Computational Methods for Shape Modelling and Analysis

Genova, 14-18 June 2004, Area della Ricerca, CNR, Genova

The School will
provide training courses aimed at PhD, PostDoc or researchers with
either a computer science, informatics or mathematics background,
and prior knowledge of geometric modelling techniques.

Download the leaflet of the school programme (.PDF)

The school will focus on different aspects related to shape modelling, processing and analysis, and the final programme will include training on the following topics:

Download the leaflet of the school programme (.PDF)

The school will focus on different aspects related to shape modelling, processing and analysis, and the final programme will include training on the following topics:

Despite a recent effort to make digital geometry tools robust to arbitrarily irregular meshes, most scanned surfaces need to undergo complete remeshing (alteration of the sampling and of the connectivity) before any further processing: results of finite element computations, compression, or editing rely heavily on an good description of the original geometry. In the first part of this course, three different approaches for remeshing will be presented (isotropic, anisotropic and efficient remeshing), while in the second part of the course applications of remeshing to model compression will be described and methods for post-processing remeshed models will be discussed.

PART I:

Speaker: Pierre Alliez (INRIA Sophia-Antipolis)

Duration: 2 hours

- Isotropic remeshing

Isotropic
remeshing leads to well-shaped triangles, and thus high-quality
meshes when the notion of quality is related to the shape of the
triangles.
Such meshes are important for simulation or geometry processing
(smoothing,
compression) where the quality of the mesh elements is critical. In
this
work, we achieve isotropic vertex sampling prescribed by a given
density
function on the mesh. We use a modification of Lloyd's relaxation
method
to construct a weighted centroidal Voronoi tessellation of the mesh. We
apply these iterations locally on small patches of the mesh that are
parameterized
into the 2D plane.

- Anisotropic remeshing

Anisotropic
polygonal remeshing exploits the intrinsic anisotropy of natural
or man-made geometry. In this work, we use the principal curvature
directions
to drive the remeshing process, mimicking the lines that artists
themselves
would use when creating 3D models from scratch. After extracting and
smoothing
the curvature tensor field of an input surface, lines of minimum and
maximum
curvatures are used to determine appropriate edges for the remeshed
version
in anisotropic regions, while spherical regions are simply
isotropically
point-sampled.

- Efficient remeshing

In this
work, we depart from the accustomed approximation strategy
by casting shape approximation as a variational geometric partitioning
problem. Using a new concept of geometric proxies, we drive the
distortion
error down through repeated clustering of faces into best-fitting
regions.
Our approach is entirely discrete and error-driven, and does not
require
parameterization or local estimations of differential quantities. We
also
introduce a new metric based on normal deviation, and demonstrate its
superior
behavior at capturing anisotropy.

Time permitting, I will run several demos made with the computational geometry algorithm library CGAL (http://www.cgal.org).

These work have been done in collaboration with Mathieu Desbrun, Olivier Devillers, David Cohen-Steiner, Craig Gotsman, Vitaly Surazhsky and Bruno Levy.

Time permitting, I will run several demos made with the computational geometry algorithm library CGAL (http://www.cgal.org).

These work have been done in collaboration with Mathieu Desbrun, Olivier Devillers, David Cohen-Steiner, Craig Gotsman, Vitaly Surazhsky and Bruno Levy.

PART II:

Speaker: Marco Attene (IMATI-CNR Genova)

Duration: 1:30

**Remeshing for Compression**

In the
latest years, remeshing proved to be one of the most promising
directions when dealing with the compression of polygonal models. Most
applications, in fact, do not require that the precise vertex positions
on the surface and the original mesh connectivity is preserved. In all
these cases, lossy techniques based on a remeshing of the model promise
to provide higher compression ratios.

In this
lecture, I will describe the SwingWrapper algorithm for remeshing-based
compression of manifold triangle meshes. Due to the regularity of the
meshes produced by SwingWrapper, their connectivity can be compressed
to less than a bit per triangle. Moreover, the remeshing is performed
so that the position of each vertex can be expressed with a single
parameter. After quantization and arithmetic coding, SwingWrapper leads
to an average compression rate of 0.4 bits/triangle with an L2
distortion of about 0.01% of the bounding box diagonal.

**Post-processing (re)meshed surfaces**

The
SwingWrapper scheme, as well as various 3D acquisition, analysis,
visualization and other remeshing approaches, samples surfaces of 3D
shapes in a uniform fashion, without any attempt to align the samples
with the sharp edges and corners of the original shape. Consequently,
the interpolating triangle meshes chamfer these sharp features and thus
exhibit a relatively large error in their vicinity. In this lecture I
will describe EdgeSharpener, which is an
automatic method for restoring most of the sharp edges and corners lost
by
feature-insensitive (re)meshing techniques. Also, I will present the
Bender
algorithm, which subdivides the resulting triangle mesh using a
combination
of the Butterfly subdivision scheme, for the smooth portion of the
mesh,
with a four-point subdivision scheme, for the sharp edges, in order to
preserve
the sharpness of the recovered sharp edges while bending their polyline
approximations into smooth curves. Besides improving the visual
appearance of the model, this combined Sharpen&Bend post-processing
significantly reduces the error
produced by feature-insensitive sampling processes.

These work
have been developed at IMATI-CNR, in collaboration with Jarek
Rossignac, within the Project
Surface Analysis.

Computational
topology
is gaining increasing importance in computer graphics and vision. These
lectures will deal with topological representations of digital shapes,
focusing
on size theory and Reeb graphs. Size theory will be introduced as a
geometric-topological method for shape comparison, with definition of
size functions, their
main mathematical properties and size function computation methods. The
definition of Reeb graph will be introduced, with its properties, and
algorithms for its computation in different application fields.

** Details on the programme: **

** Size theory as a geometric-topological
method for shape comparison**

Speaker: Patrizio Frosini (ARCES, Bologna)

Duration: 6 hours

1. The natural pseudodistance: a geometric-topological tool for comparing shapes. (1 hour)

a) introduction to the problem;

b) definition of the natural pseudodistance between

c) size pairs (manifolds paired with real functions);

d) main properties of the natural pseudodistance.

2. Size functions: comparing shapes by counting equivalence classes (2 hours)

a) definition of size function and examples;

b) main mathematical properties of size functions;

c) invariance under transformation groups;

d) size functions, noise and occlusions;

e) algebraic representation;

f) comparing size functions.

3. Size functions as a tool for evaluating the natural pseudodistance (1 hour)

a) the link between the natural pseudodistance and

b) size functions: the lower bound theorem;

c) computing the natural pseudodistance via the lower

d) bound theorem.

4. Computing size functions (1 hour)

a) size graphs and discrete size functions;

b) the approximation theorem;

c) reduction of size graphs.

**Morse theory and Reeb graphs for shape
understanding and coding**

Speaker: Silvia Biasotti (IMATI, CNR,
Genova)

Duration: 1:30 hours

1. Homology and Morse Theory: an introduction

a) Elements of geometry and topology of surfaces

b) Elements of computational topology

2. Reeb Graphs

a) Definition

b) Properties and relations with Morse theory

3. Reeb Graphs and mapping functions

a) height function

b) integral of the geodesic distance

c) distance from the barycenter

4. Applications of Reeb Graphs

a) DTM

b) Surface simplification

c) Shape matching

** SHAPE ACQUISITION
AND RECONSTRUCTION**

Speaker: Roberto Scopigno (ISTI, CNR, Pisa)

Duration: 4 hours

** Abstract: **

These lectures relate to the pipeline of tasks for the acquisition of the shape and colour of 3D objects, and for the creation of digital models to be efficiently used in local and/or remote graphics applications. The shape acquisition process, based on the adoption of optical 3D scanning approaches, implies the analysis, design, and implementation of efficient algorithms for the registration and alignment of the multiple scans into a common reference system, for the fusion of the scans into a unique digital model, the geometric simplification of the generated models, the editing and interactive corrections of small acquisition flaws, the acquisition of the colour and of the original texture, the efficient use of the models in local and/or distributed applications. Applications in the field of 3D Cultural Heritage will be shown.

- 3D Scanning Technology

- Fundamentals of 3-D sensing:

active 3D sensing (basic optical triangulation; pattern projection;

time of flight systems)

passive 3D sensing (silhouettes, space carving, stereo)

- Range Data Registration and Merging

- Two-scan registration (iterative closest point);

Multi-view registration

- Volumetric methods for scan integration / merging

- Connect-the-dots -- Delaunay sculpting; alpha-shapes; ball-pivoting;

- Point-based methods

- Surface Attributes Acquisition and Management

- Using color images directly as texture maps

- Using "unlit" color images to estimate diffuse reflectance

- Estimated BRDF

- Simplification and Rendering

- Approaches for huge meshes simplification (external memory)

- Rendering huge meshes on low-cost computers: triangle-based

approaches (LOD, bump-mapping), hierarchical point-based approaches

- Secure rendering of scanned models

- 3D Scanning Experiences in Cultural Heritage Applications

**SHAPE
INTERROGATION**

Speaker: Nicholas M. Patrikalakis and Takis
Sakkalis (Massachusetts
Institute of Technology)

Duration: 1:30 hours

**Abstract:**
** SHAPE SIMILARITY:
Ambient Isotopy and Free-Form Object Matching**

Speaker: Nicholas M. Patrikalakis
and Takis
Sakkalis (Massachusetts
Institute of Technology)

Duration: 1:30 hours

Abstract:

**
**

SHAPE MATCHING

Speaker:
Remco Veltkamp (Utrecht
University)

Duration: 4 hour

Abstract:

** SKELETAL
STRUCTURES FOR SHAPE CODING AND MATCHING**

Speaker: Michela Mortara,
Giuseppe Patenè, Simone Marini (IMATI,
CNR,
Genova)

Duration: 2 hours

Abstract:

A skeletal structure is a lower-dimensional representation, which encodes the decomposition of a shape into relevant parts that may have either a geometric or an application-dependent meaning. Several well-known skeletal descriptors of shapes will be introduced, such as the medial axis transformation and the Reeb graph, with their properties and limits. We will show how each representation has peculiarities that makes it more feasible for certain applications and unfeasible for others.

Outline:

1. Introduction on Shape descriptors

2. the Medial Axis Transformation and its properties

3. Brief recall about Reeb Graphs

4. Other skelatal structures, among which:

a) approximated multi-scale MAT for planar shapes

b) curvature-base skeleton

c) approximated axis of tubular shapes

Speaker: Patrizio Frosini (ARCES, Bologna)

Duration: 6 hours

1. The natural pseudodistance: a geometric-topological tool for comparing shapes. (1 hour)

a) introduction to the problem;

b) definition of the natural pseudodistance between

c) size pairs (manifolds paired with real functions);

d) main properties of the natural pseudodistance.

2. Size functions: comparing shapes by counting equivalence classes (2 hours)

a) definition of size function and examples;

b) main mathematical properties of size functions;

c) invariance under transformation groups;

d) size functions, noise and occlusions;

e) algebraic representation;

f) comparing size functions.

3. Size functions as a tool for evaluating the natural pseudodistance (1 hour)

a) the link between the natural pseudodistance and

b) size functions: the lower bound theorem;

c) computing the natural pseudodistance via the lower

d) bound theorem.

4. Computing size functions (1 hour)

a) size graphs and discrete size functions;

b) the approximation theorem;

c) reduction of size graphs.

Duration: 1:30 hours

1. Homology and Morse Theory: an introduction

a) Elements of geometry and topology of surfaces

b) Elements of computational topology

2. Reeb Graphs

a) Definition

b) Properties and relations with Morse theory

3. Reeb Graphs and mapping functions

a) height function

b) integral of the geodesic distance

c) distance from the barycenter

4. Applications of Reeb Graphs

a) DTM

b) Surface simplification

c) Shape matching

Speaker: Roberto Scopigno (ISTI, CNR, Pisa)

Duration: 4 hours

These lectures relate to the pipeline of tasks for the acquisition of the shape and colour of 3D objects, and for the creation of digital models to be efficiently used in local and/or remote graphics applications. The shape acquisition process, based on the adoption of optical 3D scanning approaches, implies the analysis, design, and implementation of efficient algorithms for the registration and alignment of the multiple scans into a common reference system, for the fusion of the scans into a unique digital model, the geometric simplification of the generated models, the editing and interactive corrections of small acquisition flaws, the acquisition of the colour and of the original texture, the efficient use of the models in local and/or distributed applications. Applications in the field of 3D Cultural Heritage will be shown.

- 3D Scanning Technology

- Fundamentals of 3-D sensing:

active 3D sensing (basic optical triangulation; pattern projection;

time of flight systems)

passive 3D sensing (silhouettes, space carving, stereo)

- Range Data Registration and Merging

- Two-scan registration (iterative closest point);

Multi-view registration

- Volumetric methods for scan integration / merging

- Connect-the-dots -- Delaunay sculpting; alpha-shapes; ball-pivoting;

- Point-based methods

- Surface Attributes Acquisition and Management

- Using color images directly as texture maps

- Using "unlit" color images to estimate diffuse reflectance

- Estimated BRDF

- Simplification and Rendering

- Approaches for huge meshes simplification (external memory)

- Rendering huge meshes on low-cost computers: triangle-based

approaches (LOD, bump-mapping), hierarchical point-based approaches

- Secure rendering of scanned models

- 3D Scanning Experiences in Cultural Heritage Applications

Duration: 1:30 hours

Shape
interrogation is
the process of extraction of
information from a geometric model. It is a fundamental component
of CAD/CAM systems. In this lecture, we focus on shape interrogation of
geometric models bounded by free-form or sculptured surfaces. Such
surfaces are widely used in the bodies of ships, automobiles, aircraft,
propeller and turbine blades, and various consumer devices. Our
basic thesis is that shape interrogation problems can usually be recast
in terms of the solution of a nonlinear system of equations, typically
a polynomial system. Much of our work is based on the Interval
Projected Polyhedron (IPP) Algorithm, which reduces a continuous shape
interrogation problem into the discrete problem of computing convex
hulls and their intersections. In this way, a bridge between the
largely disparate fields of geometric modeling of free-form shapes
(based on numerical analysis and approximation theory) and discrete
computational geometry (based on the theory of algorithms and
combinatorics) is established. Various applications arising from
surface intersections, distance function computations, global>
differential geometry of curves and surfaces, and offsets are described
and are reduced to the same unified solution framework. A
discussion of unresolved problems in this area is also provided.

- Nonlinear Polynomial Solvers

* Introduction

* Algebraic and hybrid techniques

* Subdivision methods

- The Projected Polyhedron (PP) algorithm

- The Interval Projected Polyhedron (IPP) algorithm

- Intersection Problems and their Applications

* Curve/curve intersection

* Curve/surface intersection

* Surface/surface intersection

* Global differential geometry

* Distance functions and offsets

- Nonlinear Polynomial Solvers

* Introduction

* Algebraic and hybrid techniques

* Subdivision methods

- The Projected Polyhedron (PP) algorithm

- The Interval Projected Polyhedron (IPP) algorithm

- Intersection Problems and their Applications

* Curve/curve intersection

* Curve/surface intersection

* Surface/surface intersection

* Global differential geometry

* Distance functions and offsets

Duration: 1:30 hours

Abstract:

This
talk will address problems of similarity of 2D and 3D objects. The
first part of the talk will consist of the notion of ambient isotopy as
a means of similarity of two shapes, usually taken as two-dimensional
manifolds. The second part will present problems of free-form matching
for the point vs. NURBS surface and the NURBS surface vs. NURBS surface
cases, and its application to copyright protection. Two new methods are
developed to solve a global and partial matching problem with no a
priori information on correspondence or initial transformation and no
scaling effects: the KH and the umbilic method. The KH method
establishes a correspondence between two objects by utilizing the
Gaussian and mean curvatures. The umbilic method uses the qualitative
properties of umbilical points to find correspondence information
between two objects. The matching algorithms are applied to
problems of copyright protection. Three types of tests, the weak,
intermediate and strong tests, are proposed for similarity assessment
between two objects. They are organized in two decision algorithms so
that they produce systematic and statistical measures for a similarity
decision between two objects in a hierarchical manner. Based on
the systematic statistical evaluation of similarity, a decision can be
reached whether the suspect model is a copy of the original model.

- Ambient Isotopy

* Introduction and motivation

* Preliminaries

* Topological equivalence versus ambient isotopy

* Ambient isotopic approximations

* Interval solids

* Piecewise linear approximations of curves and surfaces

* Applications

- 3D Free-Form Object Matching

* Introduction and motivation

* Classification of matching problems

* Umbilical point method

* Curvature method: KH method

* Resolving scaling effects

* Similarity evaluation

* Application to copyright protection

- Ambient Isotopy

* Introduction and motivation

* Preliminaries

* Topological equivalence versus ambient isotopy

* Ambient isotopic approximations

* Interval solids

* Piecewise linear approximations of curves and surfaces

* Applications

- 3D Free-Form Object Matching

* Introduction and motivation

* Classification of matching problems

* Umbilical point method

* Curvature method: KH method

* Resolving scaling effects

* Similarity evaluation

* Application to copyright protection

SHAPE MATCHING

Duration: 4 hour

Abstract:

Shape
matching is a
central problem in visual
information systems, computer vision, pattern recognition, and
robotics. Applications of shape matching include industrial inspection,
fingerprint matching, and content-based image retrieval. A few
examples are:

- Applications in agricultural inspection. A typical problem here is to find a matching transformation. Based on shape characteristics, we can find the transformation that matches one piece of fruit with another.

- Point matching in fingerprint identification applications. After extraction of featuring points, two point sets must be matched. The difficulty here is that there is typically no one to one correspondence between the two point sets. The matching technique should be robust against noise and occlusion.

- Application in multimedia retrieval. Given the query shape, the task is to find all pictures that contain similar shapes. The typical problem is that only pieces of the query shape appear in only parts of some of the database pictures.

This tutorial is about the matching of shape, both in 2D and in 3D. We will survey:

- Classes of applications

- Vaious matching problem

- Shape features

- Similarity measures

- Algorithms

We will address perceptual issues, as well as formal properties of features, similarity measures, and algorithms.

- Applications in agricultural inspection. A typical problem here is to find a matching transformation. Based on shape characteristics, we can find the transformation that matches one piece of fruit with another.

- Point matching in fingerprint identification applications. After extraction of featuring points, two point sets must be matched. The difficulty here is that there is typically no one to one correspondence between the two point sets. The matching technique should be robust against noise and occlusion.

- Application in multimedia retrieval. Given the query shape, the task is to find all pictures that contain similar shapes. The typical problem is that only pieces of the query shape appear in only parts of some of the database pictures.

This tutorial is about the matching of shape, both in 2D and in 3D. We will survey:

- Classes of applications

- Vaious matching problem

- Shape features

- Similarity measures

- Algorithms

We will address perceptual issues, as well as formal properties of features, similarity measures, and algorithms.

Duration: 2 hours

Abstract:

A skeletal structure is a lower-dimensional representation, which encodes the decomposition of a shape into relevant parts that may have either a geometric or an application-dependent meaning. Several well-known skeletal descriptors of shapes will be introduced, such as the medial axis transformation and the Reeb graph, with their properties and limits. We will show how each representation has peculiarities that makes it more feasible for certain applications and unfeasible for others.

Outline:

1. Introduction on Shape descriptors

2. the Medial Axis Transformation and its properties

3. Brief recall about Reeb Graphs

4. Other skelatal structures, among which:

a) approximated multi-scale MAT for planar shapes

b) curvature-base skeleton

c) approximated axis of tubular shapes

LEVEL-OF-DETAIL IN MESH-BASED REPRESENTATIONS

Speakers: Leila De Floriani (DISI, UNIGE, Genova), Enrico Puppo (DISI, UNIGE, Genova), Paolo Cignoni (ISTI, CNR, Pisa)

Duration: 5 hours

Abstract:

Triangular
meshes are
probably the most common way to represent the geometry of 3d surface
shapes. In
many cases, this representation results too verbose and possibly too
detailed for the needs of applications. More generally, it is desirable
to have
more or less detailed representations of the same shape available,
where
detail may also vary on different parts of the object and through time.

The task of finding a compact representation in terms of number of triangles, goes under the name of simplification. Many different algorithms and strategies have been presented and many different ways of evaluating the importance of the surface features that have to been presented exist and will be discussed in this course.

By elaborating upon the simplification technology, Level of Detail models are obtained. These models offer the possibility of extracting, through queries, several different representations with a level of detail satisfying specific requirements posed by the user in the query parameters. We will introduce the basic concepts of Level-Of-Detail modeling by presenting a general framework which encompasses existing models proposed in the literature and allows for their analysis and comparison.

Level-Of-Detail models can be divided into two broad classes: those designed for regularly-spaced data, and those for scattered data. We define the basic queries on a Level-Of-Detail model, and identify algorithms for answering such queries as well as primitives involved in such algorithms which must be supported by data structures.

We will then present
a
survey of data structures for encoding Level-Of-Detail models,
according
to the classification into regular and irregular meshes.

Simplification algorithms and level-of-detail models can be extended to volumetric models representing scalar data in 3D by means of tetrahedral decompositions. We will also present such extensions and discuss both simplification algorithms, as well as LOD data structures and query algorithms.

Simplification algorithms and level-of-detail models can be extended to volumetric models representing scalar data in 3D by means of tetrahedral decompositions. We will also present such extensions and discuss both simplification algorithms, as well as LOD data structures and query algorithms.

Outline:

· Mesh-based shape representations: data structures and update operations

· Error metric for mesh-based shape approximation

· Simplification algorithms for surfaces and 2D/3D scalar fields

· A framework for Level-Of-Detail (LOD) shape modeling

· LOD models for surfaces

· LOD models for volume data sets

SPEAKERS:

Pierre Alliez

Marco Attene

Silvia Biasotti

Paolo Cignoni

Leila De Floriani

Bianca Falcidieno

Patrizio Frosini

Simone Marini

Michela Mortara

Giuseppe Patanè

Nicholas M. Patrikalakis

Enrico Puppo

Takis Sakkalis

Roberto Scopigno

Michela Spagnuolo

Remco Veltkamp

The
School is
organized within and sponsored by the following projects:

MACROGeo: Metodi Algoritmici e Computazionali per la Rappresentazione di Oggetti Geometrici

AIM@SHAPE: Advanced and Innovative Models And Tools for the development of Semantic-based systems for Handling, Acquiring, and Processing knowledge Embedded in multidimensional digital objects

The number of participants to the School is limited to 80 participants

Registration fee:

200 € 150 € for AIM@SHAPE and MACROGeo fellows

The registration fee includes school material, lunch coupons, coffee breaks, and social dinner.

Registration fees can be paid either by money order or cash at the registration desk. Please note that payment by credit card will not be accepted.

**Details for money order payment:**

Bank accountN°: c/c 218155

holder: Consiglio Nazionale delle Ricerche,

Piazzale Aldo Moro 7, 00185 Roma, ITALY

description: "Incassi Giornalieri da Altre Dipendenze"

** Payment reference:** IMATI-GE 050002
REGISTRATION TO THE SUMMER
SCHOOL

** Bank details:**

Bank name: Banca Nazionale del Lavoro, Sportello CNR 6392

Bank/Sort/Swift code: ABI: 01005 CAB: 03392 SWIFT:BNLIITRARBE

Street name: Piazzale Aldo Moro 7

PostCode: 00185

City: Rome

Country: Italy

**To register:**

1.
Download the REGISTRATION FORM (.doc
or .pdf)

2. Fill in the form and send it by Fax.

3. Fax the copy of the bank transfer (if this is your choice of payment).

Our Fax number: +390106475660.

For accommodation information, please refer to the convention web site http://smism04.ge.imati.cnr.it/accommodation.html

MACROGeo: Metodi Algoritmici e Computazionali per la Rappresentazione di Oggetti Geometrici

AIM@SHAPE: Advanced and Innovative Models And Tools for the development of Semantic-based systems for Handling, Acquiring, and Processing knowledge Embedded in multidimensional digital objects

The number of participants to the School is limited to 80 participants

Registration fee:

200 € 150 € for AIM@SHAPE and MACROGeo fellows

The registration fee includes school material, lunch coupons, coffee breaks, and social dinner.

Registration fees can be paid either by money order or cash at the registration desk. Please note that payment by credit card will not be accepted.

Bank account

holder: Consiglio Nazionale delle Ricerche,

Piazzale Aldo Moro 7, 00185 Roma, ITALY

description: "Incassi Giornalieri da Altre Dipendenze"

Bank/Sort/Swift code: ABI: 01005 CAB: 03392 SWIFT:BNLIITRARBE

Street name: Piazzale Aldo Moro 7

PostCode: 00185

City: Rome

Country: Italy

2. Fill in the form and send it by Fax.

3. Fax the copy of the bank transfer (if this is your choice of payment).

Our Fax number: +390106475660.

For accommodation information, please refer to the convention web site http://smism04.ge.imati.cnr.it/accommodation.html

Please note that Genova is
the European Capital of Culture in 2004. We strongly recommend to book
your accommodation as soon as possible!

Shape Modelling Group CNR-GE-IMATI |