Hyperspheres in digital geometry
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Cited by (15)
Weighted distances based on neighborhood sequences for point-lattices
2009, Discrete Applied MathematicsCitation Excerpt :One of the definitions in [11] also includes the distance function obtained by using both weights and a neighborhood sequence — the weighted distance based on neighborhood sequences (weighted ns-distances). The theory for ns-distances with periodic neighborhood sequences was further developed in [12–15], where for example formulas for point-to-point distance and conditions for metricity were given. In [16–20], ns-distances for the non-periodic case were considered for standard and non-standard grids.
Distance with generalized neighbourhood sequences in n D and ∞ D
2008, Discrete Applied MathematicsCitation Excerpt :In [3] Das examined the digital circles in two dimensions, in [1] Danielsson analyzed the digital spheres in 3D digital space with periodic neighbourhood sequences. In [4] hyperspheres based only on simple neighbourhood relations were investigated in arbitrary finite-dimensional spaces, while in [7] Hajdu described hyperspheres in an arbitrary finite dimension with generalized neighbourhood sequences. Our aim is to get a more simple formula which calculates the distance with non-periodic neighbourhood sequences also.
General neighborhood sequences in Z<sup>n</sup>
2007, Discrete Applied MathematicsCitation Excerpt :Das et al. [6] specialized this theory to the so-called octagonal sequences, based on the traditional neighboring relations of digital image processing. For various results in this direction we refer to [1,4,5,7–10,23,27], and the references given there. Recently, Fazekas et al. [12] dropped the periodicity requirement from the model of [6] by introducing general (not necessarily periodic) octagonal neighborhood sequences.
Metrical neighborhood sequences in ℤ<inf>n</inf>
2005, Pattern Recognition LettersGeometry of neighbourhood sequences
2003, Pattern Recognition LettersImage analysis and computer vision: 1990
1991, CVGIP: Image Understanding