A working group about Shapes
Talks originally planned for the first meeting and postponed
Talk 1 : Estimating suitable metrics for an empirical manifold of
shapes, with application to human silhouettes
by Guillaume Charpiat (Pulsar team)
- Abstract:
Shape evolutions, as well as shape matchings or image segmentation with
shape prior, involve the preliminary choice of a suitable metric in the
space of shapes. Instead of choosing a particular one, we propose a
framework to learn shape metrics from a set of examples of shapes,
designed to be able to handle sparse sets of highly varying shapes,
since typical shape datasets, like human silhouettes, are intrinsically
high-dimensional and non-dense.
Details: The tangent space of a shape being the set of all infinitesimal
deformations that can be applied to it, an inner product in a tangent
space can be seen as a deformation prior, and thus as a Gaussian
distribution. We formulate the task of finding the optimal metrics, i.e.
the inner products in tangent spaces which suit the best a given
empirical manifold of shapes, as a classical minimization problem. The
energy to be minimized involves the inner product cost of observed local
deformations (reliable matchings between close shapes) as well as a
regularization term based on transport of deformations and
Kullback-Leibler divergence. Surprisingly, the global minimum of this
functional on metrics is related to principal component analyses and is
easy to compute.
- Slides soon
Talk 2 : Statistical models of currents for measuring the variability
of anatomical curves and surfaces
by Stanley Durrleman (Asclepios team)
- Abstract:
This presentation is about the definition, the implementation and the evaluation of statistical models of curves and surfaces based on currents in the context of Computational Anatomy. Currents were introduced in medical imaging to define a metric between curves and surfaces which does not assume point correspondence between structures. This metric was used to drive the registration of anatomical data. In this presentation, we will show how to extend this tool to analyze the variability of anatomical structures via the inference of generative statistical models. Given a set of anatomical structures, we infer a template shape along with the deformation of this template to each subject. This decomposes the anatomical variability into two terms: the geometrical variability captured by the deformations and the "texture" captured by the residuals. We use this approach to infer the variability of the cortex surface from the position of the sulcal lines and to give a description of the variability of white matter fiber bundles of the brain.
- Slides soon
