By Nicolas Normand, Jeanpierre Guédon, Florent Autrusseau

ISBN-10: 3319323598

ISBN-13: 9783319323596

ISBN-10: 3319323601

ISBN-13: 9783319323602

This ebook constitutes the refereed complaints of the nineteenth IAPR foreign convention on Discrete Geometry for desktop Imagery, DGCI 2016, held in Nantes, France, in April 2016.

The 32 revised complete papers awarded including 2 invited talks have been conscientiously chosen from fifty one submissions. The papers are equipped in topical sections on combinatorial instruments; discretization; discrete tomography; discrete and combinatorial topology; form descriptors; types for discrete geometry; circle drawing; morphological research; geometric transforms; and discrete form illustration, attractiveness and analysis.

**Read Online or Download Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings PDF**

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**Extra info for Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings**

**Sample text**

3. A small graph and its associated incidence matrix. A weighted version of the TV model can be written in the following way [23], in the continuous framework: wx,y (uy − ux )2 dy min u regularization R(u) 1/2 dx + 1 2λ (ux − fx )2 dx, data ﬁdelity (12) Φ(u) with λ a Lagrange multiplier. It is equivalent to the following min-max problem [10] min max u ||p||∞ ≤1 1/2 (uy − ux )px,y dxdy + Φ(u), wx,y (13) with p a projection vector ﬁeld. Such min-max formulations are called primaldual in optimization.

References 1. : Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011) 2. : A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009) 3. : Robust anisotropic diﬀusion. IEEE Trans. Image Process. 7(3), 421–432 (1998) 4. : Convex Optimization. Cambridge University Press, New York (2004) 5. : Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001) 6.

The subword 12 is region equivalent to subword 21. Proof. By Proposition 2 one can see, that 12 is region equivalent to 111, and thus, to 21. Proposition 4. The subword 32 is region equivalent to subwords 23. Moreover, they are region equivalent to 33. Proof. At 3-steps all the three coordinates can be changed (by ±1). However, there are only two types of pixels, namely 0-sum (even) and 1-sum (odd) pixels. Therefore, one can see that by two consecutive 3-steps those points can be reached for which one of the coordinates is changed with at most +2, the other with at most −2, and the third one by at most ±1, depending on the parity.

### Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings by Nicolas Normand, Jeanpierre Guédon, Florent Autrusseau

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