Real m-neighbor distance

P. P. Das

doi:10.1117/12.142157

9 April 1993 Real m-neighbor distance

P. P. Das

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 dⁿ_m, 1 ≤ m ≤ n, m integer, in the n- D digital geometry has been extended under the name of real m-Neighbor Distance (delta) ⁿ_m, in this paper, to n-D real space. Complete analyses of the hyperspheres H(m,n;r) of (delta) ⁿ_m have been carried out to show that the maxima of the absolute and relative errors between this metric and the Euclidean norm E_n 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) ⁿ_m 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 L_INF equals (delta) ⁿ_n norms in a natural yet non- Minkowski way. Finally it is shown that real m-neighbor distance has direct applications in scheduling problems.

Citation Download Citation

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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