Further Improving Geometric Fitting

Kanatani, Kenichi

doi:10.1109/3dim.2005.49

Cited by 14 publications

(20 citation statements)

References 21 publications

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“…12), we must use an iterative method. Fortunately, a number of iterative AML methods have been developed [15,16,17] -all of which have been shown to converge very quickly in theory for data with small noise [15]. All of these methods are based on solving a similar eigenvalue problem to the direct methods (Sec.…”

Section: Iterative Aml Methods: Heiv and Reducedmentioning

confidence: 99%

Generalized, basis-independent kinematic surface fitting

Andrews

Séquin

2013

Computer-Aided Design

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Kinematic surfaces form a general class of surfaces, including surfaces of revolution, helices, spirals, and more. Standard methods for fitting such surfaces are either specialized to a small subset of these surface types (either focusing exclusively on cylinders or exclusively on surfaces of revolution) or otherwise are basis-dependent (leading to scale-dependent results). Previous work has suggested re-scaling data to a fixed size bounding box to avoid the basis-dependence issues. We show that this method fails on some simple, common cases such as a box or a cone with small noise. We propose instead adapting a well-studied approximate maximum-likelihood method to the kinematic surface fitting problem, which solves the basis-dependence issue. Because this technique is not designed for a specific type of kinematic surface, it also opens the door to the possibility of new variants of kinematic surfaces, such as affinely-scaled surfaces of revolution.Keywords: kinematic surface fitting, reverse engineering, slippable surfaces, velocity fields, approximate maximum likelihood, Taubin's method

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Section: Iterative Aml Methods: Heiv and Reducedmentioning

confidence: 99%

Generalized, basis-independent kinematic surface fitting

Andrews

Séquin

2013

Computer-Aided Design

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“…It can be shown that the covariance matrix of the resulting solutionû coincides with the the KCR lower bound (the right-hand side of eq. (8) except for O(σ 4 ) [1,8,9]. The fundamental matrix F should also satisfy the constraint det F = 0 [5].…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…The solution is optimal in the sense that its covariance matrix agrees with the theoretical accuracy bound (KCR lower bound) except for higher order terms in noise [1,8]. Kanatani's renormalization [8] is also known to be nearly equivalent to FNS and HEIV [9]. In this paper, we add a fourth method: directly computing ML by Gauss-Newton iterations.…”

Section: Introductionmentioning

confidence: 99%

High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

Kanatani

Sugaya

2006

Procedings of the British Machine Vision Conference 2006

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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 well-known methods: FNS, HEIV, and renormalization, to which we add Gauss-Newton 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.

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“…If ξ α is regarded as an independent Gaussian random variable of meanξ α and covariance matrix V [ξ α ], maximum likelihood (ML) estimation is to minimize the sum of the square Mahalanobis distances of the data points ξ α to the hyperplane to be fitted in R 9 , minimizing…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%