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16
High accuracy computation of rankconstrained fundamental matrix by efficient search
 Proc. 10th Meeting Image Recog. Understand. (MIRU2007
, 2007
"... A new method is presented for computing the fundamental matrix from point correspondences: its singular value decomposition (SVD) is optimized by the LevenbergMarquard (LM) method. The search is initialized by optimal correction of unconstrained ML. There is no need for tentative 3D reconstruction ..."
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Cited by 13 (7 self)
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A new method is presented for computing the fundamental matrix from point correspondences: its singular value decomposition (SVD) is optimized by the LevenbergMarquard (LM) method. The search is initialized by optimal correction of unconstrained ML. There is no need for tentative 3D reconstruction. The accuracy achieves the theoretical bound (the KCR lower bound). 1
Extended FNS for constrained parameter estimation
 In: Proc. 10th Meeting Image Recog. Understand
, 2007
"... Abstract We present a new method, called “EFNS ” (“extended FNS”), for linearizable constrained maximum likelihood estimation. This complements the CFNS of Chojnacki et al. and is a true extension of the FNS of Chojnacki et al. to an arbitrary number of intrinsic constraints. Computing the fundament ..."
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Abstract We present a new method, called “EFNS ” (“extended FNS”), for linearizable constrained maximum likelihood estimation. This complements the CFNS of Chojnacki et al. and is a true extension of the FNS of Chojnacki et al. to an arbitrary number of intrinsic constraints. Computing the fundamental matrix as an illustration, we demonstrate that CFNS does not necessarily converge to a correct solution, while EFNS converges to an optimal value which nearly satisfies the theoretical accuracy bound (KCR lower bound).
Compact fundamental matrix computation
 Proc. 3rd Pacific Rim Symp. Image and Video Technology
, 2009
"... Abstract. A very compact algorithm is presented for fundamental matrix computation from point correspondences over two images. The computation is based on the strict maximum likelihood (ML) principle, minimizing the reprojection error. The rank constraint is incorporated by the EFNS procedure. Altho ..."
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Cited by 6 (4 self)
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Abstract. A very compact algorithm is presented for fundamental matrix computation from point correspondences over two images. The computation is based on the strict maximum likelihood (ML) principle, minimizing the reprojection error. The rank constraint is incorporated by the EFNS procedure. Although our algorithm produces the same solution as all existing MLbased methods, it is probably the most practical of all, being small and simple. By numerical experiments, we confirm that our algorithm behaves as expected. 1
Unified Computation of Strict Maximum Likelihood for Geometric Fitting
"... A new numerical scheme is presented for strictly computing maximum likelihood (ML) of geometric fitting problems. Intensively studied in the past are those methods that first transform the data into a computationally convenient form and then assume Gaussian noise in the transformed space. In contras ..."
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Cited by 5 (4 self)
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A new numerical scheme is presented for strictly computing maximum likelihood (ML) of geometric fitting problems. Intensively studied in the past are those methods that first transform the data into a computationally convenient form and then assume Gaussian noise in the transformed space. In contrast, our method assumes Gaussian noise in the original data space. It is shown that the strict ML solution can be computed by iteratively using existing methods. Then, our method is applied to ellipse fitting and fundamental matrix computation. Our method is also shown to encompasses optimal correction, computing, e.g., perpendiculars to an ellipse and triangulating stereo images. While such applications have been studied individually, our method generalizes them into an application independent form from a unified point of view. 1.
Highest Accuracy Fundamental Matrix Computation
"... Abstract. We compare algorithms for fundamental matrix computation, which we classify into “a posteriori correction”, “internal access”, and “external access”. Doing experimental comparison, we show that the 7parameter LevenbergMarquardt (LM) search and the extended FNS (EFNS) exhibit the best per ..."
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Abstract. We compare algorithms for fundamental matrix computation, which we classify into “a posteriori correction”, “internal access”, and “external access”. Doing experimental comparison, we show that the 7parameter LevenbergMarquardt (LM) search and the extended FNS (EFNS) exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree. 1
Y.: Small algorithm for fundamental matrix computation
 In: Proc. Meeting Image Recognition and Understanding
, 2008
"... Abstract A very small algorithm is presented for computing the fundamental matrix from point correspondences over two images. The computation is based on the strict maximum likelihood (ML) principle, minimizing the reprojection error. The rank constraint is incorporated by the EFNS procedure. Althou ..."
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Cited by 2 (2 self)
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Abstract A very small algorithm is presented for computing the fundamental matrix from point correspondences over two images. The computation is based on the strict maximum likelihood (ML) principle, minimizing the reprojection error. The rank constraint is incorporated by the EFNS procedure. Although our algorithm produces the same solution as all existing MLbased methods, it is probably the smallest of all. By numerical experiments, we confirm that our algorithm behaves as expected.
Intelligent frame selection for anatomic reconstruction from endoscopic video
 in Applications of Computer Vision (WACV), 2009 Workshop on
, 2009
"... Using endoscopic video, it is possible to perform 3D reconstruction of the anatomy using the well known epipolar constraint between matched feature points. Through this constraint, it is possible to recover the translation and rotation between camera positions and thus reconstruct the 3D anatomy b ..."
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Using endoscopic video, it is possible to perform 3D reconstruction of the anatomy using the well known epipolar constraint between matched feature points. Through this constraint, it is possible to recover the translation and rotation between camera positions and thus reconstruct the 3D anatomy by triangulation. However, these motion estimates are not stable for small camera motions. In this work, we propose a covariance estimation scheme to select pairs of frames which give rise to stable motion estimates, i.e. minimal variance with respect to pixel match error. We parameterize the essential matrix using a minimal 5 parameter representation and estimate motion covariance based upon the estimated feature match variance. The proposed algorithm is applied to endoscopic video sequences recorded in porcine sinus passages in order to extract stable motion estimates. 1.
Fundamental Matrix Computation: Theory and Practice
, 2007
"... We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7parameter LevenbergMarquardt (LM) search, EFNS, and EFNSbased bundle adjustment. Doing experimental comparison, we show that EFNS and the 7parameter LM s ..."
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Cited by 1 (0 self)
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We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7parameter LevenbergMarquardt (LM) search, EFNS, and EFNSbased bundle adjustment. Doing experimental comparison, we show that EFNS and the 7parameter LM search exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree. 1.
Fundamental Matrix Computation: Theory and Practice
"... We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7parameter LevenbergMarquardt (LM) search, extended FNS, and EFNSbased bundle adjustment. Doing experimental comparison, we show that EFNS and the 7parame ..."
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We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7parameter LevenbergMarquardt (LM) search, extended FNS, and EFNSbased bundle adjustment. Doing experimental comparison, we show that EFNS and the 7parameter LM search exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree. 1.
Multiprojective parameter estimation for sets of homogeneous matrices
 in Proc. Digital Image Computing: Techniques and Applications Conf., 2009
"... Abstract—A number of problems in computer vision require the estimation of a set of matrices, each of which is defined only up to an individual scale factor and represents the parameters of a separate model, under the assumption that the models are intrinsically interconnected. One example of such a ..."
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Abstract—A number of problems in computer vision require the estimation of a set of matrices, each of which is defined only up to an individual scale factor and represents the parameters of a separate model, under the assumption that the models are intrinsically interconnected. One example of such a set is a family of fundamental matrices sharing an infinite homography. Here an approach is presented to estimating a general set of interdependent matrices defined to within separate scales. The input data is assumed to consist of individually estimated matrices for particular models, which when considered collectively may fail to satisfy the constraints representing the intermodel relationships. Two cost functions are proposed for upgrading, via optimisation, the data of this sort to a collection of matrices satisfying the intermodel constraints. One of these functions incorporates error covariances. Each function is invariant to any change of scale for the input estimates. The proposed approach is applied to the particular problem of estimating a set of fundamental matrices of the form of the example set above. Experimental results are given which demonstrate the effectiveness of the approach. Keywordsmultiprojective parameter estimation, scale independence, maximum likelihood, covariance, homogeneous matrix, fundamental matrix, homography, infinite homography I.