Transferência de cores entre duas imagens

Nesta dissertação, apresentamos o problema de transferência de cores entre duas imagens, ou seja, o problema de representar a estrutura de uma imagem utilizando as cores de outra. Realizamos a construção teórica do problema e construímos um código de programação em linguagem Python que o resolve. Para realizar a transferência de cores, resolvemos um problema de transporte ótimo discreto entre as distribuições de cores das duas imagens, utilizando um algoritmo de programação linear. Além disso, para melhorar o resultado visual, realizamos um relaxamento na condição usual de conservação de massa pontual da teoria de transporte ótimo e uma regularização dos mapas de transporte. Este trabalho é baseado no artigo: Ferradans, Papadakis, Peyré, and Aujol, “Regularized discrete optimal transport”, SIAM J Imaging Sciences, Vol. 7, No. 3, pp. 1853-1882.In this thesis, we present the color transfer problem between two images, that is, the problem of representing the structure of an image by using the colors of another. We present the theoretical construction of the problem and we build a programming code in Python in order to solve it. To perform the color transfer, we solve a discrete optimal transport problem between the color distributions of the two images, by using a linear programming algorithm. Moreover, to improve the final visual result, we perform a relaxation in the usual point mass conservation condition from optimal transport theory and a regularization of the transport map. This work is based in the paper: Ferradans, Papadakis, Peyré, and Aujol, “Regularized discrete optimal transport”, SIAM J Imaging Sciences, Vol. 7, No. 3, pp. 1853-1882

Optimal Transport for Domain Adaptation

Domain adaptation from one data space (or domain) to another is one of the most challenging tasks of modern data analytics. If the adaptation is done correctly, models built on a specific data space become more robust when confronted to data depicting the same semantic concepts (the classes), but observed by another observation system with its own specificities. Among the many strategies proposed to adapt a domain to another, finding a common representation has shown excellent properties: by finding a common representation for both domains, a single classifier can be effective in both and use labelled samples from the source domain to predict the unlabelled samples of the target domain. In this paper, we propose a regularized unsupervised optimal transportation model to perform the alignment of the representations in the source and target domains. We learn a transportation plan matching both PDFs, which constrains labelled samples in the source domain to remain close during transport. This way, we exploit at the same time the few labeled information in the source and the unlabelled distributions observed in both domains. Experiments in toy and challenging real visual adaptation examples show the interest of the method, that consistently outperforms state of the art approaches

Graph Signal Representation with Wasserstein Barycenters

In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised dimensionality reduction methods for graph signals have focused on dictionary learning. In these works the graph is taken into consideration by imposing a structure or a parametrization on the dictionary and the signals are represented as linear combinations of the atoms in the dictionary. However, the assumption that graph signals can be represented using linear combinations of atoms is not always appropriate. In this paper we propose a novel representation framework based on non-linear and geometry-aware combinations of graph signals by leveraging the mathematical theory of Optimal Transport. We represent graph signals as Wasserstein barycenters and demonstrate through our experiments the potential of our proposed framework for low-dimensional graph signal representation