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On the computation of the Minkowski dimension using morphological operations
Author(s) -
KANMANI S.,
RAO C. BABU,
RAJ B.
Publication year - 1993
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1993.tb03325.x
Subject(s) - minkowski space , minkowski addition , minkowski–bouligand dimension , dimension (graph theory) , fractal dimension , minkowski's theorem , computation , fractal , mathematics , hausdorff dimension , grid , symmetry (geometry) , relation (database) , element (criminal law) , geometry , pure mathematics , mathematical analysis , computer science , algorithm , law , political science , database
SUMMARY The Minkowski dimension as a complexity measure, and its relation to the other dimensions in the case of self‐similar fractal objects, is discussed. An implementation of the Minkowski dimension, using morphological operations on a square grid, is presented. The effect of resolution, orientation and the symmetry of the structuring element used on the estimation of the Minkowski dimension is studied. The corrections required for free end points are presented.