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93
Y.: Performance evaluation of iterative geometric fitting algorithms
 Comput. Stat. Data Anal
, 2007
"... The convergence performance of typical numerical schemes for geometric fitting for computer vision applications is compared. First, the problem and the associated KCR lower bound are stated. Then, three well known fitting algorithms are described: FNS, HEIV, and renormalization. To these, we add a ..."
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Cited by 14 (11 self)
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The convergence performance of typical numerical schemes for geometric fitting for computer vision applications is compared. First, the problem and the associated KCR lower bound are stated. Then, three well known fitting algorithms are described: FNS, HEIV, and renormalization. To these, we add a special variant of GaussNewton iterations. For initialization of iterations, random choice, least squares, and Taubin’s method are tested. Simulation is conducted for fundamental matrix computation and ellipse fitting, which reveals different characteristics of each method. c°2007 Published by Elsevier B.V. All rights reserved.
Statistical optimization for geometric fitting: Theoretical accuracy analysis and high order error analysis
 Int. J. Comput. Vis
, 2008
"... A rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data for computer vision applications. First, it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and ..."
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Cited by 14 (8 self)
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A rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data for computer vision applications. First, it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and hence a different mathematical framework is necessary in such a domain. After general theories on estimation and accuracy are given, typical existing techniques are selected, and their accuracy is evaluated up to higher order terms. This leads to a “hyperaccurate ” method that outperforms existing methods. 1.
High accuracy fundamental matrix computation and its performance evaluation
 Proc. 17th British Machine Vision Conf (BMVC 2006), vol.1
, 2006
"... We compare the convergence performance of different numerical schemes for computing the fundamental matrix from point correspondences over two images. First, we state the problem and the associated KCR lower bound. Then, we describe the algorithms of three wellknown methods: FNS, HEIV, and renormal ..."
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Cited by 14 (10 self)
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We compare the convergence performance of different numerical schemes for computing the fundamental matrix from point correspondences over two images. First, we state the problem and the associated KCR lower bound. Then, we describe the algorithms of three wellknown methods: FNS, HEIV, and renormalization, to which we add GaussNewton iterations. For initial values, we test random choice, least squares, and Taubin’s method. Experiments using simulated and real images reveal different characteristics of each method. Overall, FNS exhibits the best convergence performance. 1
Robust realtime myocardial border tracking for echocardiography: An information fusion approach
 MEDICAL IMAGING, IEEE TRANSACTIONS ON
, 2004
"... Ultrasound is a main noninvasive modality for the assessment of the heart function. Wall tracking from ultrasound data is, however, inherently difficult due to weak echoes, clutter, poor signaltonoise ratio, and signal dropouts. To cope with these artifacts, pretrained shape models can be appli ..."
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Cited by 14 (2 self)
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Ultrasound is a main noninvasive modality for the assessment of the heart function. Wall tracking from ultrasound data is, however, inherently difficult due to weak echoes, clutter, poor signaltonoise ratio, and signal dropouts. To cope with these artifacts, pretrained shape models can be applied to constrain the tracking. However, existing methods for incorporating subspace shape constraints in myocardial border tracking use only partial information from the model distribution, and do not exploit spatially varying uncertainties from feature tracking. In this paper, we propose a complete fusion formulation in the information space for robust shape tracking, optimally resolving uncertainties from the system dynamics, heteroscedastic measurement noise, and subspace shape model. We also exploit information from the ground truth initialization where this is available. The new framework is applied for tracking of myocardial borders in very noisy echocardiography sequences. Numerous myocardium tracking experiments validate the theory and show the potential of very accurate wall motion measurements. The proposed framework outperforms the traditional shapespaceconstrained tracking algorithm by a significant margin. Due to the optimal fusion of different sources of uncertainties, robust performance is observed even on the most challenging cases.
What value covariance information in estimating vision parameters
 In Eighth IEEE International Conference on Computer Vision (ICCV 2001
, 2001
"... Many parameter estimation methods used in computer vision are able to utilise covariance information describing the uncertainty of data measurements. This paper considers the value of this information to the estimation process when applied to measured image point locations. Covariance matrices are f ..."
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Cited by 13 (4 self)
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Many parameter estimation methods used in computer vision are able to utilise covariance information describing the uncertainty of data measurements. This paper considers the value of this information to the estimation process when applied to measured image point locations. Covariance matrices are first described and a procedure is then outlined whereby covariances may be associated with image features located via a measurement process. An empirical study is made of the conditions under which covariance information enables generation of improved parameter estimates. Also explored is the extent to which the noise should be anisotropic and inhomogeneous if improvements are to be obtained over covariancefree methods. Critical in this is the devising of synthetic experiments under which noise conditions can be precisely controlled. Given that covariance information is, in itself, subject to estimation error, tests are also undertaken to determine the impact of imprecise covariance information upon the quality of parameter estimates. Finally, an experiment is carried out to assess the value of covariances in estimating the fundamental matrix from real images. 1.
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
Another way of looking at planebased calibration: The centre circle constraint
 Proc. ECCV ’02
, 2002
"... Abstract. The planebased calibration consists in recovering the internal parameters of the camera from the views of a planar pattern with a known geometric structure. The existing direct algorithms use a problem formulation based on the properties of basis vectors. They minimize algebraic distances ..."
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Cited by 13 (2 self)
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Abstract. The planebased calibration consists in recovering the internal parameters of the camera from the views of a planar pattern with a known geometric structure. The existing direct algorithms use a problem formulation based on the properties of basis vectors. They minimize algebraic distances and may require a ‘good ’ choice of system normalization. Our contribution is to put this problem into a more intuitive geometric framework. A solution can be obtained by intersecting circles, called Centre Circles, whose parameters are computed from the worldtoimage homographies. The Centre Circle is the camera centre locus when planar figures are in perpective correspondence, in accordance with a Poncelet’s theorem. An interesting aspect of our formulation, using the Centre Circle constraint, is that we can easily transform the cost function into a sum of squared Euclidean distances. The simulations on synthetic data and an application with real images confirm the strong points of our method.
The modified pbMestimator method and a runtime analysis technique for the ransac family
 in Proc. IEEE Conf. on Computer Vision and Pattern Recognition
, 2005
"... Robust regression techniques are used today in many computer vision algorithms. Chen and Meer recently presented a new robust regression technique named the projection based Mestimator. Unlike other methods in the RANSAC family of techniques, where performance depends on a user supplied scale param ..."
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Cited by 12 (2 self)
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Robust regression techniques are used today in many computer vision algorithms. Chen and Meer recently presented a new robust regression technique named the projection based Mestimator. Unlike other methods in the RANSAC family of techniques, where performance depends on a user supplied scale parameter, in the pbMestimator technique this scale parameter is estimated automatically from the data using kernel smoothing density estimation. In this work we improve the performance of the pbMestimator by changing its cost function. Replacing the cost function of the pbMestimator with the changed one yields the modified pbMestimator. The cost function of the modified pbMestimator is more stable relative to the scale parameter and is also a better classifier. Thus we get a more robust and effective technique. A new general method to estimate the runtime of robust regression algorithms is proposed. Using it we show, that the modified pbMestimator runs 23 times faster than the pbMestimator. Experimental results of fundamental matrix estimation are presented demonstrating the correctness of the proposed analysis method and the advantages of the modified pbMestimator. 1
Ellipse Fitting with Hyperaccuracy
"... Abstract. For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a “hyperaccurate ” method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of high ..."
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Cited by 11 (6 self)
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Abstract. For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a “hyperaccurate ” method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of highorder bias terms. Since ML nearly achieves the theoretical accuracy bound (the KCR lower bound), the resulting improvement is very small. Nevertheless, our analysis has theoretical significance, illuminating the relationship between ML and 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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Cited by 9 (8 self)
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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).