust to initial sparse match outliers due to the best rst strategy; It is ecient in time and space as it is only output sensitive; It handles halfoccluded areas because of the simultaneous enforcement of newly introduced discrete 2D gradient disparity limit and the uniqueness constraint. The properties of the algorithm are discussed and empirically demonstrated.