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.
C++ open-source software of “Variational Exemplar-Based Image Colorization”
Colorization is an important issue for example for the restoration of old documents, but also for the entertainment industry. The methods fall into two categories, manual methods and example-based methods for which the user provides a color image which serves as a source of information. The comparison of textures used to extract color. Regularization is then required, that is carried out in our case by minimizing a non-convex function. To propose a reasonable model for colorization and an efficient algorithm to minimize the proposed functional constituted the bulk of the beginning of the thesis.
However, methods-based example exhibited difficulty in finding a relevant source image. It is difficult to find a relevant source image for a given colorization, and the method fails frequently, just for example, when a color is not present in the source image, or when two smooth portions or similar textures expressed a different color. To avoid these issues, we proposed a method called collaborative colorization, based on an interactive method in which the user supervises the result. It has the ability to integrate color points in the result where the result appears unsatisfactory. This new information is integrated into the process by exploiting the non-convexity of the model.