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tutorial 12
T12  3D Shape Description and Matching Based on Properties of Real Functions

Date: Tuesday, September 4th, Time: 14:00 - 17:30, Location: Lecture Room 133

Organizers:  Bianca Falcidieno (CNR - IMATI - GE, Italy)
Michela Spagnuolo (CNR - IMATI - GE, Italy)
 
Speakers:  Bianca Falcidieno (CNR - IMATI - GE, Italy)
Daniela Giorgi (CNR - IMATI - GE, Italy)
Simone Marini (CNR - IMATI - GE, Italy)
Giuseppe Patané (CNR - IMATI - GE, Italy)
Michela Spagnuolo (CNR - IMATI - GE, Italy)
 
Authors:  Silvia Biasotti (CNR - IMATI - GE, Italy)
Bianca Falcidieno (CNR - IMATI - GE, Italy)
Patrizio Frosini (University of Bologna, Italy)
Daniela Giorgi (CNR - IMATI - GE, Italy)
Claudia Landi (University of Modena e Reggio Emilia, Italy)
Simone Marini (CNR - IMATI - GE, Italy)
Giuseppe Patané (CNR - IMATI - GE, Italy)
Michela Spagnuolo (CNR - IMATI - GE, Italy)


Abstract:

This tutorial attempts to formalize a variety of methods for 3D shape matching in an abstract conceptual framework, that distinguishes among the three main components of a shape matching system (i.e. shape analysis, description, and comparison). The goal is to facilitate the assessment of the properties of the various methods at different levels. More precisely, we will deal with 3D shape comparison tools based on the analysis of quantitative geometric properties provided by a real function defined on the surface representing the 3D object.




Extended Summary

A variety of methods have been proposed in the literature to tackle the problem of 3D shape matching and retrieval. While the retrieval performance can be evaluated in qualitative and quantitative terms using appropriate benchmarks and ground truth, it is not easy to understand the strengths and weaknesses of each technique and assist in the selection of the most appropriate tool for different applications.

The main contribution of the tutorial is the attempt to formalize a variety of methods in an abstract conceptual framework which is used to discuss and analyse different methods at the levels of the three main components of a shape matching system (i.e. shape analysis, description, and comparison). More precisely, we will analyze 3D shape comparison tools that analyse quantitative geometric properties provided by a real function defined on the surface representing the 3D object.

The underlying conceptual framework is structured in three-steps:
  1. choice and evaluation of the real functions on 3D shapes;
  2. construction of high-level descriptors, using these functions;
  3. choice of the comparison techniques to be used for the set of shapes and descriptors.
We believe that the distinction among these three levels will facilitate a theoretical and practical evaluation of the methods. It will also yield insights on the use of the different functions, shape descriptors and techniques to compare them, according to the properties and invariants that one wishes to investigate. We will analyze a large set of solutions, evaluate their effectiveness, and discuss perspectives and open issues.


Outline and Syllabus

After describing the scientific scenario motivating this tutorial, we will examine a series of 3D shape matching techniques. For each step of the matching pipeline, we will present and discuss definitions, properties and examples.
  1. Introduction (25 mins)

    Speaker: M. Spagnuolo

    • Motivations
    • Outline

  2. Real functions for shape analysis (45 mins)

    Speaker: G. Patané

    • Height & Elevation
    • Curvature-based, geodesic and Euclidean distances
    • Local diameters and distance transforms
    • Harmonic and Laplacian functions

  3. Shape descriptors (45 mins)

    Speaker: D. Giorgi

    • Morphological decompositions
    • Spectral analysis
    • Topological methods
    • Others

  4. Comparison techniques (40 mins)

    Speaker: S. Marini

    • Linear algebraic and statistical methods
    • Graph-matching techniques
    • Distances between algebraic structures
    • Others

  5. Discussions and perspectives (25 mins)

    Speakers: B. Falcidieno, M. Spagnuolo

    • Comparison of methods: towards a systematic evaluation of shape matching algorithms
    • Shape matching: is geometry sufficient for assessing the similarity ?
    • Closing


Authors' Background

Silvia Biasotti is a researcher at IMATI-GE. She received her Ph.D. in Mathematics and Applications from the University of Genova in 2004. Her research interests include computational topology, shape abstraction and skeleton representation of polyhedral surfaces.

Bianca Falcidieno is a research director at CNR and the head of the Shape Modelling Group at IMATI-GE, working in the field of Applied Mathematics and Computer Science, with applications in Computer Graphics, Geographic Information Systems, and Industrial Design. She is the Editor in chief of the International Journal of Shape Modelling, and has authored more than 200 scientific refereed papers and books. Bianca Falcidieno is the coordinator of the FP6 Network of Excellence AIM@SHAPE.

Patrizio Frosini is an assistant professor in the Faculty of Engineering at the University of Bologna. He is a member of the ARCES group at the University of Bologna. He received the Ph.D. degree in Mathematics from the University of Florence (1991). His research interests include the study of geometrical topological methods for shape comparison and related applications in Computer Vision.

Daniela Giorgi is a research fellow at IMATI-GE. She received her Ph.D. in Computational Mathematics in 2006 from the University of Padova. Her research interests are related to geometrical and topological methods for shape analysis, description and matching.

Claudia Landi is an assistant professor at the University of Modena and Reggio Emilia in Reggio Emilia. She obtained a Ph.D. in Mathematics in 2000, at the University of Pisa. Since 1994 she is a member of the Vision Mathematics Group of the University of Bologna. Her main research interest shape description via geometry and topology.

Simone Marini is a researcher at IMATI-GE. He received a Ph.D. in Electronic and Computer Engineering from the University of Genova in 2005. His main interests concern evaluation of 3D shape similarity, graph comparison, and ontological representation of scientific concepts.

Giuseppe Patané is a researcher at IMATI-GE. He received a Ph.D. in Mathematics and Applications from the University of Genova in 2005. His research interests include numerical analysis (implicit surfaces), shape analysis, computational geometry (topological graphs, local and global parameterization).

Michela Spagnuolo is a senior researcher at IMATI-GE. She received the Ph.D. in Computer Science Engineering from the INSA, Lyon, France (1997). Her research interests are related to shape-based approaches to the modeling of digital shapes, computational topology techniques for shape analysis, geometric reasoning for the extraction of shape features from discrete surface models, and geometric models to code uncertainty in data samples (fuzzy-based modeling).



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