Journal Article10.1007/S10851-011-0270-6
Determining Digital Circularity Using Integer Intervals
Shyamosree Pal,Partha Bhowmick +1 more
16
TL;DR: The proposed work reveals a novel technique to determine whether a digital curve segment is digitally circular using the correspondence of its constituent runs with the square numbers in integer intervals using the notion of radii nesting.
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Abstract: Digital circularity is a well-researched topic for its real-world practicality to circularity measure, estimation of discrete curvature, circular arc segmentation, etc The proposed work reveals a novel technique to determine whether a digital curve segment is digitally circular using the correspondence of its constituent runs with the square numbers in integer intervals The notion of radii nesting is used to successively analyze these runs of digital points Two algorithms have been proposed along with their demonstrations and detailed analysis, and a simple-yet-effective solution has been provided to expedite them using infimum circle and supremum circles that bound the initial range of radii We have also shown how the proposed technique can be used for segmentation of an arbitrary digital curve segment into a sequence of circular arcs Experimental results have been given to demonstrate the efficiency and elegance of the proposed technique
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Citations
On Digital Circles.
Akira Nakamura,Kunio Aizawa +1 more
- 01 Jul 1982
TL;DR: This paper characterizes sets of lattice points which are digitizations of circles, and states that these points are equivalent to circles in the lattice.
64
•Book
Computational Modeling of Objects Represented in Images
Valentin E. Brimkov,Reneta P. Barneva +1 more
- 01 Jan 2011
TL;DR: This special issue of Graphical Models contains six articles, which are substantial extensions of papers presented at the International Symposium ‘‘Computational Modeling of Objects Represented in Images’’ (CompIMAGE 2010), and believes that as a result of the long and rigorous selection process it contains only papers of very high quality.
31
On covering a digital disc with concentric circles in Z2
TL;DR: This paper presents, for the first time, a mathematical characterization of absentee pixels that appear while covering a digital disc with concentric digital circles based on number theory and digital geometry, and derives a necessary and sufficient condition for a pixel to be a disc absentee.
10
From prima quadraginta octant to lattice sphere through primitive integer operations
Ranita Biswas,Partha Bhowmick +1 more
TL;DR: The first integer-based algorithm for constructing a well-defined lattice sphere specified by integer radius and integer center is presented, which evolves from a unique correspondence between the lattice points comprising the sphere and the distribution of sum of three square numbers in integer intervals.
10
A Digital-Geometric Algorithm for Generating a Complete Spherical Surface in ℤ 3
Sahadev Bera,Partha Bhowmick,Bhargab B. Bhattacharya +2 more
- 13 Jan 2014
TL;DR: An algorithm is designed to fill up the absentee voxels so as to generate a spherical surface of revolution, which is complete and realistic from the viewpoint of visual perception and will find many potential applications in computer graphics and 3D imaging.
8
References
Digitized circular arcs: characterization and parameter estimation
TL;DR: The authors derive an optimal estimator and give expressions for the bound on the precision of estimation of this bound due to digitization is the deterministic equivalent of the Cramer/Rao bound known from parameter estimation theory.
Digital disks and a digital compactness measure
Chul E. Kim,Timothy A. Anderson +1 more
- 01 Dec 1984
TL;DR: An O(n2) time algorithm is presented that determines whether or not a given convex digital region is a digital disk.
55
A high speed algorithm for circular object location
TL;DR: An effective but simply implemented strategy is devised which achieves speedup factors of up to ∼25 with real images and is highly robust against shape defects and partial occlusions, and in addition robustness is easily monitored in practical situations.
54
An elementary algorithm for digital arc segmentation
David Coeurjolly,Yan Gerard,Jean-Pierre Reveillès,Laure Tougne +3 more
- 30 Apr 2004
TL;DR: General fundamentals, based on classical tools, as well as algorithmic details, are given and an incremental algorithm to segment a discrete curve into digital arcs is presented.
51
•Book
Geometry, Morphology, and Computational Imaging
Tetsuo Asano,Reinhard Klette,Chrisitan Ronse +2 more
- 29 Jul 2003
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