By Nicolas Normand, Jeanpierre Guédon, Florent Autrusseau

This e-book constitutes the refereed lawsuits 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 offered 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, popularity and analysis.

**Read 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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**Sample text**

4(g,h,i) we restore a noisy 3D mesh, with the same framework. Only the graph changes. Discrete Calculus, Optimisation and Inverse Problems in Imaging (a) Original (b) Degraded (g) Original (c) Restored (d) Original (h) Noisy (e) Degraded 25 (f) Restored (i) Restored Fig. 4. 2 dB. 1 dB, (f) DCTV result PSNR = 35 dB. (g) Original mesh, (h) noisy mesh, (i) restored mesh 7 Discussion Results presented here are interesting to some degree because we have kept the spatial part of the formulation fully discrete, with at its heart a graph representation for the numerical operators we use.

A special two-dimensional representation of some traces is given by trajectories (usually on the square grid). These trajectories were also used to describe syntactic constraints for shuﬄing two parallel events (described by words) in [7]. We believe that trajectories connected to other regular grids are also interesting. A kind of generalization of traces is presented in [6], where apart from the usual permutation rules, some other rewriting rules, namely serialisation equations, are also allowed.

Let X be a GCF-algorithm and v a vector with relatively prime coordinates. The length, noted lengthX (v), is, if it exists, the smallest integer N 0 such that vN = 1. In Sect. 1) that, if X is one of these, then lengthX (v) exists. Under such assumption, the points of the body are always included in a digital plane of normal vector v. 3. Let X be a GCF-algorithm such that each step is either S, B or FS and N = lengthX (v) exists. For each n ∈ {0, 1, . . , N }, Bn ⊆ P(v, v 1 − 2). Proof. For each n 1, let gn be the value of the coordinate of vn−1 that is subtracted.