Octagonal distances for digital pictures

Das, Partha Pratim; Chatterji, B. N.

doi:10.1016/0020-0255(90)90008-x

Cited by 40 publications

(29 citation statements)

References 3 publications

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“…Several error functions minimizing the asymptotic maximum difference of two balls of equal radius using a distance based on periodic neighbourhood sequences and a Euclidean sphere, respectively, is presented in [5,8,30] (Z 2 ), [18] (Z 3 ). An investigation of optimal non-periodic neighbourhood sequences in Z 2 with optimal sequences also for finite distances is found in [12].…”

Section: Introductionmentioning

confidence: 99%

Distances based on neighbourhood sequences in non-standard three-dimensional grids

Strand¹,

Nagy²

2007

Discrete Applied Mathematics

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Properties for distances based on neighbourhood sequences on the face-centred cubic (fcc) and the body-centred cubic (bcc) grids are presented. Formulas to both compute the distances and assure that the distances satisfy the conditions for being metrics are presented and proved to be correct. The formulas are used to calculate the neighbourhood sequences that generates distances with lowest deviation from the Euclidean distance.

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Section: Introductionmentioning

confidence: 99%

Distances based on neighbourhood sequences in non-standard three-dimensional grids

Strand¹,

Nagy²

2007

Discrete Applied Mathematics

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“…The examination of hyperspheres with neighbourhood sequences started in [3] in two dimension with periodic neighbourhood sequences. In higher dimension hyperspheres were also analyzed using only constant neighbouring criteria in [4].…”

Section: Hyperspheres In Nd and ∞Dmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

Distance with generalized neighbourhood sequences innDand∞D

Nagy¹

2008

Discrete Applied Mathematics

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In this paper we generalize some former results of Das et al. about distances with n-dimensional periodic neighbourhood sequences. We use a more general definition of neighbourhood sequences, which does not require periodicity. As an extension of the earlier results, we give a formula to calculate the distance between two arbitrary points with general neighbourhood sequences in an arbitrary finite dimension. Moreover we extend the result to the infinite-dimensional digital space.

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“…This can be generalized as proposed in [35] to more complicated combinations of D 4 and D 8 . These distances, called generalized octagonal distances, are metrics only when the simple path generated DTs are combined in a proper way [16]. Using the series (D 4 ,…”

Section: Comparison Between Different Distance Transformsmentioning

confidence: 99%