International Workshop on
Mathematical Foundations
of Computational Anatomy


Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability

MFCA-2006 is a satellite workshop of MICCAI 2006 which is devoted to statistical and geometrical aspects of the modelling of the variability of biological shapes. It will be held in Copenhagen on October 1st, in conjunction with (and one day before) MICCAI 2006.

Scope of the workshop

Non-linear registration is a well developped research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the  underlying biomechanical behavior of intra-subject deformations. However, it is more difficult to relate the anatomies of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of non-linear transformations. In the absence of any justified physical model, it seems natural to rely on the most general mathematical framework that still provides a topological consistency: diffeomorphisms. However, working with this infinite dimensional space raises some deep computational and mathematical problems, in particular for doing statistics. Likewise, modeling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed (e.g. smooth left-invariant metrics, focus on well-behaved subspaces of diffeomorphisms, modeling surfaces using courants, etc.) The goal of the workshop is to foster interactions between researchers investigating the combination of geometry and statistics in non-linear image and surface registration in the context of computational anatomy from different points of view. A special emphasis will be put on theoretical developments, applications and results being welcomed as illustrations.


Contributions are solicited in (but not limited to) the following areas:

The program will be composed of keynotes addressed by invited speakers and contributions of participants. To foster interactions as much as possible, a large amount of time will be reserved for discussions after each presentation or at least at the end of each session.

Key dates


IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S (See map for location).


The registration is organized in coordination with the MICCAI main conference. Online registration is available from the web site for the main conference at under "Registration". On-site registration at the day of the workshop is also possible between 8am and 9am in the main atrium at the IT University of Copenhagen. The workshop fee is 120 Euro and covers attendance, proceedings, coffee breaks, and lunch.


Proceedings are freeely available at


Download pdf program.

08:00 - 08:50 Registration
08:50 - 09:00 Opening remarks
09:00 - 10:40 Metrics on curves and surfaces
  • Statistical linear models in Procrustes shape space
  • An H2 type Riemannian metric on the space of planar curves
  • Riemannian Metrics on the Space of Solid Shapes
  • A New Closed-Form Information Metric for Shape Analysis
10:40 - 11:10 Coffea break and posters
11:10 - 12:00 Point set methods
  • Entropy-Based Particule Systems for Shape Correspondence
  • Template estimation from unlabeld point set data and surfaces for Computational Anatomy
12:00 - 13:30 Lunch
13:30 - 15:10 Statistics on diffeomorphisms
  • Left-Invariant Riemannian Elasticity: a distance an shape diffeomorphisms?
  • Statistics on Diffeomorphisms in a Log-Euclidean Framework
  • Multivariate Statistics of the Jacobian Matrices in Tensor Based Morphometry and their application to HIV/AIDS
  • Singular solutions, momentum maps and computational anatomy
15:10 - 15:30 Coffea break and posters
15:30 - 16:20 New methods for warping, statistics and shape description
  • Intrinsic and Extrinsic Analysis on Computational Anatomy
  • A Continuous 3-D Medial Shape Model With Branching
16:20 - 17:30
  • Geometric Surface and Brain Warping via Geodesic Minimizing Lipschitz Extensions
  • Hippocampus-Specific fMRI Group Activation Analysis with Continuous M-Reps
  • An intrinsic Geometric Framework for Simultaneous Non-Rigid Registration and Segmentation of Surfaces
  • Symmetric Image Normalization in the Space of Diffeomorphisms
  • Statistics on Anatomic Objects Reflecting Inter-Object Relations
  • Topological repair on Voxel-Based Quadrangular Meshes
  • Non-parametric Image Registration Using Generalized Elastic Nets
  • Measurements of folding in surfaces of arbitrary size in humain brain development
  • Realizing Unbiased Deformation: A Theoretical Consideration

Instructions for presenters

Oral presentations will be held in the Auditorium 2, on the ground floor. Presenters are asumed to bring their own laptop. If this is not the case, please contact Xavier Pennec beforehand. Each oral presentation should last 20 minutes maximum. 5 more minutes will be reserved for questions. As the goal of the workshop is foster interaction, please respect the timing to allow for discussion.

Posters will be placed in the atrium of the university. Each poster will be allocated space of A0 size, i.e. 84.1 cm. wide by 118.9 cm. high (33.1 by 46.8 inches). The poster boards will be available from 8 a.m. Posters may be mounted with tape only. The conference will supply tape for mounting the posters.


Program committee