arXiv subjects

Fabien Feschet

Publications and source records attributed to Fabien Feschet.

4 recordsLinked to original sources

arXiv2026

How to~Peel Fully Convex Digital Sets

Full convexity is an interesting alternative to classical digital convexity since it guarantees connectedness and even simple connectedness in digital spaces Z d , for any dimension d. This paper aims at giving a better understanding of the monotonicity properties of fully convex digital sets, since earlier works showed that the question was difficult for thin fully convex sets. To decipher the hierarchy of fully convex sets ordered by inclusion, we study how we can peel a fully convex set progressively while keeping its full convexity. We provide a characterization of peelable points and fast algorithms to identify them. Furthermore we show that fully convex set can be peeled one point at a time till reduced to the empty set, similarly to digitally convex sets in the classical sense. The peeling of a fully convex set can be seen as an analog to homotopic thinning processes, but with an additional geometric property.

cs.CG↗

arXiv2026

Shadoks Approach to Parallel Reconfiguration of Triangulations

We describe the methods used by Team Shadoks to win the CG:SHOP 2026 Challenge on parallel reconfiguration of planar triangulations. An instance is a collection of triangulations of a common point set. We must select a center triangulation and find short parallel-flip paths from each input triangulation to the center, minimizing the sum of path lengths. Our approach combines exact methods based on SAT with several greedy heuristics, and also makes use of SAT and MaxSAT for solution improvement. We present a SAT encoding for bounded-length paths and a global formulation for fixed path-length vectors. We discuss how these components interact in practice and summarize the performance of our solvers on the benchmark instances.

cs.CG↗

arXiv2021

Robust reconstructions by multi-scale/irregular tangential covering

In this paper, we propose an original manner to employ a tangential cover algorithm - minDSS - in order to geometrically reconstruct noisy digital contours. To do so, we exploit the representation of graphical objects by maximal primitives we have introduced in previous works. By calculating multi-scale and irregular isothetic representations of the contour, we obtained 1-D (one-dimensional) intervals, and achieved afterwards a decomposition into maximal line segments or circular arcs. By adapting minDSS to this sparse and irregular data of 1-D intervals supporting the maximal primitives, we are now able to reconstruct the input noisy objects into cyclic contours made of lines or arcs with a minimal number of primitives. In this work, we explain our novel complete pipeline, and present its experimental evaluation by considering both synthetic and real image data. We also show that this is a robust approach, with respect to selected references from state-of-the-art, and by considering a multi-scale noise evaluation process.

cs.CV↗

arXiv2018

The Saturated Subpaths Decomposition in Z 2 : a short note on generalized Tangential Cover

In this short note, we generalized the Tangential Cover used in Digital Geometry in order to use very general geometric predicates. We present the required notions of saturated $α$-paths of a digital curve as well as conservative predicates which indeed cover nearly all geometric digital primitives published so far. The goal of this note is to prove that under a very general situation, the size of the Tangential Cover is linear with the number of points of the input curve. The computation complexity of the Tangential Cover depends on the complexity of incremental recognition of geometric predicates. Moreover, in the discussion, we show that our approach does not rely on connectivity of points as it might be though first.

cs.CG↗