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The governance of the department is managed by a board composed of the head of the department, currently Sylvain Lazard, and the team leaders.

## PIXEL: Geometry and Light

## PIXEL: Shape fidelity

ALICE studies some fundamental aspects of Computer Graphics. More specifically, we study the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, scalable and numerically stable. Besides Computer Graphics, we have cooperations with researchers and people from the industry, who experiment applications of our general solutions to various domains, comprising CAD, industrial design, oil exploration, plasma physics...

PIXEL is a research team in digital geometry processing. More specifically, we are interested in parameterization techniques, meshing and reconstruction of objects from 3D point clouds.

We investigate mathematically correct, scalable and numerically stable solutions, by studying the properties of the objective function in order to develop efficient optimization algorithms.

Our methods have applications in both Computer Graphics and Scientific Computing which we develop in cooperation with researchers and industrial partners from various fields. These applications include oil exploration, plasma physics, bio-chemistry and computer-aided design.

Our main results are made available to the community in the form of original software.

## ALICE: Geometry and Light

## PIXEL: Geometry and Light

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## ALICE: Geometry and Light

ALICE studies some fundamental aspects of Computer Graphics. More specifically, we study the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, scalable and numerically stable. Besides Computer Graphics, we have cooperations with researchers and people from the industry, who experiment applications of our general solutions to various domains, comprising CAD, industrial design, oil exploration, plasma physics...

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## MFX: Matter from Graphics

MFX focuses on challenges related to shape complexity in the context of Computer Graphics and Additive Manufacturing. We consider the entire chain from modeling, visualization to interaction and part geometry processing before fabrication. In particular, we investigate how to assist engineers and designers in creating complex geometries enforcing strict fabrication, geometric and functional requirements.

Our methodologies are rooted in procedural synthesis methods that can automatically create details within parts, under user control, such as to achieve the desired functionality after the shapes are fabricated. As the models we create are highly detailed, we develop specialized algorithms to visualize them, interact with their properties, and process their geometries before fabrication. We also investigate algorithms improving fabrication time and part quality. Our research is made available through the software developed within the team, IceSL.

Our methods have applications in both Additive Manufacturing and Computer Graphics, where the need for automatic synthesis of detailed, yet structured and functional content is constantly increasing.

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## ALICE: Geometry and Light

ALICE studies some fundamental aspects of Computer Graphics. More specifically, we study the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, scalable and numerically stable. Besides Computer Graphics, we have cooperations with researchers and people from the industry, who experiment applications of our general solutions to various domains, comprising CAD, industrial design, oil exploration, plasma physics...

read more...

that requires computing with arbitrary precision integers or floating-point numbers) is also of common interest to CARAMBA, GAMBLE, ADAGIO, and ALICE. The main common interest of ABC with the other

that requires computing with arbitrary precision) is also of common interest to CARAMBA and GAMBLE. The main common interest of ABC with the other

regroups six teams (ABC, ADAGIO, ALICE, CARAMBA, GAMBLE, MAGRIT)

regroups 7 teams (ABC, ADAGIO, CARAMBA, GAMBLE, MAGRIT, MFX, PIXEL)

i.e., ADAGIO, ALICE, CARAMBA, GAMBLE, and MAGRIT.

i.e., ADAGIO, CARAMBA, GAMBLE, MAGRIT, MFX and PIXEL.

image is of interest to ADAGIO, ALICE and MAGRIT,

image is of interest to ADAGIO, MAGRIT and PIXEL,

## GAMBLE: Geometric Algorithms and Models Beyond the Linear and Euclidean realm

Classical computational geometry usually deals with linear objects in a Euclidean setting and when other situations happen, curved objects are typically linearized and non-Euclidean spaces are locally approximated by Euclidean spaces. The goals of the Gamble team are to address such limitations of classical computational geometry.

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## GAMBLE: Geometric Algorithms and Models Beyond the Linear and Euclidean realm

Classical computational geometry usually deals with linear objects in a Euclidean setting and when other situations happen, curved objects are typically linearized and non-Euclidean spaces are locally approximated by Euclidean spaces. The goals of the Gamble team are to address such limitations of classical computational geometry.

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i.e., ADAGIO, ALICE, CARAMBA, MAGRIT, and VEGAS. Symbolic and algebraic computing is of common interest of CARAMBA and VEGAS,

i.e., ADAGIO, ALICE, CARAMBA, GAMBLE, and MAGRIT. Symbolic and algebraic computing is of common interest of CARAMBA and GAMBLE,

ADAGIO, CARAMBA, and VEGAS, certified computing (in a sense

ADAGIO, CARAMBA, and GAMBLE, certified computing (in a sense

floating-point numbers) is also of common interest to CARAMBA, VEGAS,

floating-point numbers) is also of common interest to CARAMBA, GAMBLE,

## GAMBLE: Geometric Algorithms and Models Beyond the Linear and Euclidean realm

## GAMBLE: Geometric Algorithms and Models Beyond the Linear and Euclidean realm

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## VEGAS: Effective Geometric Algorithms for Surfaces and Visibility

## GAMBLE: Geometric Algorithms and Models Beyond the Linear and Euclidean realm

The main scientific focus of our group is the design and implementation of technology-independent, robust and efficient geometric algorithms for 3D visibility and low-degree algebraic surfaces. Meeting our computational objectives requires mathematical tools that are both geometric and algebraic. In particular, we need further knowledge of the basic geometry of lines and surfaces in a variety of spaces and dimensions as well as to adapt sophisticated algebraic methods, often computationally prohibitive in the most general setting, for use in solving seemingly simple geometric problems.

Classical computational geometry usually deals with linear objects in a Euclidean setting and when other situations happen, curved objects are typically linearized and non-Euclidean spaces are locally approximated by Euclidean spaces. The goals of the Gamble team are to address such limitations of classical computational geometry.

regroups six teams (ABC, ADAGIO, ALICE, CARAMBA, MAGRIT, VEGAS)

regroups six teams (ABC, ADAGIO, ALICE, CARAMBA, GAMBLE, MAGRIT)

i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. Symbolic and algebraic computing is of common interest of CARAMEL and VEGAS,

i.e., ADAGIO, ALICE, CARAMBA, MAGRIT, and VEGAS. Symbolic and algebraic computing is of common interest of CARAMBA and VEGAS,

ADAGIO, CARAMEL, and VEGAS, certified computing (in a sense

ADAGIO, CARAMBA, and VEGAS, certified computing (in a sense

floating-point numbers) is also of common interest to CARAMEL, VEGAS,

floating-point numbers) is also of common interest to CARAMBA, VEGAS,

read more...

read more...

## CARAMEL: Computer Arithmetics

The CARAMEL team conducts research in computer arithmetics. The goal is to push forward the possibilities to compute efficiently with objects having an arithmetic nature. This includes integers, real and complex numbers, polynomials, finite fields, and even more complicated objects such as algebraic curves. The main application domains are cryptography and computer algebra systems. CARAMEL studies arithmetics at various abstraction levels, from most low-level software or hardware implementation of basic building blocks to complicated high-level algorithms like integer factorization or point counting. Studying the interactions between low-level and high-level algorithms are of utmost importance for arithmetic applications, yielding important improvements that would not be possible with a vision restricted to low- or high-level algorithms.

## CARAMBA: Computer Arithmetic, Algebraic algorithms for cryptanalysis

The CARAMBA team addresses the broad application domain of cryptography and cryptanalysis from the algorithmic perspective. We study all the algorithmic aspects, from the top-level mathematical background down to the optimized high-performance software implementations. Several kinds of mathematical objects are commonly encountered in our research. Some basic ones are truly ubiquitous: integers, finite fields, polynomials, real and complex numbers. We also work with more structured objects such as number fields, algebraic curves, or polynomial systems. In all cases, our work is geared towards making computations with these objects effective and fast.

The mathematical objects we deal with are of utmost importance for the applications to cryptology, as they are the background of the most widely developed cryptographic primitives, such as the RSA cryptosystem or the Diffie-Hellman key exchange. The key challenges are the assessment of the security of proposed cryptographic primitives, through the study of the cornerstone problems, which are the integer factorization and discrete logarithm problems, as well as the optimization work in order to enable cryptographic implementations that are both efficient and secure.

regroups six teams (ABC, ADAGIO, ALICE, CARAMEL, MAGRIT, VEGAS)

regroups six teams (ABC, ADAGIO, ALICE, CARAMBA, MAGRIT, VEGAS)

ALICE is an INRIA project-team that aims at studying some fundamental aspects of Computer Graphics. More specifically, we study the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, scalable and numerically stable.

ALICE studies some fundamental aspects of Computer Graphics. More specifically, we study the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, scalable and numerically stable.

## IGC website

The Department Algorithms, Computation, Image and Geometry

## Department 1 website

The Department Algorithms, Computation, Geometry and Image

regroups six teams that share scientific interests on

regroups six teams (ABC, ADAGIO, ALICE, CARAMEL, MAGRIT, VEGAS) that share scientific interests on

i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. [+Symbolic and

algebraic computing+] is of common interest of CARAMEL and VEGAS,

i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. Symbolic and algebraic computing is of common interest of CARAMEL and VEGAS,

these topics. Beside ""algorithms"" which is a common center of

these topics. Beside algorithms which is a common center of

several teams. "Geometry" plays an important role in most teams, i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. \emph{Symbolic and

algebraic computing} is of common interest of CARAMEL and VEGAS,

"image" is of interest to ADAGIO, ALICE and MAGRIT, "combinatorics and complexity" also concerns several groups as ADAGIO, CARAMEL, and VEGAS, "certified computing" (in a sense

several teams. Geometry plays an important role in most teams, i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. [+Symbolic and

algebraic computing+] is of common interest of CARAMEL and VEGAS,

image is of interest to ADAGIO, ALICE and MAGRIT, combinatorics and complexity also concerns several groups as ADAGIO, CARAMEL, and VEGAS, certified computing (in a sense

The Department *Algorithms, Computation, Image and Geometry*

The Department Algorithms, Computation, Image and Geometry

The Department ""Algorithms, Computation, Image and Geometry""

The Department *Algorithms, Computation, Image and Geometry*

The Department "Algorithms, Computation, Image and Geometry"

The Department ""Algorithms, Computation, Image and Geometry""

these topics. Beside "algorithms" which is a common center of

these topics. Beside ""algorithms"" which is a common center of

The Department "Algorithms, Computation, Image and

Geometry" regroups six teams that share scientific interests on

The Department "Algorithms, Computation, Image and Geometry" regroups six teams that share scientific interests on

This website is shared between ABC, ADAGIO, ALICE, CARAMEL, MAGRIT and VEGAS, six research teams in LORIA-INRIA Nancy Grand-Est doing research in Computation, Geometry and Image.

The Department "Algorithms, Computation, Image and

Geometry" regroups six teams that share scientific interests on

these topics. Beside "algorithms" which is a common center of interest to all these teams (and of course to some teams of other departments as well), there are various centers of interest common to several teams. "Geometry" plays an important role in most teams, i.e., ADAGIO, ALICE, CARAMEL, MAGRIT, and VEGAS. \emph{Symbolic and

algebraic computing} is of common interest of CARAMEL and VEGAS,

"image" is of interest to ADAGIO, ALICE and MAGRIT, "combinatorics and complexity" also concerns several groups as ADAGIO, CARAMEL, and VEGAS, "certified computing" (in a sense that requires computing with arbitrary precision integers or floating-point numbers) is also of common interest to CARAMEL, VEGAS, ADAGIO, and ALICE. The main common interest of ABC with the other groups is the algorithmic culture they share, though there is also some more technical connexions with other groups.

The {\bf CARAMEL} team conducts research in computer arithmetics. The goal

The CARAMEL team conducts research in computer arithmetics. The goal

This website is shared between ABC, ADAGIO, ALICE, CARAMEL, MAGRIT and VEGAS, six research teams in LORIA-INRIA Nancy Grand-Est doing research in Image, Geometry and Computation.

This website is shared between ABC, ADAGIO, ALICE, CARAMEL, MAGRIT and VEGAS, six research teams in LORIA-INRIA Nancy Grand-Est doing research in Computation, Geometry and Image.

## ABC: [- Machine learning, bioinformatics and statistics]

## ABC: Machine learning, bioinformatics and statistics

This website is shared between ADAGIO, ALICE, MAGRIT and VEGAS, four research teams in LORIA-INRIA Nancy Grand-Est doing research in Image, Geometry and Computation.

This website is shared between ABC, ADAGIO, ALICE, CARAMEL, MAGRIT and VEGAS, six research teams in LORIA-INRIA Nancy Grand-Est doing research in Image, Geometry and Computation.

## ABC: [- Machine learning, bioinformatics and statistics]

The ABC team contributes to three different fields: machine learning, bioinformatics and statistics. Our main scientific goal is to develop the theory and practice of supervised and unsupervised learning. We focus on the theory of multi-class pattern recognition, deriving uniform convergence results which primarily deal with multi-class kernel machines such as multi-class support vector machines (M-SVMs). Our applications are in the field of biological sequence processing. More precisely, we develop theoretical bounds on the risk of classifiers, methods of model selection, multi-class support vector machines, methods for robust data mining and methods for statistical processing of biological sequences (e.g., prediction of the secondary structure of proteins).

read more...

## CARAMEL: Computer Arithmetics

The {\bf CARAMEL} team conducts research in computer arithmetics. The goal is to push forward the possibilities to compute efficiently with objects having an arithmetic nature. This includes integers, real and complex numbers, polynomials, finite fields, and even more complicated objects such as algebraic curves. The main application domains are cryptography and computer algebra systems. CARAMEL studies arithmetics at various abstraction levels, from most low-level software or hardware implementation of basic building blocks to complicated high-level algorithms like integer factorization or point counting. Studying the interactions between low-level and high-level algorithms are of utmost importance for arithmetic applications, yielding important improvements that would not be possible with a vision restricted to low- or high-level algorithms.

read more...