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9 April 1993 Real m-neighbor distance
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Proceedings Volume 1832, Vision Geometry; (1993) https://doi.org/10.1117/12.142157
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States
Abstract
The notion of m-Neighbor Distance dnm, 1 ≤ m ≤ n, m integer, in the n- D digital geometry has been extended under the name of real m-Neighbor Distance (delta) nm, in this paper, to n-D real space. Complete analyses of the hyperspheres H(m,n;r) of (delta) nm have been carried out to show that the maxima of the absolute and relative errors between this metric and the Euclidean norm En minimizes at certain extreme symmetric points on the hypersphere. The coherence between these results and those already available in the digital domain has been mentioned to project (delta) nm as a powerful tool in metric analyses in digital geometry. The paper also makes fundamental contributions in the study of non-Euclidean metric spaces, extending the L1 equals (delta) n1 and LINF equals (delta) nn norms in a natural yet non- Minkowski way. Finally it is shown that real m-neighbor distance has direct applications in scheduling problems.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
P. P. Das "Real m-neighbor distance", Proc. SPIE 1832, Vision Geometry, (9 April 1993); https://doi.org/10.1117/12.142157
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