By Elena Barcucci, Andrea Frosini, Simone Rinaldi
This ebook constitutes the completely refereed lawsuits of the 18th overseas convention on Discrete Geometry for machine Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised complete papers provided have been rigorously chosen from 60 submissions. The papers are equipped in topical sections on types 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 photograph 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
Moreover, we extend the notion of pattern in a polyomino, by introducing generalized polyomino patterns, so that to be able to describe more families of polyominoes known in the literature. 1 Patterns in Binary Pictures and Polyomino Classes In recent years a considerable interest in the study of the notion of pattern within a combinatorial structure has grown. This kind of research started with patterns in permutations , while in the last few years it is being carried on in several directions.
A k-path (with k = 4 or 8) is a sequence of pixels such that two consecutive pixels of the sequence are k-adjacent. A set of pixels S is k-connected if for each pair of pixels (p1 , p2 ) ∈ S 2 there is a k-path from p1 to p2 having all its pixels in S. A region in a labeled image i = (Id , L, l) is a maximal set of 4-connected pixels having the same label. , inﬁnite(i) = Z2 \Id . The set of regions of i, including inﬁnite(i), is denoted regions(i) and is a partition of Z2 . A region R is enclosed in another region R if all 8-paths from one pixel of R to a pixel of inﬁnite(i) contains at least one pixel of R .
2 leads to the following result: Theorem 1. Let i and i be two labeled images, and T M (i) and T M (i ) be their associated 2D topological maps. T M (i) and T M (i ) are isomorphic iﬀ the partitions into regions of i and i are homeomorphic embeddings in the plane. Two embeddings are homeomorphic in the plane when they describe the same regions and the same adjacency relations and region enclosure relations. In  the deﬁnition of maptree is given. This is a 2D combinatorial map plus a black and white adjacency tree.