Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the convex hull of the integer points in a disc
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Computer Vision and Image Understanding
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Estimation of Curvature and Tangent Direction by Median Filtered Differencing
ICIAP '95 Proceedings of the 8th International Conference on Image Analysis and Processing
Geometrical parameters extraction from discrete paths
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Different Digitisations of Displaced Discs
Foundations of Computational Mathematics
Journal of Mathematical Imaging and Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Optimal blurred segments decomposition of noisy shapes in linear time
Computers and Graphics
Curvature and torsion estimators based on parametric curve fitting
Computers and Graphics
Robust estimation of curvature along digital contours with global optimization
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Binomial convolutions and derivatives estimation from noisy discretizations
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Experimental comparison of continuous and discrete tangent estimators along digital curves
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
On discrete moments of unbounded order
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
An error bounded tangent estimator for digitized elliptic curves
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Maximal planes and multiscale tangential cover of 3D digital objects
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Edge curvature and convexity based ellipse detection method
Pattern Recognition
Convergence of level-wise convolution differential estimators
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Many contour-based applications rely on the estimation of the geometry of the shape, such as pattern recognition or classification methods. This paper proposes a comprehensive evaluation on the problem of tangent estimators on digital curves. The methods taken into account use different paradigms: approximation and digital geometry. In the former paradigm, methods based on polynomial fitting, smoothing and filtering are reviewed. In the latter case of digital geometry, we consider two methods that mainly rely on digital straight line recognition [J.-O. Lachaud, A. Vialard, F. de Vieilleville, Fast, accurate and convergent tangent estimation on digital contours, Image and Vision Computing 25(10) (2007) 1572-1587] and optimization [B. Kerautret, J.-O. Lachaud, Robust estimation of curvature along digital contours with global optimization, in: Proceedings of Discrete Geometry for Computer Imagery, Lyon, France, Lecture Notes in Computer Science, vol. 4992, Springer, Berlin, 2008]. The comparison takes into account objective criteria such as multi-grid convergence, average error, maximum error, isotropy and length estimation. Experiments underline that adaptive methods based on digital straight line recognition often propose a good trade-off between time and precision and that if precision is to be sought, non-adaptive methods can be easily transformed into adaptive methods to get more accurate estimations.