Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
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
Scientific American
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
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
On the number of factors of Sturmian words
Theoretical Computer Science
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
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
Hybrid Scan-Conversion of Circles
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
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
An effective voting method for circle detection
Pattern Recognition Letters
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
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Approximating Euclidean circles by neighbourhood sequences in a hexagonal grid
Theoretical Computer Science
Determining Digital Circularity Using Integer Intervals
Journal of Mathematical Imaging and Vision
Hi-index | 5.23 |
Digital circles and digital discs satisfy many bizarre anisotropic properties, understanding of which is essential for solving various problems in image analysis and computer graphics. In this paper we study the underlying properties of absentee pixels that appear while covering a digital disc with concentric digital circles. We present, for the first time, a mathematical characterization of these pixels based on number theory and digital geometry. Interestingly, the absentees occur in multitude, and we show that their count varies quadratically with the radius. The notion of infimum parabola and supremum parabola has been used to derive the count of these absentees. Using this parabolic characterization, we derive a necessary and sufficient condition for a pixel to be a disc absentee, and obtain the geometric properties of the absentees. An algorithm to locate the absentees is presented. We show that the ratio of the absentee pixels to the total number of disc pixels approaches a constant with increasing radius. Test results have been furnished to substantiate our theoretical findings.