Comparison and improvement of tangent estimators on digital curves

Lachaud, Jacques-Olivier

doi:10.1016/j.patcog.2008.11.034

Cited by 18 publications

(22 citation statements)

References 20 publications

(34 reference statements)

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“…Tn this comparison, we shall consider noisy ellipses and various performance criteria like precision, maximal error, isotropy, convergence, convexity on ideal digital shape, and time complexity [12].…”

Section: Resultsmentioning

confidence: 99%

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An error bounded tangent estimator for digital curves

Prasad

Leung

2010

2010 25th International Conference of Image and Vision Computing New Zealand

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Section: Resultsmentioning

confidence: 99%

“…Examples include corner detection, inflection curve which cannot be analyzed using equations [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

An error bounded tangent estimator for digital curves

Prasad

Leung

2010

2010 25th International Conference of Image and Vision Computing New Zealand

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“…The commun way to link the estimated differential quantities to the expect Euclidean one is the multigrid convergence principle: when the shape is digitized on a grid with gridstep h tending to zero, the estimated quantity should converge to the expected one. In dimension 2, several multigrid convergent estimators have been introduced to approach normals [2,3] and curvatures [3][4][5]. In 3D, empirical methods for normal and curvature estimation have been introduced in [6].…”

Section: Introductionmentioning

confidence: 99%

Voronoi-Based Geometry Estimator for 3D Digital Surfaces

Cuel

Lachaud

Thibert

2014

Advanced Information Systems Engineering

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Abstract. We propose a robust estimator of geometric quantities such as normals, curvature directions and sharp features for 3D digital surfaces. This estimator only depends on the digitisation gridstep and is defined using a digital version of the Voronoi Covariance Measure, which exploits the robust geometric information contained in the Voronoi cells. It has been proved in [1] that the Voronoi Covariance Measure is resilient to Hausdorff noise. Our main theorem explicits the conditions under which this estimator is multigrid convergent for digital data. Moreover, we determine what are the parameters which maximise the convergence speed of this estimator, when the normal vector is sought. Numerical experiments show that the digital VCM estimator reliably estimates normals, curvature directions and sharp features of 3D noisy digital shapes.

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“…Two main variations in this approach are in vogue. The first variation is based on the theory of maximal segments [8]. At the point of interest, the maximal line segments passing through it are found and weighted convex combination of their slopes is 1057-7149 © 2014 IEEE.…”

Section: Introductionmentioning

confidence: 99%

DEB: Definite Error Bounded Tangent Estimator for Digital Curves

Prasad

Leung

Quek

et al. 2014

IEEE Trans. on Image Process.

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We propose a simple and fast method for tangent estimation of digital curves. This geometric-based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics, i.e., circles, ellipses, parabolas, and hyperbolas. Explicit expressions of the upper bounds for continuous and digitized curves are derived, which can also be applied to nonconic curves. Our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic, nonconic, and noisy curves. In addition, we demonstrate a good multigrid and isotropic performance and low computational complexity of O(1) and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves.

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Comparison and improvement of tangent estimators on digital curves

Cited by 18 publications

References 20 publications

An error bounded tangent estimator for digital curves

An error bounded tangent estimator for digital curves

Voronoi-Based Geometry Estimator for 3D Digital Surfaces

DEB: Definite Error Bounded Tangent Estimator for Digital Curves

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