Fast, accurate and convergent tangent estimation on digital contours

Authors:
Jacques-Olivier Lachaud;Anne Vialard;François de Vieilleville
Affiliations:
LaBRI, University of Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France;LaBRI, University of Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France;LaBRI, University of Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France
Venue:
Image and Vision Computing
Year:
2007

Citing 14
Cited 36

Best Linear Unbiased Estimators for Properties of Digitized Straight Lines

IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital curvature estimation

CVGIP: Image Understanding
Euclidean paths: a new representation of boundary of discrete regions

Graphical Models and Image Processing
Multigrid Convergence of Calculated Features in Image Analysis

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

DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Geometrical parameters extraction from discrete paths

DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Detection of the discrete convexity of polyominoes

Discrete Applied Mathematics
A Comparative Evaluation of Length Estimators of Digital Curves

IEEE Transactions on Pattern Analysis and Machine Intelligence
On the min DSS problem of closed discrete curves

Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Curvature and Tangential Deflection of Discrete Arcs: A Theory Based on the Commutator of Scatter Matrix Pairs and Its Application to Vertex Detection in Planar Shape Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Maximal digital straight segments and convergence of discrete geometric estimators

SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Analysis and comparative evaluation of discrete tangent estimators

DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Digital Convexity, Straightness, and Convex Polygons

IEEE Transactions on Pattern Analysis and Machine Intelligence

Technical Section: Normals estimation for digital surfaces based on convolutions

Computers and Graphics
Digitization scheme that assures faithful reconstruction of plane figures

Pattern Recognition
Comparison and improvement of tangent estimators on digital curves

Pattern Recognition
Lyndon + Christoffel = digitally convex

Pattern Recognition
Curvature estimation along noisy digital contours by approximate global optimization

Pattern Recognition
Tangential cover for thick digital curves

Pattern Recognition
Multi-primitive Analysis of Digital Curves

IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
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
Multi-scale Analysis of Discrete Contours for Unsupervised Noise Detection

IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Top-Down Segmentation of Histological Images Using a Digital Deformable Model

ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Combinatorial view of digital convexity

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Normals and curvature estimation for digital surfaces based on convolutions

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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
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
Convergence of binomial-based derivative estimation for C2noisy discretized curves

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Two linear-time algorithms for computing the minimum length polygon of a digital contour

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Multiscale discrete geometry

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A novel curvature estimator for digital curves and images

Proceedings of the 32nd DAGM conference on Pattern recognition
Regularization of Discrete Contour by Willmore Energy

Journal of Mathematical Imaging and Vision
Fully deformable 3D digital partition model with topological control

Pattern Recognition Letters
Estimation of the derivatives of a digital function with a convergent bounded error

DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Faithful polygonal representation of the convex and concave parts of a digital curve

Pattern Recognition
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
Unsupervised polygonal reconstruction of noisy contours by a discrete irregular approach

IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Convergence of binomial-based derivative estimation for C2 noisy discretized curves

Theoretical Computer Science
Technical Section: Geometric properties estimation from discrete curves using discrete derivatives

Computers and Graphics
Two linear-time algorithms for computing the minimum length polygon of a digital contour

Discrete Applied Mathematics
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
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 combined multi-scale/irregular algorithm for the vectorization of noisy digital contours

Computer Vision and Image Understanding
Convergence of level-wise convolution differential estimators

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Multigrid convergent curvature estimator

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a new tangent estimator to digitized curves based on digital line recognition. It outperforms existing ones on important criteria while keeping the same computation time: accuracy on smooth or polygonal shapes, isotropy, preservation of inflexion points and convexity, asymptotic behaviour. Its asymptotic convergence (sometimes called multigrid convergence) is proved in the case of convex shapes with C^3 boundary.