A new constrained parameter estimator for computer vision applications

Chojnacki, Wojciech; Brooks, Michael J.; Hengel, Anton van den; Gawley, Darren

doi:10.1016/s0262-8856(03)00140-9

Cited by 39 publications

(36 citation statements)

References 13 publications

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“…Else, let u ← u and go back to Step 2. Chojnacki et al [3] also showed how to incorporate the constraint det F = 0 in the above iterations. Later, they pointed out that convergence performance improves if we choose in…”

Section: Compute the Matrices M And L In Eqs (12)mentioning

confidence: 99%

High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

Kanatani¹,

Sugaya²

2007

IEICE Transactions on Information and Systems

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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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Section: Compute the Matrices M And L In Eqs (12)mentioning

confidence: 99%

High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

Kanatani¹,

Sugaya²

2007

IEICE Transactions on Information and Systems

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“…(13), for which we used the FNS of Chojnacki et al [3]. "CFNS" [4] computes the rank-constrained fundamental matrix by repeated eigenvalue computation. The LM and CFNS are initialized by LS.…”

Section: Methodsmentioning

confidence: 99%

“…Another approach is to do optimization subject to the rank constraint [1,4,13,14]. In this paper, we propose a new method in this line.…”

Section: Introductionmentioning

confidence: 99%

High Accuracy Computation of Rank-Constrained Fundamental Matrix

Sugaya¹,

Kanatani²

2007

Procedings of the British Machine Vision Conference 2007

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“…To show the equivalence of (7) and the system comprising (16) and (17), first note that, by (10) and (12)…”

Section: Upon Introducingmentioning

confidence: 99%

“…Recently, an integrated method for calculating θ AML was proposed that extends the FNS technique [10], [11]. The present contribution may provide a basis 1) Set θ 0 = θ ALS .…”

mentioning

confidence: 99%

From fns to heiv: a link between two vision parameter estimation methods

Chojnacki

Brooks

Hengel

et al. 2004

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem, and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.

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A new constrained parameter estimator for computer vision applications

Cited by 39 publications

References 13 publications

High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

High Accuracy Computation of Rank-Constrained Fundamental Matrix

From fns to heiv: a link between two vision parameter estimation methods

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