Digitized Circular Arcs: Characterization and Parameter Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometrical parameters extraction from discrete paths
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Curvature and Torsion Estimators for 3D Curves
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Comparison of Discrete Curvature Estimators and Application to Corner Detection
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Discrete Contour Extraction from Reference Curvature Function
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
What Does Digital Straightness Tell about Digital Convexity?
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Blurred Segments in Gray Level Images for Interactive Line Extraction
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
A discrete geometry approach for dominant point detection
Pattern Recognition
Regularization of Discrete Contour by Willmore Energy
Journal of Mathematical Imaging and Vision
Accurate curvature estimation along digital contours with maximal digital circular arcs
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Maximal planes and multiscale tangential cover of 3D digital objects
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Two linear-time algorithms for computing the minimum length polygon of a digital contour
Discrete Applied Mathematics
Combinatorial pyramids and discrete geometry for energy-minimizing segmentation
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Convex shapes and convergence speed of discrete tangent estimators
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Fast guaranteed polygonal approximations of closed digital curves
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Maximal digital straight segments and convergence of discrete geometric estimators
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Revisiting digital straight segment recognition
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Optimal blurred segments decomposition in linear time
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Curvature estimation for discrete curves based on auto-adaptive masks of convolution
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
A linear algorithm for polygonal representations of digital sets
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Multigrid convergent curvature estimator
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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With the definition of discrete lines introduced by RÉveillès [REV91], there has been a wide range of research in discrete geometry and more precisely on the study of discrete lines. By the use of the linear time segment recognition algorithm of Debled and RÉveillès [DR94], Vialard [VIA96a] has proposed a O(l) algorithm for computing the tangent in one point of a discrete curve where l is the average length of the tangent. By applying her algorithm to n points of a discrete curve, the complexity becomes O(n.l). This paper proposes a new approach for computing the tangent. It is based on a precise study of the tangent evolution along a discrete curve. The resulting algorithm has a O(n) complexity and is thus optimal. Some applications in curvature computation and a tombstones contours study are also presented.