A working group about Shapes
Fourth meeting : Wednesday 19th May 2010
Shape modelling via phase field higher-order active contours: application
to road and river network extraction from remote sensing images.
by Aymen El Ghoul (Ariana team)
This talk is twofold. Firstly, I introduce a phase field higher-order
active contour (HOAC) model of undirected networks (e.g. roads).
The phase field function is a scalar field representing a region
(i.e. shape) by its smoothed characteristic function and interacting
nonlocally so as to favour network configurations.
Secondly, I introduce a phase field HOAC model of *directed networks*
(e.g. rivers). Directed networks carry a unidirectional flow in each branch,
which leads to characteristic geometric properties. The model contains,
in addition to the scalar field, a vector field representing the "flow" through
the network branches. The vector field is strongly encouraged
to be zero outside, and of unit magnitude inside the region; and to have
zero divergence. This prolongs network branches; controls width
variation along a branch; and produces asymmetric junctions for which
total incoming branch width approximately equals total outgoing branch
width. Both models are tested on very high resolution (VHR) Quickbird
images for road and river network extraction.
- Slides : pdf, movies
Third meeting : Monday 29th March 2010
Estimating suitable metrics for an empirical manifold of shapes, with application to human silhouettes
by Guillaume Charpiat (Pulsar team)
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 : pdf, movies ; related publication.
Second meeting : Tuesday 2nd March 2010
10:00, Euler bleu
Statistical models of currents for measuring the variability
of anatomical curves and surfaces
by Stanley Durrleman (Asclepios team)
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 : pdf, movies
First meeting : Wednesday 17th February 2010
15:45, Coriolis room (Galois building)
Two presentations (announced here)
will be were supposed to be given, and there will be drinks and cakes ;)
Introduction to the Shape Working Group : Shapes and related topics
- State of the art / thoughts about shapes, classified in the following categories : What for / What / Pairwise shape comparison / Where from / Shape statistics / Using information about shapes
- original slides and comments
Here is the e-mail I sent to announce the creation of this working group.
I would like to know who would be interested in the creation of a
"working group" about shapes.
The notion of "shape" is rather intuitive, but usually difficult to
model and to deal with, both mathematically and practically (it's not
just a parameter in R^n). The concept of "shape" is wide, and can be
understood differently by different people, depending on the problem of
interest where shapes are involved. For example in computer vision, the
word "shape", in its continuous interpretation, can stand for "the
surface of the object of interest" (in 3D), or for "the (2D) contour of
the object in an image", or a gesture (in a video); in its "patch-based"
interpretation, it usually stands for a rough geometric model linking a
few characteristic patches; shapes can be represented by polygons,
meshes, splines, implicitely by level-sets, as zeros of polynomials, by
local shape descriptors or small patches... One may be interested into
global properties of the shape (principal modes of deformation), or into
local ones (precise small deformations along a cell membrane). The
concept of "shape" is not specific to computer vision, for instance in
molecular biology, shapes may also be decisive for interaction
The precise definition of shape spaces (What is a shape ?) is often an
issue, as well as the metrics to consider (What is the distance between
two shapes ?) and shape statistics (What is this object supposed to look
like, given these previous examples ?). Comparing, optimizing, detecting
or recognizing shapes are also important issues.
The aim of the working group would be to understand better the notion
of "shape", to review its different aspects, possibly in order to try to
unify them into a single framework.
I suggest starting with an overview of the state of the art, for
example with a series of presentations by the participants about their
own work, where they would emphasize what they mean by "shape", what the
precise quantities of interest are (local/global deformations, patches,
patterns, movement, curvature, topology, energy to be optimized, etc.),
and of course the theories/algorithms/techniques they use/developped.
So far, a few persons from computer vision teams, namely Ariana,
Asclepios and Pulsar, have already agreed to participate, but this
working group is open to anyone who has to deal with the concept of
"shape". Please e-mail me if you are interested, willing to participate
actively or just to attend, so that I build a mailing-list and a