(Sparsity, Image and Geometry to Model Adaptively Visual Processings)
is a research group financed by the
ERC Starting Grant program.
Σ-Vision will develop the next generation algorithms and methodologies
for image processing. These algorithms will rely on several mathematical
breakthroughs in image modeling: structured sparsity, geometric representations
and adaptivity. They will be implemented using fast optimization codes that can handle
massive datasets with gigapixels images and videos. These algorithms will have far
reaching applications in computer vision, graphics and neuroscience.
These cutting edge mathematical approaches will go beyond traditional image processing
scenarios and impact significantly object recognition, dynamical special effects and
exploration of the visual cortex.
Theme 1 - Theoritical guarantees for sparse regularization:
We analyze theoritically the performances of various kind of sparse regularizations in the framework
of imaging problems (super-resolution, tomography, compressed sensing, etc.).
The goal is to design data-dependent criteria that take into account the geometry
of the signal and its interaction with the imaging operator.
Theme 2 - Mathematical modeling of dynamical textures:
We develop deterministic and stochastic models of natural textures that take into account both
the texture material (albedo, illumination, reflectance, etc) and its time dynamic.
We propose novel statistical estimators based on the theory of optimal transport that allows us to interactively
navigate in a database of textures for computer graphics applications.
Theme 3 - Modeling the visual brain dynamics:
We propose an integrated pipeline for the modeling and the processing of
cortical imaging data. In particular, we develop tools to model the brain dynamics observed
using Voltage Sensitive Dye Optical Imaging and multi-electrodes arrays recordings.