This axis focuses on the development of new methodologies for large data analysis such as histograms, images, or point clouds, based on concepts from the optimal transport theory. This methodology results in the use of non-Euclidean metric (such as Wasserstein distances) to extract the geometrical information in the presence of non-linear sources of variability in the data. In this context, a new method of Principal Component Analysis based on the Wasserstein distance has recently been proposed with applications to statistical analysis of histograms.
The use of optimal transport has also been proposed for various image processing problems. By generalizing transport distances by regularizing the associated transport plans, new image interpolation methods were developed for applications in oceanography. The Wasserstein distance was also considered to more traditional problems such as image segmentation or color transfer.
The team organized early June 2015 the international conference SSVM 2015 (Scale-Space and Variational Methods in Image Processing) in the Arcachon bay. More than 120 researchers from around the world participated. The conference proceedings were published in a book by Springer.
Matlab open-source software of “Regularized Discrete Optimal Transport “
C++ open-source software of “Variational Exemplar-Based Image Colorization”
Matlab open-source software of “Optimal Transport with Proximal Splitting”
Optimal transport is nowadays a major statistical tool for computer vision and image processing. It may be used for measuring similarity between features, matching and averaging features or registrating images. However, a major drawback of this framework is the lack of regularity of the transport map and the robustness to outliers. The computational cost associated to the estimation of optimal transport is also very high and the application of such theory is difficult for problems of large dimensions. Hence, we are interested in the definition of new algorithms for computing solutions of generalized optimal transports that include some regularity priors.