# Analysis and Comparative Evaluation of Discrete Tangent Estimators

@inproceedings{Lachaud2005AnalysisAC, title={Analysis and Comparative Evaluation of Discrete Tangent Estimators}, author={Jacques-Olivier Lachaud and Anne Vialard and François de Vieilleville}, booktitle={Discrete Geometry for Computer Imagery}, year={2005} }

This paper presents a comparative evaluation of tangent estimators based on digital line recognition on digital curves. The comparison is carried out with a comprehensive set of criteria: accuracy on smooth or polygonal shapes, behaviour on convex/concave parts, computation time, isotropy, asymptotic convergence. We further propose a new estimator mixing the qualities of existing ones and outperforming them on most mentioned points.

## 52 Citations

### Fast, accurate and convergent tangent estimation on digital contours

- Computer Science, MathematicsImage Vis. Comput.
- 2007

### Experimental Comparison of Continuous and Discrete Tangent Estimators Along Digital Curves

- MathematicsIWCIA
- 2008

This paper proposes an in-depth experimental comparison between various continuous tangent estimators and a representative digital Tangent estimator, based on the extraction of maximal digital straight segments, that is in general as good - if not better - than continuous methods.

### Convex Shapes and Convergence Speed of Discrete Tangent Estimators

- Mathematics, Computer ScienceISVC
- 2006

It is shown that tangent estimators based on maximal digital straight segment recognition are multigrid convergent for some family of convex shapes and that their speed of convergence is on average .

### Robust Estimation of Curvature along Digital Contours with Global Optimization

- Computer ScienceDGCI
- 2008

A new curvature estimator based on global optimisation is introduced that exploits the geometric properties of digital contours by using local bounds on tangent directions defined by the maximal digital straight segments.

### Comparison and improvement of tangent estimators on digital curves

- Computer SciencePattern Recognit.
- 2009

### Analysis of Noisy Digital Contours with Adaptive Tangential Cover

- Computer Science, MathematicsJournal of Mathematical Imaging and Vision
- 2017

This study investigates a discrete structure, named adaptive tangential cover (ATC), which is composed of maximal segments with different widths deduced from the local noise values estimated at each point of the contour, and proposes several applications of ATC on noisy digital contours.

### DEB: Definite Error Bounded Tangent Estimator for Digital Curves

- Computer Science, MathematicsIEEE Transactions on Image Processing
- 2014

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.

### Curvature Estimation in Noisy Curves

- Computer Science, MathematicsCAIP
- 2007

An algorithm of estimation of the curvature at each point of a general discrete curve in O(n log2 n) is proposed. It uses the notion of blurred segment, extending the definition of segment of…

### Curvature estimation in noisy curves

- Computer Science, Mathematics
- 2018

An algorithm of estimation of the curvature at each point of a general discrete curve in O(nlogn) is proposed. It uses the notion of blurred segment, extending the definition of segment of arithmetic…

### Maximal digital straight segments and convergence of discrete geometric estimators

- MathematicsSCIA
- 2005

The convergence of local estimators based on Digital Straight Segment (DSS) recognition is studied, closely linked to the asymptotic growth of maximal DSS, for which bounds are shown both about their number and sizes.

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