By Peter W. Hawkes

ISBN-10: 0120147734

ISBN-13: 9780120147731

The themes reviewed within the 'Advances' sequence conceal a extensive diversity of subject matters together with microscopy, electromagnetic fields and photograph coding. This e-book is vital interpreting for electric engineers, utilized mathematicians and robotics specialists. Emphasizes extensive and intensive article collaborations among world-renowned scientists within the box of photo and electron physics offers concept and it is program in a pragmatic experience, delivering lengthy awaited options and new findings Bridges the space among educational researchers and R&D designers by way of addressing and fixing day-by-day concerns

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Extra info for Advances in Imaging and Electron Physics, Vol. 131

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Vi g. , 1994; Pearson and Jeavons, 1997). 5. Hypergraphs and Database Schemes The hypergraph theory has been introduced in databases in order to model relational database schemes. The classes of acyclicity hypergraphs (defined in the last section) play an important part in the modeling of relational database schemes. A database can be viewed in the following way: . A set of attributes. A set of relations between these attributes. Hence we have the following hypergraph: . The set of vertices is the set of attributes.

Every position keeps in memory two values: Max and Min. For each pixel (i, j, I(i, j)) of I, do; Mark(i, j) ¼ 0; end for For each pixel (i, j, I(i, j)) of I, do; k ¼ 0; t ¼ 0; Markði À k; jÞ ¼ 1; Maxi(i À k, j) ¼ Min(i À k, j) ¼ I(i, j); While (i ! k, and Mark(i À k, j) ¼ 1) do; Maxi(i À (k þ 1), j) ¼ max{Maxi(i À k, j); I(i À (k þ 1), j)}; Mini(i À (k þ 1), j) ¼ min{Mini(i À k, j); I(i À (k þ 1), j)}; If Maxi(i À (k þ 1, j) À Mini(i À (k þ 1, j) < 2Áa then Mark(i À (k þ 1), j) ¼ 1; k ¼ k þ 1; Else k ¼ 0; Maxi(i, j À (t þ 1)) ¼ max{I(i, j), I(i, j À (t þ 1))}; Min(i, j À (t þ 1)) ¼ min{I(i, j), I(i, j À (t þ 1))}; If Maxi(i, j À (t þ 1)) À Min(i, j À (t þ 1)) < 2Áa then Mark(i, j À (t þ 1)) ¼ 1; While (i !

Assume that there exists two polyominoes hypergraphs associated with the image I. Let us call these two hypergraphs HI;a ¼ ðX ; Ei Þi2I and 0 ¼ ðX ; E 0 Þ 0 HI;a j j2J . There exists i 2 I such that for any j 2 J, Ei 6¼ Ej . For any x 2 Ei there exists k 2 J such that x 2 Ek0 . For all x 2 Ei, I(x) belongs to [Àa; a]. So, there is h 2 J such that Ei  Eh . 0 . & From proposition 14, Ei ¼ Eh . Hence HI;a ¼ HI;a Proposition 15. Let I be a digital image and HI,a its associated polyominoes hypergraph.

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Advances in Imaging and Electron Physics, Vol. 131 by Peter W. Hawkes

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