Research carried out by the Geometrica project team is dedicated to Computational Geometry and Topology and follows three major directions: (a). mesh generation and geometry processing; (b). topological and geometric inference; (c). data structures and robust geometric computation. The overall objective of the project-team is to give effective computational geometry and topology solid mathematical and algorithmic foundations, to provide solutions to key problems as well as to validate theoretical advances through extensive experimental research and the development of software packages that may serve as steps toward a standard for reliable and effective geometric computing. Most notably, Geometrica, together with several partners in Europe, plays a prominent role in the development of cgal, a large library of computational geometry algorithms.

Meshes are becoming commonplace in a number of applications ranging from engineering to multimedia through biomedecine and geology. For rendering, the quality of a mesh refers to its approximation properties. For numerical simulation, a mesh is not only required to faithfully approximate the domain of simulation, but also to satisfy size as well as shape constraints. The elaboration of algorithms for automatic mesh generation is a notoriously difficult task as it involves numerous geometric components: Complex data structures and algorithms, surface approximation, robustness as well as scalability issues. The recent trend to reconstruct domain boundaries from measurements adds even further hurdles. Armed with our experience on triangulations and algorithms, and with components from the cgal library, we aim at devising robust algorithms for 2D, surface, 3D mesh generation as well as anisotropic meshes. Our research in mesh generation primarily focuses on the generation of simplicial meshes, i.e. triangular and tetrahedral meshes. We investigate both greedy approaches based upon Delaunay refinement and filtering, and variational approaches based upon energy functionals and associated minimizers.

The search for new methods and tools to process digital geometry is motivated by the fact that previous attempts to adapt common signal processing methods have led to limited success: Shapes are not just another signal but a new challenge to face due to distinctive properties of complex shapes such as topology, metric, lack of global parameterization, non-uniform sampling and irregular discretization. Our research in geometry processing ranges from surface reconstruction to surface remeshing through curvature estimation, principal component analysis, surface approximationand surface mesh parameterization. Another focus is on the robustness of the algorithms to defect-laden data. This focus stems from the fact that acquired geometric data obtained through measurements or designs are rarely usable directly by downstream applications. This generates bottlenecks, i.e., parts of the processing pipeline which are too labor-intensive or too brittle for practitioners. Beyond reliability and theoretical foundations, our goal is to design methods which are also robust to raw, unprocessed inputs.

Due to the fast evolution of data acquisition devices and computational power, scientists in many areas are asking for efficient algorithmic tools for analyzing, manipulating and visualizing more and more complex shapes or complex systems from approximative data. Many of the existing algorithmic solutions which come with little theoretical guarantee provide unsatisfactory and/or unpredictable results. Since these algorithms take as input discrete geometric data, it is mandatory to develop concepts that are rich enough to robustly and correctly approximate continuous shapes and their geometric properties by discrete models. Ensuring the correctness of geometric estimations and approximations on discrete data is a sensitive problem in many applications.

Data sets being often represented as point sets in high dimensional spaces, there is a considerable interest in analyzing and processing data in such spaces. Although these point sets usually live in high dimensional spaces, one often expects them to be located around unknown, possibly non linear, low dimensional shapes. These shapes are usually assumed to be smooth submanifolds or more generally compact subsets of the ambient space. It is then desirable to infer topological (dimension, Betti numbers,...) and geometric characteristics (singularities, volume, curvature,...) of these shapes from the data. The hope is that this information will help to better understand the underlying complex systems from which the data are generated. In spite of recent promising results, many problems still remain open and to be addressed, need a tight collaboration between mathematicians and computer scientists. In this context, our goal is to contribute to the development of new mathematically well founded and algorithmically efficient geometric tools for data analysis and processing of complex geometric objects. Our main targeted areas of application include machine learning, data mining, statistical analysis, and sensor networks.

Geometrica has a large expertise of algorithms and data structures for geometric problems.We are pursuing efforts to design efficient algorithms from a theoretical point of view, but we also put efforts in the effective implementation of these results.

In the past years, we made significant contributions to algorithms for computing Delaunay triangulations (which are used by meshes in the above paragraph). We are still working on the practical efficiency of existing algorithms to compute or to exploit classical Euclidean triangulations in 2 and 3 dimensions, but the current focus of our research is more aimed towards extending the triangulation efforts in several new directions of research.

One of these directions is the triangulation of non Euclidean spaces such as periodic or projective spaces, with various potential applications ranging from astronomy to granular material simulation.

Another direction is the triangulation of moving points, with potential applications to fluid dynamics where the points represent some particles of some evolving physical material, and to variational methods devised to optimize point placement for meshing a domain with a high quality elements.

Increasing the dimension of space is also a stimulating direction of research, as triangulating points in medium dimension (say 4 to 15) has potential applications and raises new challenges to trade exponential complexity of the problem in the dimension for the possibility to reach effective and practical results in reasonably small dimensions.

On the complexity analysis side, we pursue efforts to obtain complexity analysis in some practical situations involving randomized or stochastic hypotheses. On the algorithm design side, we are looking for new paradigms to exploit parallelism on modern multicore hardware architectures.

Finally, all this work is done while keeping in mind concerns related to effective implementation of our work, practical efficiency and robustness issues which have become a background task of all different works made by Geometrica.

Medical Imaging

Numerical simulation

Geometric modeling

Geographic information systems

Visualization

Data analysis

Astrophysics

Material physics

With the collaboration of
Pierre Alliez,
Hervé Brönnimann,
Manuel Caroli,
Pedro Machado Manhães de Castro,
Frédéric Cazals,
Frank Da,
Christophe Delage,
Andreas Fabri,
Julia Flötotto,
Philippe Guigue,
Michael Hemmer,
Samuel Hornus,
Clément Jamin,
Menelaos Karavelas,
Sébastien Loriot,
Abdelkrim Mebarki,
Naceur Meskini,
Andreas Meyer,
Sylvain Pion,
Marc Pouget,
François Rebufat,
Laurent Rineau,
Laurent Saboret,
Stéphane Tayeb,
Jane Tournois,
Radu Ursu, and
Camille Wormser
http://

cgal is a C++ library of geometric algorithms and data structures. Its development has been initially funded and further supported by several European projects (CGAL, GALIA, ECG, ACS, AIM@SHAPE) since 1996. The long term partners of the project are research teams from the following institutes: Inria Sophia Antipolis - Méditerranée, Max-Planck Institut Saarbrücken, ETH Zürich, Tel Aviv University, together with several others. In 2003, cgal became an Open Source project (under the LGPL and QPL licenses).

The transfer and diffusion of cgal in industry is achieved through
the company Geometry Factory (http://*Born of Inria*
company, founded by Andreas Fabri in
January 2003.
The goal of this company is to pursue the development of the library
and to offer services in connection with cgal (maintenance, support,
teaching, advice). Geometry Factory is a link between the researchers from the
computational geometry community and the industrial users.

The aim of the cgal project is to create a platform for geometric computing supporting usage in both industry and academia. The main design goals are genericity, numerical robustness, efficiency and ease of use. These goals are enforced by a review of all submissions managed by an editorial board. As the focus is on fundamental geometric algorithms and data structures, the target application domains are numerous: from geological modeling to medical images, from antenna placement to geographic information systems, etc.

The cgal library consists of a kernel, a list of algorithmic packages,
and a support
library. The kernel is made of classes that represent elementary
geometric objects (points, vectors, lines, segments, planes,
simplices, isothetic boxes, circles, spheres, circular arcs...),
as well as affine transformations and
a number of predicates and geometric constructions over these objects.
These classes exist in dimensions 2 and 3 (static dimension) and

A number of packages provide geometric data structures as
well as algorithms. The data structures are polygons, polyhedra,
triangulations, planar maps, arrangements and various search
structures (segment trees,

Finally, the support library provides random generators, and interfacing code with other libraries, tools, or file formats (ASCII files, QT or LEDA Windows, OpenGL, Open Inventor, Postscript, Geomview...). Partial interfaces with Python, scilab and the Ipe drawing editor are now also available.

Geometrica is particularly involved in general maintenance, in the arithmetic issues that arise in the treatment of robustness issues, in the kernel, in triangulation packages and their close applications such as alpha shapes, in mesh generation and related packages. Two researchers of Geometrica are members of the cgal Editorial Board, whose main responsibilities are the control of the quality of cgal, making decisions about technical matters, coordinating communication and promotion of cgal.

cgal is about 700,000 lines of code and supports various platforms: GCC (Linux, Mac OS X, Cygwin...), Visual C++ (Windows), Intel C++. A new version of cgal is released twice a year, and it is downloaded about 10000 times a year. Moreover, cgal is directly available as packages for the Debian, Ubuntu and Fedora Linux distributions.

More numbers about cgal: there are now 12 editors in the editorial board, with approximately 20 additional developers. The user discussion mailing-list has more than 1000 subscribers with a relatively high traffic of 5-10 mails a day. The announcement mailing-list has more than 3000 subscribers.

We implemented a new high-dimensional kernel taking advantage of the progress that was made in dimensions 2 and 3. It is meant to be used with a reimplementation of high-dimensional triangulations (in progress).

We added a new exact ring number type that can represent all finite double floating-point numbers. It makes building a Delaunay triangulation 8 times faster than with earlier cgal releases in some degenerate cases.

In collaboration with Pierre Alliez (EPI Titane), ClémentJamin (EPI Titane)

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (cgal). It generates isotropic simplicial meshes – surface triangular meshes or volume tetrahedral meshes – from input surfaces, 3D domains as well as 3D multi-domains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces, and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality as well as on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.

There is a growing need for a 3D periodic mesh generator for various fields, such as material engineering or modeling of nano-structures. We are writing a software package answering this need, and which will be made publicly available in the open source library cgal. The software is based on the cgal 3D volume mesh generator package and the cgal 3D periodic triangulations package.

With the collaboration of David Salinas

The GUDHI open source library will provide the central data structures and algorithms that underly applications in geometry understanding in higher dimensions. It is intended to both help the development of new algorithmic solutions inside and outside the project, and to facilitate the transfert of results in applied fields. The first release of the GUDHI library includes: – Data structures to represent, construct and manipulate simplicial complexes; – Algorithms to compute persistent homology and multi-field persistent homology.

was elected among the notable articles of 2013 by ACM and Computing Reviews (see http://

In collaboration with Pierre Alliez (EPI Titane), Ricard Campos (University of Girona), Raphael Garcia (University of Girona)

Underwater range scanning techniques are starting to gain interest in underwater exploration, providing new tools to represent the seafloor. These scans (often) acquired by underwater robots usually result in an unstructured point cloud, but given the common downward-looking or forward-looking configuration of these sensors with respect to the scene, the problem of recovering a piecewise linear approximation representing the scene is normally solved by approximating these 3D points using a heightmap (2.5D). Nevertheless, this representation is not able to correctly represent complex structures, especially those presenting arbitrary concavities normally exhibited in underwater objects. We present a method devoted to full 3D surface reconstruction that does not assume any specific sensor configuration. The method presented is robust to common defects in raw scanned data such as outliers and noise often present in extreme environments such as underwater, both for sonar and optical surveys. Moreover, the proposed method does not need a manual preprocessing step. It is also generic as it does not need any information other than the points themselves to work. This property leads to its wide application to any kind of range scanning technologies and we demonstrate its versatility by using it on synthetic data, controlled laser-scans, and multibeam sonar surveys. Finally, and given the unbeatable level of detail that optical methods can provide, we analyze the application of this method on optical datasets related to biology, geology and archeology.

In collaboration with Omid Amini (ENS),

In this paper, we prove a variant of the Burger-Brooks transfer principle which, combined with recent eigenvalue bounds for surfaces, allows to obtain upper bounds on the eigenvalues of graphs as a function of their genus. More precisely, we show the existence of a universal constants C such that the k-th eigenvalue

In collaboration with Ramsay Dyer (Johann Bernouilli Institute, University of Groningen, Pays Bas) and Arijit Ghosh (Max-Planck-Institut für Informatik, Saarbrücken, Germany).

In collaboration with Dominique Attali (Gipsa-lab, Grenoble), Sylvain Lazard (Inria Nancy - Grand Est)

We say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (three-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes which are not shrinkable.

In collaboration with Donald Sheehy (University of Connecticut)

For points sampled near a compact set X, the persistence barcode of the Rips filtration built from the sample contains information about the homology of X as long as X satisfies some geometric assumptions. The Rips filtration is prohibitively large, however zigzag persistence can be used to keep the size linear. We present several species of Rips-like zigzags and compare them with respect to the signal-to-noise ratio, a measure of how well the underlying homology is represented in the persistence barcode relative to the noise in the barcode at the relevant scales. Some of these Rips-like zigzags have been available as part of the Dionysus library for several years while others are new. Interestingly, we show that some species of Rips zigzags will exhibit less noise than the (non-zigzag) Rips filtration itself. Thus, the Rips zigzag can offer improvements in both size complexity and signal-to-noise ratio. Along the way, we develop new techniques for manipulating and comparing persistence barcodes from zigzag modules. We give methods for reversing arrows and removing spaces from a zigzag. We also discuss factoring zigzags and a kind of interleaving of two zigzags that allows their barcodes to be compared. These techniques were developed to provide our theoretical analysis of the signal-to-noise ratio of Rips-like zigzags, but they are of independent interest as they apply to zigzag modules generally.

In collaboration with Tamal K. Dey (University of Ohio) Fengtao Fan (University of Ohio) Yusu Wang (University of Ohio)

In collaboration with Donald Sheehy (University of Connecticut)

In collaboration with Chunyuan Li (former intern in Saclay in 2013)

In collaboration with Catherine Labruère (University of Burgundy)

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In , we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.

In collaboration with Brittany Fasy (Tulane University) Fabrizio Lecci (Carnegie Mellon University) Alessandro Rinaldo (Carnegie Mellon University) Larry Wasserman (Carnegie Mellon University)

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we can summarize the persistent homology with the persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. In , we investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.

In collaboration with Brittany Fasy (Tulane University) Fabrizio Lecci (Carnegie Mellon University) Alessandro Rinaldo (Carnegie Mellon University) Larry Wasserman (Carnegie Mellon University)

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates. We study the risk of two estimators and we prove that the subsampling approach carries stable topological information while achieving a great reduction in computational complexity.

In collaboration with Vin de Silva (Pomona College) William Crawley-Boevey (University of Leeds)

In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is de- finable. However, unlike persistence modules indexed over a totally ordered finite set or the natural numbers, such diagrams do not provide a complete invariant of q-tame modules. The purpose of is to show that the category of persistence modules can be adjusted to overcome this issue. We introduce the observable category of persis- tence modules: a localization of the usual category, in which the classical properties of q-tame modules still hold but where the persistence diagram is a complete isomorphism invariant and all q-tame modules admit an interval decomposition.

In collaboration with Nicolas Broutin (EPI rap)

Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. Whilst many algorithms have been proposed, very little theoretical analysis is available for the properties of the paths generated or the computational resources required to generate them. In this work, we propose and analyse a new planar navigation algorithm for the Delaunay triangulation. We then demonstrate a number of strong theoretical guarantees for the algorithm when it is applied to a random set of points in a convex region . In a side result, we give a new polylogarithmic bound on the maximum degree of a random Delaunay triangulation in a smooth convex, that holds with probability one as the number of points goes to infinity. In particular, our new bound holds even for points arbitrarily close to the boundary of the domain.

The asymptotic behavior of the expected size of the convex hull of
uniformly random points in a convex body in

In collaboration with Philippe Duchon (LABRI)

Let

where

In collaboration with Karthik C.S (Weizmann Institute of Science, Israël) and Sébastien Tavenas (Max-Planck-Institut für Informatik, Saarbrücken, Germany).

The Simplex Tree is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows to efficiently implement a large range of basic operations on simplicial complexes. In this paper, we show how to optimally compress the simplex tree while retaining its functionalities. In addition, we propose two new data structures called Maximal Simplex Tree and Compact Simplex Tree. We analyze the Compressed Simplex Tree, the Maximal Simplex Tree and the Compact Simplex Tree under various settings.

In collaboration with Ramsay Dyer (Johann Bernouilli Institute, University of Groningen, Pays Bas) and Arijit Ghosh (Max-Planck-Institut für Informatik, Saarbrücken, Germany).

The witness complex was introduced by Carlsson and de Silva as a
weak form of the Delaunay complex that is suitable for finite metric
spaces and is computed using only distance comparisons. The witness
complex

The only numerical operations used by our algorithms are (squared)
distance comparisons (i.e., predicates of degree 2). In particular,
we do not use orientation or in-sphere predicates, whose degree
depends on the dimension

Mael Rouxel-Labbé's PhD thesis is supported by a Cifre contract with
Geometry Factory (http://

In 2014, Geometry Factory (http://

LMI Technologies (Canada, GIS): 2D triangulations

Rio Tinto (Australie, mining): 2D triangulations

Geovariances (France, oil and gas): 3D triangulations and meshes

Elektrobit (Allemagne, GIS): 2D triangulations

First Light Fusion (UK, energie): 2D triangulations

- Title: Persistent Homology

- Coordinator: Mariette Yvinec (Geometrica)

- Duration: 1 year renewable once, starting date December 2012. Renewed for 1 year from January 1st 2014 to December 31t 2014

- Others Partners: Inria team abs,
Gipsa Lab (UMR 5216, Grenoble, http://

- Abstract: Geometric Inference is a rapidly emerging field that aims to analyse the structural, geometric and topological, properties of point cloud data in high dimensional spaces. The goal of the ADT PH is to make available, a robust and comprehensive set of algorithmic tools resulting from recent advances in Geometric Inference. The software will include:

tools to extract from the data sets, families of simplicial complexes,

data structures to handle those simplicial complexes,

algorithmic modules to compute the persistent homology of those complexes,

applications to clustering, segmentation and analysis of scalar fields such as the energy landscape of macromolecular systems.

- Title: OrbiCGAL

- Coordinator: Monique Teillaud (Geometrica)

- Duration: 1 year renewable once, starting date September 2013.

- Abstract: OrbiCGAL is a software project supported by Inria as a Technological Development Action (ADT). It is motivated by applications ranging from infinitely small (nano-structures) to infinitely large (astronomy), through material engineering, physics of condensed matter, solid chemistry, etc

The project consists in developing or improving software packages to compute triangulations and meshes in several types of non-Euclidean spaces: sphere, 3D closed flat manifolds, hyperbolic plane.

TOPERA is a project that aims at developing methods from Topological Data Analysis to study covering properties and quality of cellular networks. It also involves L. Decreusefond and P. Martins from Telecom Paris.

- Starting date: December 2013

- Duration: 18 months

- Acronym: Presage.

- Type: ANR blanc.

- Title: *méthodes PRobabilistes pour l'Éfficacité des Structures et
Algorithmes GÉométriques*.

- Coordinator: Xavier Goaoc.

- Duration: 31 december 2011 - 31 december 2015.

- Other partners: Inria vegas team, University of Rouen.

- Abstract: This project brings together computational and probabilistic geometers to tackle new probabilistic geometry problems arising from the design and analysis of geometric algorithms and data structures. We focus on properties of discrete structures induced by or underlying random continuous geometric objects. This raises questions such as:

What does a random geometric structure (convex hulls, tessellations, visibility regions...) look like?

How to analyze and optimize the behavior of classical
geometric algorithms on *usual* inputs?

How can we generate randomly *interesting* discrete geometric
structures?

- Acronym : TopData.

- Title : Topological Data Analysis: Statistical Methods and Inference.

- Type : ANR blanc

- Coordinator : Frédéric Chazal (Geometrica)

- Duration : 4 years starting October 2013.

- Others Partners: Département de Mathématiques (Université Paris Sud), Institut de Mathḿatiques ( Université de Bourgogne), LPMA ( Université Paris Diderot), LSTA (Université Pierre et Marie Curie)

- Abstract: TopData aims at designing new mathematical frameworks, models and algorithmic tools to infer and analyze the topological and geometric structure of data in different statistical settings. Its goal is to set up the mathematical and algorithmic foundations of Statistical Topological and Geometric Data Analysis and to provide robust and efficient tools to explore, infer and exploit the underlying geometric structure of various data.

Our conviction, at the root of this project, is that there is a real need to combine statistical and topological/geometric approaches in a common framework, in order to face the challenges raised by the inference and the study of topological and geometric properties of the wide variety of larger and larger available data. We are also convinced that these challenges need to be addressed both from the mathematical side and the algorithmic and application sides. Our project brings together in a unique way experts in Statistics, Geometric Inference and Computational Topology and Geometry. Our common objective is to design new theoretical frameworks and algorithmic tools and thus to contribute to the emergence of a new field at the crossroads of these domains. Beyond the purely scientific aspects we hope this project will help to give birth to an active interdisciplinary community. With these goals in mind we intend to promote, disseminate and make our tools available and useful for a broad audience, including people from other fields.

- See also: http://

Type: FP7

Instrument: ERC Advanced Grant

Duration: February 2014 - January 2019

Coordinator: Jean-Daniel Boissonnat

Inria contact: Jean-Daniel Boissonnat

Abstract: The central goal of this project is to settle the algorithmic foundations of geometry understanding in dimensions higher than 3. Geometry understanding encompasses a collection of tasks including the approximation and computer representation of geometric structures, and the inference of geometric or topological properties of sampled shapes.

See also https://

Pedro Machado Manhães de Castro (Universidade Federal de Pernambuco)

Arijit Ghosh (MPII, Saarbrucken), april, november-december

Antoine Vigneron (KAUST), may

Ramsay Dyer (Johann Bernouilli Institute, University of Groningen), octobre

Kira Vyatkina (Saint Petersburg Academic University), october

Vissarion Fisikopoulos (Université Libre de Bruxelles), november

Monique Teillaud co-organized the “Workshop on Geometric Structures
with Symmetry and Periodicity”, part of the Computational Geometry
Week 2014, with Ileana Streinu (Smith College, Northampton, MA), in Kyoto University, Japan, June 8-9.
http://

Jean-Daniel Boissonnat organized the first GUDHI workshop in Sophia
Antipolis, October
27-29. https://

Olivier Devillers was program co-chair of 2014 Symposium on Computational Geometry.

Monique Teillaud, European Symposium on Algorithms, ESA, http://

Jean-Daniel Boissonnat is a member of the steering committee of the international conference on Curves and Surfaces.

Monique Teillaud is a member of the Steering Committee of the European Symposium on Algorithms (ESA).

Jean-Daniel Boissonnat is a member of the Editorial Board of
*Journal of the ACM*, *Discrete and Computational Geometry*,
*Algorithmica*, *Journal on Computational Geometry*, *International Journal on Computational
Geometry and Applications*.

Frédéric Chazal is a member of the Editorial Board of *SIAM Journal on Imaging Sciences*, *Graphical Models* and *Discrete and Computational Geometry*.

Olivier Devillers is a member of the Editorial Board of *Graphical Models*.

Monique Teillaud is a member of the Editorial Boards of
CGTA, *Computational Geometry: Theory and Applications*,
and of IJCGA, *International Journal of Computational Geometry
and Applications*.

M. Yvinec is a member of the editorial board of
*Journal of Discrete Algorithms*.

Monique Teillaud and Mariette Yvinec are members of the cgal editorial board.

Frédéric Chazal was a member of the recruitment committee of Inria Saclay (vice-chair).

Monique Teillaud was a member of the Inria Evaluation Committee until August.

She was a member of the national Inria DR2 interview committee and the local CR2 interview committees in Nancy and Lille.

She was also a member of the Advanced and Starting “Research Positions” interview committees.

Monique Teillaud was a member of the local Committee for Technologic Development until her move to Nancy.

She was also a member of the local committee for transversal masters.

Jean-Daniel Boissonnat was a member of the Conseil de l'AERES (Agence d'Evaluation de la Recherche et de l'Enseignement Supérieur).

Frédéric Chazal was a member of the Comités d'évaluation scientifique "Mathématiques et Informatique Théorique" of the ANR.

M. Teillaud is maintaining the Computational Geometry Web Pages
http://

The seminar featured presentations by the following scientists:

Omri Azencot (Technion) : An Operator Approach to Tangent Vector Field Processing

Mirela Ben Chen (Technion - Israel Institute of Technology) : Can Mean-Curvature Flow be Modified to be Non-singular?

Benjamin Burton (University of Queensland) : Untangling knots using combinatorial optimisation

A. Chiara de Vitis (Pavia) : Geometrical and Topological Descriptors for Protein Structures

C. Couprie (Courant Institute) : Graph-based Variational Optimization and Applications in Computer Vision

J. Demantke (IGN) : Geometric Feature Extraction from LIDAR Point Clouds and Photorealistic 3D Facade Model Reconstruction from Terrestrial LIDAR and Image Data

Kyle Heath (Stanford University) : Image Webs: Discovering and using object-manifold structure in large-scale image collections

N. Mitra (UCL London) : Computational Design Tools for Smart Models Synthesis

P. Machado Manhães de Castro (UFPE, Brasil) : Invariance for Single Curved Manifolds

Natan Rubin (Freie Universität Berlin) : On Kinetic Delaunay Triangulations: A Near Quadratic Bound for Unit Speed Motions

D. Salinas (Gipsa Lab, Grenoble) : Using the Rips complex for Topologically Certified Manifold Learning

Régis Straubhaar (Université de Neuchâtel) : Numerical optimization of an eigenvalue of the Laplacian on a domain in surfaces

Jian Sun (Mathematical Sciences Center, Tsinghua University) : Rigidity of Infinite Hexagonal Triangulation of Plane

Anaïs Vergne (Télécom ParisTech) : Algebraic topology and sensor networks

Yuan Yao (School of Mathematical Sciences, Peking University) : The Landscape of Complex Networks

H. Zimmer (Aachen) : Geometry Optimization for Dual-Layer Support Structures

Master : J.D. Boissonnat,
C. Maria, M. Yvinec, *Algorithmic Geometry of Triangulations*,
24h, International Master Sophia Antipolis.

Master : S. Oudot, *Computational Geometry: from Theory to Applications*, 18h, École polytechnique.

Master : S. Oudot, *Geometric Methods for Data Analysis*, 12h, École Centrale Paris.

Master: Jean-Daniel Boissonnat, Frédéric Chazal *Computational Geometric Learning*, 24h, Master MPRI,
Paris.

M. Teillaud, *Génération de maillages dans la bibliothèque
CGAL*, in the framework of a training course for young researchers
(PhD students and master students on environmental sciences) on
modelling, organized by ECCOREV, 3h, Aix-en-Provence.

HDR: Steve Oudot, Persistence Theory: From Quiver Representations to Data Analysis , Université Paris-Sud, November 26th 2014.

PhD : Clément Maria, Algorithms and Data Structures in Computational Topology , Université de Nice Sophia Antipolis, October 28, 2014, Jean-Daniel Boissonnat.

PhD: Ross Hemsley, Probabilistic methods for the analysis of algorithms on random tessellations , Université de Nice Sophia Antipolis, December 16, 2014, Olivier Devillers.

PhD: Mickaël Buchet, Topological and geometric inference from measures , Université Paris XI, December 2014, Frédéric Chazal and Steve Oudot.

PhD in progress: Thomas Bonis, Topological persistence for learning, started on December 2013, Frédéric Chazal.

PhD in progress: Mathieu Carrière, Topological signatures for geometric shapes, started in November 2014, Steve Oudot.

PhD in progress: Ruqi Huang, Algorithms for topological inference in metric spaces, started on December 2013, Frédéric Chazal.

PhD in progress: Eddie Amaari, A statistical approach of topological Data Analysis, started on Sept. 2014, Frédéric Chazal (co-advised with Pascal Massart).

PhD in progress : Rémy Thomasse, Smoothed complexity of geometric structures and algorithms, started December 1st 2012, Olivier Devillers.

PhD in progress : Mael Rouxel-Labbé, Anisotropic Mesh Generation, started October 1st, 2013, Jean-Daniel Boissonnat and Mariette Yvinec.

PhD in progress : Alba Chiri de Vitis, Computational Geometry in High Dimensions, started February 2014. Jean-Daniel Boissonnat and David Cohen-Steiner.

Monique Teillaud was a member of the HDR defense committee of Francis Lazarus (univ. Grenoble).

Monique Teillaud was a member of the PhD defense committee of Yacine Bouzidi (Univ. de Lorraine).

Monique Teillaud was a member of the PhD defense committee (member of the three-member advisory committee) of Vissarion Fisikopoulos (Univ. Athens, Grece).

Monique Teillaud was a member of the PhD defense committee of Arnaud de Mesmay (École Normale Supérieure).

Jean-Daniel Boissonnat was a member of the HDR defense committees of Q. Mérigot and S. Oudot.

Frédéric Chazal was a member (reviewer) of the PhD defense of Arnaud de Mesmay (Ecole Normale Supérieure de Paris).

Frédéric Chazal was a member of the PhD defense of Clément Levrard (Université Paris-Sud).

Steve Oudot was a member of the PhD defense of Clément Maria (Université Nice Sophia Antipolis).

Marc Glisse was a member of the PhD defense committee of Octavio Razafindramanana, Université François Rabelais de Tours.

Thomas Bonis, image and shape classification using persistent homology (F. Chazal)

François Godi, Computing the bottleneck distance for persistence diagrams (Jean-Daniel Boissonnat)

Venkata Yamajala, Equating the witness and the Delaunay complexes (Jean-Daniel Boissonnat)

Chunyuan Li, Persistence-based object recognition (F. Chazal and M. Ovsjanikov)

Eddie Aamari, topological Data Analysis (F. Chazal)

Mathieu Carrière, local topological signatures for shapes (S. Oudot)

Thomas Bonis and Mathieu Carrière presented the *Photomaton 3d*
at the *Fête de la Science* in October 2014. This animation
consists in scanning a volunteering person in 3d using a Kinect and
dedicated software, then illustrating the concepts of 3d shape
comparison, retrieval and matching.