Σ-Vision (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 using tools such as sparse regularization, optimal transport and non-smooth optimization. They will be implemented using fast algorithms 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 supper-resolution imaging, image and movie synthesis and understanding of the visual cortex.
Theme 1 - Theoretical 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.