Summer 2007 Program on the Geometry and Statistics of Shape Spaces
July 7-13, 2007

Scientific Context
Description of Activities

• Tutorials
• Workshop
• Working Groups

Scientific Context

Shapes are prevalent in the outside world and in science. They manifest themselves in live animals, plants, landscapes, or in man-made materials, like cars, planes, building, bridges, and they are designed from aesthetic as well as efficacy considerations. Internal organs of humans or other animals also have a commonly accepted, well-defined shape, and their study is an old science called anatomy. For the human mind, there is an intuitive notion of what shapes are, why they differ or look alike, or when they present abnormalities with respect to ordinary observations. Sculpture is the art of rendering existing shapes, or creating new ones, and the fact that artists are still able to provide unambiguous instances of subjects through distorted or schematic representations is a strong indication of the robustness of the human shape recognition engine.

However, an analytical description of a shape is much less obvious, and humans are much less efficient for this task, as if the understanding and recognition of forms works without an accurate extraction of their constituting components, which is probably the case. We can recognize a squash from an eggplant or a pepper using a simple outline, and even provide a series of discriminative features we can distinguish, but it is much harder to instantiate a verbal description of any of them, accurate enough, say for a painter to reproduce it. It is therefore not surprising that, for mathematics, shape description remains mostly a challenge. The last fifty years of research in computer vision has shown a amazingly large variety of points of view and techniques designed for this purpose: 2D or 3D sets they delineate (via either volume or boundary), moment-based features, medial axes or surfaces, null sets of polynomials, configurations of points of interest (landmarks), to name but a few. Yet, it does not seem that any of these methods has emerged as ideal, neither conceptually nor computationally, for describing shapes.

But beyond the shape characterization issue, the more ambitious program which has interested a large group of researchers during the last two decades, starting with the seminal work of David Kendall, is the study of shapes spaces and their statistics. Here shapes are not only considered individually, but they are seen as variables, belonging to some generally infinite dimensional space which possesses a specific geometry. The theoretical study of such spaces, the definition of computationally feasible algorithmic and statistical procedures has been the subject of a still growing line of work. For example, Kendall's original contribution focused on collections of landmarks modulo the action of rotation and scale. It has since been extended to the actions of other groups and to plane curves instead of points. Other examples build shape spaces using the medial axis representation. The last few years has seen the emergence and the development of several new techniques, building infinite dimensional Riemannian metrics on curves and other shape representations, involving several groups over the world. Within applied mathematics, the analysis of shape spaces arises at a nodal point in which geometry, statistics and numerical analysis each have a fundamental contribution.

In this program, we propose a one-week program mixing tutorials, research presentation and working group activities on the subject. The goal is to provide an entry point into the field to interested students and faculty, and to allow researchers already specialized in the domain to exchange recent results and information.

Program Leaders: Darryl Holm (Imperial College, London), Peter Michor (University of Vienna), Michael Miller (Johns Hopkins University), David Mumford (Brown University), Tilak Ratnanather (Johns Hopkins University), Alain Trouvé (Ecole Normale Supérieure in Cachan) and Laurent Younes (Johns Hopkins University).

Description of Activities

The meeting consists of two days of tutorial, three days of conference on shape spaces and two days for working group meetings.

Confirmed Speakers: Stéphanie Allassonnière (LAGA, Université Paris 13), Yan Cao (University of Texas, Dallas), Guillaume Charpiat (Max Planck Institute), Daniel Cremers (University of Bonn), James Damon (University of North Carolina at Chapel Hill), Pedro Felzenszwalb (University of Chicago), Thomas Fletcher (University of Utah), Peter Giblin (The University of Liverpool), Joan Glaunes (Universite Paris 5), John Kent (University of Leeds), Benjamin Kimia (Brown University), Hamid Krim (North Carolina State University), Huiling Le (University of Nottingham), Kathryn Leonard (California Institute of Technology), Robert McCann (University of Toronto), Andrea Mennucci (Scuolo Normale Superiore Pisa), Xavier Pennec (Asclepios Team , Institut National de Recherche en Informatique Automatique (INRIA)), Stephen Pizer (University of North Carolina at Chapel Hill), Anuj Srivastava (Florida State University), Paul Thompson (University of California, Los Angeles), Namrata Vaswani (Iowa State University), Keith Worsley (McGill University), Anthony Yezzi (Georgia Institute of Technology)
Speaker Abstracts

Tutorials (July 7-8, 2007), at Radisson RTP

Saturday, July 7, 2007

Sunday, July 8, 2007

Workshop: Geometry and Statistics of Shape Spaces (July 9-11, 2007),
at Radisson RTP

Monday, July 9, 2007

Tuesday, July 10, 2007

Wednesday, July 11, 2007

Working Groups: (July 12-13, 2007), at SAMSI

The group meetings will consist in four open discussions, each during half a day.

• Topic 1: The geometry of shape spaces.
• Topic 2: Probabilistic models of shapes.
• Topic 3: Applications of 2D shape analysis.
• Topic 4: Applications of 3D shape analysis.

Application

REGISTRATION IS CLOSED

Please make reservations at the Radisson RTP as soon as possible. The SAMSI room block for the Radisson is effective until June 29, 2007. After this date, there is no guarantee a room will be available.  If you have a change in plans, individual room reservations must be cancelled 72 hours prior to arrival. Check-in is at 3:00 PM; check-out is 12:00 noon.

Further Information

For additional information about the program, send an email to [email protected]. Please send a letter describing your interest, along with a vita (if a new researcher), to the indicated e-mail address.

Application forms for workshop participation will be available later. Newer researchers and members of underrepresented groups are especially encouraged to apply.

Entire site © 2001-2009, Statistical and Applied Mathematical Sciences Institute. All Rights Reserved.