Two linear-time algorithms for computing the minimum length polygon of a digital contour

AbstractThe Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009) [26], by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP

Angular Power Spectrum Estimation of Cosmic Ray Anisotropies with Full or Partial Sky Coverage

We study the angular power spectrum estimate in order to search for large scale anisotropies in the arrival directions distribution of the highest-energy cosmic rays. We show that this estimate can be performed even in the case of partial sky coverage and validated over the full sky under the assumption that the observed fluctuations are statistically spatial stationary. If this hypothesis - which can be tested directly on the data - is not satisfied, it would prove, of course, that the cosmic ray sky is non isotropic but also that the power spectrum is not an appropriate tool to represent its anisotropies, whatever the sky coverage available. We apply the method to simulations of the Pierre Auger Observatory, reconstructing an input power spectrum with the Southern site only and with both Northern and Southern ones. Finally, we show the improvement that a full-sky observatory brings to test an isotropic distribution, and we discuss the sensitivity of the Pierre Auger Observatory to large scale anisotropies.Comment: 16 pages, 6 figures, version accepted for publication by JCA

A hierarchical approach with triangulated surfaces for 3D data segmentation

This article presents a new algorithm for segmenting three-dimensional images . It is based on a dynamic triangulated surface an d on a pyramidal representation . The triangulated surface, which follows a physical modelization and which can as well modify its geometry as its topology, segments images into their components by altering its shape according to internal and externa l constraints . In order to speed up the whole process, an algorithm of pyramid building with any reduction factor allows us t o transform the image into a set of images with progressive resolutions . This organization into a hierarchy, combined with a model that can adapt its mesh refinement to the resolution of the workspace, authorizes a fast estimation of the general forms included i n the image. After that, the model searches for finer and finer details while relying successively on the different levels of the pyramid.Ce travail présente un algorithme de segmentation d'images tridimensionnelles par utilisation de surfaces triangulées et de pyramides. Une triangulation de surface dynamique, dotée d'une modélisation physique et capable de changer sa topologie, va, en se déformant suivant certaines contraintes, segmenter l'image en ses constituants. Afin d'accélérer le processus, un algorithme de construction de pyramide de facteur de réduction quelconque permet de transformer l'image en un ensemble d'images de résolution progressive. Cette hiérarchisation, couplée à un modèle capable d'adapter la précision de sa maille à la résolution de son espace de travail, permet d'estimer très rapidement les formes générales contenues dans une image. Une fois ceci fait, le modèle recherche les détails de plus en plus petits en s'appuyant successivement sur les différents niveaux de la pyramide

Revisiting Digital Straight Segment Recognition

This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveill\`es in 1995 [Debled95]. We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation. This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description. As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them. We also show how this evolution can be projected onto the Stern-Brocot tree. These new relations have interesting consequences on the geometry of digital curves. We show how they can for instance be used to bound the slope difference between consecutive maximal segments

The SVOM gamma-ray burst mission

We briefly present the science capabilities, the instruments, the operations, and the expected performance of the SVOM mission. SVOM (Space-based multiband astronomical Variable Objects Monitor) is a Chinese-French space mission dedicated to the study of Gamma-Ray Bursts (GRBs) in the next decade. The SVOM mission encompasses a satellite carrying four instruments to detect and localize the prompt GRB emission and measure the evolution of the afterglow in the visible band and in X-rays, a VHF communication system enabling the fast transmission of SVOM alerts to the ground, and a ground segment including a wide angle camera and two follow-up telescopes. The pointing strategy of the satellite has been optimized to favor the detection of GRBs located in the night hemisphere. This strategy enables the study of the optical emission in the first minutes after the GRB with robotic observatories and the early spectroscopy of the optical afterglow with large telescopes to measure the redshifts. The study of GRBs in the next decade will benefit from a number of large facilities in all wavelengths that will contribute to increase the scientific return of the mission. Finally, SVOM will operate in the era of the next generation of gravitational wave detectors, greatly contributing to searches for the electromagnetic counterparts of gravitational wave triggers at Xray and gamma-ray energies.Comment: 13 pages, 5 figures, published by PoS, proceedings of the conference Swift: 10 Years of Discovery, 2-5 December 2014, La Sapienza University, Rome, Ital

Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on Z with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.Comment: 2 figure

The Drift Chambers Of The Nomad Experiment

We present a detailed description of the drift chambers used as an active target and a tracking device in the NOMAD experiment at CERN. The main characteristics of these chambers are a large area, a self supporting structure made of light composite materials and a low cost. A spatial resolution of 150 microns has been achieved with a single hit efficiency of 97%.Comment: 42 pages, 26 figure

One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold.Ministerio de Economía y Competitividad MTM2015-67072-