Pyramids of n-Dimensional Generalized Maps

International audienceGraph pyramids are often used for representing irregular pyramids. Combinatorial pyramids have been recently defined for this purpose. We define here pyramids of n-dimensional generalized maps. This is the main contribution of this work: a generic definition in any dimension which extend and generalize the previous works. Moreover, such pyramids explicitly represent more topological information than graph pyramids. A pyramid can be implemented in several ways, and three representations are discussed in this paper

Invariant Representative Cocycles of Cohomology Generators using Irregular Graph Pyramids

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns `quantities' to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. An extension to obtain scanning and rotation invariant cocycles is given.Comment: Special issue on Graph-Based Representations in Computer Visio

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio

Connecting Planetary Composition with Formation

The rapid advances in observations of the different populations of exoplanets, the characterization of their host stars and the links to the properties of their planetary systems, the detailed studies of protoplanetary disks, and the experimental study of the interiors and composition of the massive planets in our solar system provide a firm basis for the next big question in planet formation theory. How do the elemental and chemical compositions of planets connect with their formation? The answer to this requires that the various pieces of planet formation theory be linked together in an end-to-end picture that is capable of addressing these large data sets. In this review, we discuss the critical elements of such a picture and how they affect the chemical and elemental make up of forming planets. Important issues here include the initial state of forming and evolving disks, chemical and dust processes within them, the migration of planets and the importance of planet traps, the nature of angular momentum transport processes involving turbulence and/or MHD disk winds, planet formation theory, and advanced treatments of disk astrochemistry. All of these issues affect, and are affected by the chemistry of disks which is driven by X-ray ionization of the host stars. We discuss how these processes lead to a coherent end-to-end model and how this may address the basic question.Comment: Invited review, accepted for publication in the 'Handbook of Exoplanets', eds. H.J. Deeg and J.A. Belmonte, Springer (2018). 46 pages, 10 figure

The PLATO 2.0 mission

PLATO 2.0 has recently been selected for ESA's M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) and a large photometric magnitude range (4-16 mag). It focusses on bright (4-11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2 %, 4-10 % and 10 % for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50 % of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA's Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science

Generalized Map Pyramid for Multi-level 3D Image Segmentation

International audienceGraph pyramids are often used to represent an image with various levels of details. Generalized pyramids have been recently defined in order to deal with images in any dimension. In this work, we show how to use generalized pyramids to represent 3D multi-level segmented images. We show how to construct such a pyramid, by alternating segmentation and simplification steps. We present how cells to be removed are marked: by using an homogeneous criterion to mark faces and the cell degree to mark other cells. When the pyramid is constructed, the main problem consists in retrieving information on regions. In this work, we show how to retrieve two types of information. The first one is the low level cells that are merged into a unique high level cell. The second one is the inter-voxel cells that compose a given region

Receptive Fields for Generalized Map Pyramids: The Notion of Generalized Orbit

International audienceA pyramid of n-dimensional generalized maps is a hierarchical data structure. It can be used, for instance, in order to represent an irregular pyramid of n-dimensional images. A pyramid of generalized maps can be built by successively removing and/or contracting cells of any dimension. In this paper, we define generalized orbits, which extend the classical notion of receptive fields. Generalized orbits allow to establish the correspondence between a cell of a pyramid level and the set of cells of previous levels, the removal or contraction of which have led to the creation of this cell. In order to define generalized orbits, we extend, for generalized map pyramids, the notion of connecting walk defined by Brun and Kropatsch

Définition et étude des pyramides généralisées D (application pour la segmentation multi-échelle d'images 3D)

Dans ce travail, nous nous intéressons à la modélisation géométrique hiérarchique à base topologique en proposant la définition d'un modèle générique en dimension quelconque, et en montrant une application possible en segmentation multi-échelle d'images 3D. Dans la première partie de cette thèse, nous définissons et étudions les pyramides généralisées nD. C'est un modèle topologique hiérarchique générique qui représente toutes les cellules d'une subdivision ainsi que les relations d'adjacence et d'incidence existant entre celles-ci. Nous proposons et comparons trois représentations possibles de ces pyramides. Afin de retrouver les informations correspondant à une cellule, nous définissons la notion d'orbite généralisée étendant celle de champ récepteur. Nous définissons également une opération de modification locale d'un niveau de la pyramide permettant de conserver la cohérence du modèle en propageant les modifications aux niveaux supérieurs. Dans la deuxième partie de ce travail, nous montrons comment utiliser ce modèle dans le cadre d'une segmentation multi-échelle d'images 3D. Nous définissons les propriétés que doit satisfaire la pyramide, puis nous donnons les algorithmes qui permettent de construire une telle pyramide. Nous montrons ensuite comment utiliser les orbites généralisées afin de retrouver les voxels ou éléments inter-voxels composant une région ou son bord. Enfin nous définissons une opération permettant de modifier localement le critère de segmentation d'un ensemble de régions. Cette opération est basée sur celle définie dans la première partie afin de conserver les contraintes de cohérence.In this work, we are interested in the hierarchical geometrical modeling with a topological basis. We propose the definition of a generic model in any dimension, and we show a possible application in multi-level segmentation of 3D images. In the first part of this work, we define and study the nD generalized pyramids. This is a generic hierarchical topological model which represents all the cells of a subdivision as well as the adjacency and incidence relations existing between these cells. We propose and compare three possible representations of these pyramids. In order to retrieve the information which corresponds to a cell, we define the notion of generalized orbit. This notion extends the notion of receptive field. We also define a local modification operation of a pyramid level allowing to preserve the model coherence by propagating the modifications at the upper levels. In the second part of this work, we show how to use this model in the case of a multi-level segmentation of 3D images. We define the properties which have to be respected by the pyramid, and we give the algorithms that allow to construct such a pyramid. Then, we show how to use the generalized orbits in order to retrieve the voxels or the inter-voxel elements which compose a region or its boundary. Finally we define an operation allowing to locally modify the segmentation criterion of a region set. This operation is based on the operation defined in the first part in order to preserve the coherence constraints.POITIERS-BU Sciences (861942102) / SudocSudocFranceF