Analysis and Comparative Evaluation of Discrete Tangent Estimators

  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},
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. 

Experimental Comparison of Continuous and Discrete Tangent Estimators Along Digital Curves

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

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

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.

Analysis of Noisy Digital Contours with Adaptive Tangential Cover

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

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

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

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

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.



A Comparative Evaluation of Length Estimators of Digital Curves

This paper compares previously published length estimators in image analysis having digitized curves as input and suggests a new gradient-based method for length estimation and combines a previously proposed length estimator for straight segments with a polygonalization method.

Geometrical parameters extraction from discrete paths

The use of the Euclidean paths model is described to obtain accurate estimations of lenght, tangent orientation and curvature for geometrical analysis of a discrete curve.

Canonical representations of discrete curves

  • F. Feschet
  • Mathematics, Computer Science
    Pattern Analysis and Applications
  • 2005
A new representation of digital curves is introduced that has the property of being unique and canonical when computed on closed curves and is extended for dealing with noisy curves and a multi-scale extension is proposed.

Geometric Measures on Arbitrary Dimensional Digital Surfaces

A set of tools to analyse the geometry of multidimensional digital surfaces based on 2D tangent computation by discrete line recognition, 3D normal estimation from slice contours and geometric estimators implemented in a framework able to represent subsets of n-dimensional spaces.

Estimation of Curvature and Tangent Direction by Median Filtered Differencing

A new method, median filtered differencing, is presented, for estimation of tangent direction and curvature of digitised curves, which performs successfully on both straight and curved segments even in the neighbourhood of discontinuities.

Digital curvature estimation

It is established that almost all existing methods suffer from a severe directional inaccuracy and/or poor precision in digital curvature estimation.

Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature

Vialard 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 tangents, and the resulting algorithm has a O (n) complexity and is thus optimal.

Fast computation of the normal vector field of the surface of a 3-D discrete object

A fast computational technique to compute the normal vector field of a discrete object at a given scale, whose time cost is proportional to the number of surfels at and little dependent on the scale is presented.

A Linear Algorithm for Segmentation of Digital Curves

A new very efficient linear algorithm for the segmentation of 8-connected digital curves is given using a definition of digital lines using a linear double diophantine inequality.

Visual Form 2001

This short paper surveys methods for planar shape recognition and shape smoothing and processing invariant under viewing distortions and possibly partial occlusions. It is argued that all the results