Computational geometry: an introduction
Computational geometry: an introduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Best Linear Unbiased Estimators for Properties of Digitized Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of a circular arc center and its radius
Computer Vision, Graphics, and Image Processing
Length estimators for digitized contours
Computer Vision, Graphics, and Image Processing
A geometric approach to subpixel registration accuracy
Computer Vision, Graphics, and Image Processing
A simple approach for the estimation of circular arc center and its radius
Computer Vision, Graphics, and Image Processing
Design of Perimeter Estimators for Digitized Planar Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric Precision in Noise-Free Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVGIP: Image Understanding
Digital Picture Processing
Optimal Local Weighted Averaging Methods in Contour Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition Letters
The Discrete Moments of the Circles
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
The Reconstruction of the Digital Hyperbola Segment from Its Code
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
On Characterization of Discrete Triangles by Discrete Moments
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
On discrete triangles characterization
Computer Vision and Image Understanding
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
On the Number of Digital Discs
Journal of Mathematical Imaging and Vision
The Number of N-Point Digital Discs
IEEE Transactions on Pattern Analysis and Machine Intelligence
A curve matching algorithm for dynamic image sequences
ISCGAV'05 Proceedings of the 5th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Number-theoretic interpretation and construction of a digital circle
Discrete Applied Mathematics
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
Measure of circularity for parts of digital boundaries and its fast computation
Pattern Recognition
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Analytical description of digital circles
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Arc segmentation in linear time
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Approximation of digital circles by regular polygons
ICAPR'05 Proceedings of the Third international conference on Advances in Pattern Recognition - Volume Part I
Determining Digital Circularity Using Integer Intervals
Journal of Mathematical Imaging and Vision
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph
Journal of Mathematical Imaging and Vision
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The digitization of a circular arc causes an inherent loss of geometrical information. Arcs with slightly different local curvature or position may lead to exactly the same digital pattern. In this paper we give a characterization of all centers and radii of circular arcs yielding the same digitization pattern. The radius of the arcs varies over the set. However, only one curvature or radius estimate can be assigned to the digital pattern. We derive an optimal estimator and give expressions for the bound on the precision of estimation. This bound due to digitization is the deterministic equivalent of the Cramér/Rao bound known from parameter estimation theory.Consider the estimation of the local curvature and local radius of a smooth object. Typically such parameters are estimated by moving a window along the digital boundary. Methods in literature show a poor precision in estimating curvature values, relative errors of over 40% are often found [34]. From the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error.On the practical side we present examples of the residual error due to the discrete grid. The estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points (coded with nine Freemancodes) has a relative deviation exceeding 2%. For a full disk the deviation is below 1% when the radius r exceeds four grid units.The presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise-free sampling.