By Elena Barcucci, Andrea Frosini, Simone Rinaldi
This ebook constitutes the completely refereed complaints of the 18th overseas convention on Discrete Geometry for machine Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised complete papers offered have been rigorously chosen from 60 submissions. The papers are prepared in topical sections on versions for Discrete Geometry, Discrete and Combinatorial Topology, Geometric Transforms, Discrete form illustration, popularity and research, Discrete Tomography, Morphological research, Discrete Modelling and Visualization, Discrete and Combinatorial instruments for picture Segmentation and Analysis.
Read Online or Download Discrete Geometry for Computer Imagery: 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014. Proceedings PDF
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Additional info for Discrete Geometry for Computer Imagery: 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014. Proceedings
The family H of hollow stack polyominoes forms a polyomino class with p-basis given by: Rectangles with rectangular holes. Let R be the class of polyominoes obtained from a rectangle by removing sets of cells which have themselves a rectangular shape, and such that there is no more than one connected set of 0’s for each row and column. The family R can easily be proved to be a polyomino class, and moreover: Fig. 8. A rectangle with rectangular holes Proposition 9. The class R can be described by the avoidance of the patterns: ⎡ ⎤ 0 00 00 01 10 0 1 0 , ⎣1⎦ .
If we notice N d (l) the maximal number of hypercubes crossed by a curve of length l in dimension d, then N d (l) ≥ 2d−2 N 2 (l) which makes d l hypercubes crossed by an hyperdiagonal more hypercubes than the 2d + 2√−1 d path. 4 With Other Distances With L1 norm instead of Euclidean norm for the length of the curve, the expressions of N (l) and L(n) are quite straightforward. We just have to notice that following the curve, new squares appear each time that a line x = i or y = j is 24 Y. G´erard and A.
20 Y. G´erard and A. Vacavant √ √ – If 2mod 2 ≤ l mod 2 < 1 and l > 1, then N (l) = 3 √l 2 + 5 (optimal curves have − 1 diagonal steps and 2 horizontal or vertical steps). If √ 2 − 2 ≤ l < 1, we have still N (l) = 4 (the ﬁrst step of the staircase is broken). √ – If 1 ≤ l mod 2, then N (l) = 3 √l2 + 6 (optimal curves have √l2 diagonal steps and 1 horizontal or vertical step). √l 2 Conversely, function L(n) is: – – – – L(1) = L(2) = L(3) = L(4) = 0, L(5) = 1. √ If n mod3 = 0 (and n ≥ 6), then L(n) = 1 + ( n3 − 2) 2.