Computational geometry: an introduction
Computational geometry: an introduction
On-line construction of the convex hull of a simple polyline
Information Processing Letters
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Canonical representations of discrete curves
Pattern Analysis & Applications
On the min DSS problem of closed discrete curves
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Curvature estimation in noisy curves
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
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
Tangential cover for thick digital curves
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Robust decomposition of thick digital shapes
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Optimal blurred segments decomposition in linear time
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Digital line recognition, convex hull, thickness, a unified and logarithmic technique
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multi-primitive Analysis of Digital Curves
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
An error bounded tangent estimator for digitized elliptic curves
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
A non-heuristic dominant point detection based on suppression of break points
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
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The recognition of digital shapes is a deeply studied problem. The arithmetical framework, initiated by Reveilles [Geometrie discrete, calcul en nombres entiers et algorithmique, These d'Etat, 1991], provides a powerful theoretical basis, as well as many algorithms to deal with digital objects. The tangential cover, first presented in Feschet and Tougne [Optimal time computation of the tangent of a discrete curve: application to the curvature, in: G. Bertrand, M. Couprie, L. Perroton (Eds.), 8th Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 1568, Springer, Berlin, 1999, pp. 31-40] and Feschet [Canonical representations of discrete curves, Pattern Anal. Appl. 8(1-2) (2005) 84-94] is a useful tool for representing geometric digital primitives. It computes the set of all maximal segments of a digital curve and permits either to obtain minimal length polygonalization or asymptotic convergence of tangents estimations. Nevertheless, the arithmetical approach does not tolerate the introduction of irregularities, which are however inherent to the acquisition of digital shapes. The present paper is an extension of Faure and Feschet [Tangential cover for thick digital curves, in: D. Coeurjolly, I. Sivignon, L. Tougne, F. Dupont (Eds.), DGCI 2008, Lecture Notes in Computer Science, vol. 4992, Springer, Berlin, 2008, pp. 358-369], in which we propose a new definition for a class of the so-called ''thick digital curves'' that applies well to a large class of digital object boundaries. We then propose an extension of the tangential cover to thick digital curves and provide an algorithm with an O(nlogn) time complexity, where n denotes the number of points of specific subparts of the thick digital curve. In order to keep up with this low complexity, some critical points must be taken into account. We describe all required implementation details in this paper.