Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Algorithms for drawing anti-aliased circles and ellipses
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Double-step incremental generation of lines and circles
Computer Vision, Graphics, and Image Processing
A high speed algorithm for circular object location
Pattern Recognition Letters
A modified Hough scheme for general circle location
Pattern Recognition Letters
A hybrid sequential-parallel approach to accurate circle centre location
Pattern Recognition Letters
A simple approach for the estimation of circular arc center and its radius
Computer Vision, Graphics, and Image Processing
On the number of factors of Sturmian words
Theoretical Computer Science
Sculpting: an interactive volumetric modeling technique
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
On the recognition of digital circles in linear time
Computational Geometry: Theory and Applications
CVGIP: Image Understanding
The linear time recognition of digital arcs
Pattern Recognition Letters
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Cramer-Rao lower bounds for estimation of a circular arc center and its radius
Graphical Models and Image Processing
Recognition of partial circular shapes from segmented contours
Computer Vision and Image Understanding
A novel method for parameter estimation of digital arc
Pattern Recognition Letters
Curve-drawing algorithms for Raster displays
ACM Transactions on Graphics (TOG)
Sparse Pixel Vectorization: An Algorithm and Its Performance Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
A two-step circle detection algorithm from the intersecting chords
Pattern Recognition Letters
An efficient randomized algorithm for detecting circles
Computer Vision and Image Understanding
Digital Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hybrid Scan-Conversion of Circles
IEEE Transactions on Visualization and Computer Graphics
The Discrete Analytical Hyperspheres
IEEE Transactions on Visualization and Computer Graphics
Rendering: Parallelization of Bresenham's Line and Circle Algorithms
IEEE Computer Graphics and Applications
Digitized Circular Arcs: Characterization and Parameter Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital disks and a digital compactness measure
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Characterization of digital circles in triangular grid
Pattern Recognition Letters
Machine Vision: Theory, Algorithms, Practicalities
Machine Vision: Theory, Algorithms, Practicalities
An effective voting method for circle detection
Pattern Recognition Letters
Robust and Accurate Vectorization of Line Drawings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Computer Graphics Using OpenGL (3rd Edition)
Computer Graphics Using OpenGL (3rd Edition)
A High-Speed Algorithm for the Generation of Straight Lines and Circular Arcs
IEEE Transactions on Computers
Number-theoretic interpretation and construction of a digital circle
Discrete Applied Mathematics
How Many Ways Can You Draw a Circle?
IEEE Computer Graphics and Applications
Detection of circular arcs in a digital image using chord and sagitta properties
GREC'09 Proceedings of the 8th international conference on Graphics recognition: achievements, challenges, and evolution
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
Isoperimetrically optimal polygons in the triangular grid
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
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This paper presents a brief survey of some recently discovered properties of digital circles, digital discs, and digital surfaces of revolution, which are related with many theoretical challenges in the digital space and have diverse applications in image processing, pattern recognition, and computer graphics. These digital-geometric properties are helpful in today's context of digital revolution to eliminate the inherent discrepancies and limitations of real circles in solving various problems on characterization, construction, reconstruction, and segmentation of digital circles/discs. As a very contemporary problem, we have discussed why and how the notion of digital circularity leads to an efficient and algorithm-friendly interpretation for segmentation and parametrization of circular arcs from graphic regions in a digital document. Another problem is generating a digital surface of revolution, which needs detecting and fixing the absentee voxels in the 3D digital space in order to ensure the irreducibility and continuity of the voxel-surface of revolution. The pattern of absentee voxels in such a surface corresponds to that of absentee pixels in a cover of digital disc with concentric digital circles. Experimental results demonstrate the impact and effectiveness of digital circularity on all these state-of-the-art practices.