Image and video colorization consists in turning an original black and white image into a color version y adding a color component. This technique has been widely used for the restoration of heritage films, archival photographs, or for some artistic effects. Image colorization methods based on deep learning have met a huge success in recent years. These techniques are fully automatic and very fast, but they have not been adopted by video colorization experts. Indeed, these approaches do not ensure the temporal consistency of the colorization result, which is especially disturbing for the human vision system. To increase the accuracy of these techniques, we will propose new methods in the Arce project for video colorization algorithms which aim to be automatic, fast, and perceptually reliable. The ultimate goal of the project is the use of our work in video restoration studios.

Optimizing maps is a persistent challenge in computational mathematics, serving as a crucial component for generating high-quality quadrangular and hexahedral meshes essential for simulating highly anisotropic physical phenomena. Additionally, the significance of these maps has resurfaced in the realm of shape optimization, addressing the intricate "dehomogenization" problem. However, in both of these applications, the presence of shear in the mapping process can have catastrophic consequences, rendering a mesh unsuitable for finite element simulations or causing unexpected structural vulnerabilities. To address these challenges, I propose an investigation into "orthotropic" maps. These maps ensure an absence of shear by restricting deformations to stretching along three orthogonal directions. Rather than relying on conventional soft constraints, as is sometimes done, I draw inspiration from the remarkable success of conformal maps in the domain of texture mapping. As a result, I introduce a infinitesimal characterization of orthotropic maps, establishing a direct connection between stretch directions and their corresponding stretch factors. This project aims to investigate the effectiveness of this innovative approach for mesh generation and shape optimization. The study places particular emphasis on the computation of singular mappings which are often encountered in these applications and remain poorly understood, particularly in the volumetric case.

Additive manufacturing completely changes the way objects can be produced. On the one hand, it simplifies the manufacturing process itself, allowing everyone - including the general public - to physically realize a virtual model using a 3D printer. On the other hand, it affords for unprecedented possibilities in terms of shape complexity, both at the macro and micro scales: objects can be filled with multi-material structures that vary in size, orientation and shape to give specific properties to the final parts. Unfortunately, describing shapes at this level of customization, scale and complexity is beyond the reach of current software. The challenge lies in how to specify shapes than can be easily manipulated, optimized for properties, as well as visualized during manipulation and prepared efficiently for the manufacturing process. A key technical choice is that of shape representation. Boundary representations (e.g. triangle meshes) are very effective to represent surfaces. However, additive manufacturing blurs the frontier between surfaces and volumes. « Implicits », a mathematical definition which computes whether a point is solid or empty, provide an efficient scalable representation. Such approaches are referred to as procedural and can be used to represent both gradient of material and microstructures. This project seek to explore novel implicit representations in order to provide a unified approach for the modeling and slicing of both macro geometry, microstructures and gradient of material. Additionally, this research aims at a complete, tight integration of both standard boundary representations and novel implicit volume representations, allowing the best choice of representation for different parts of a design. In particular I will consider how to relate features of implicit volumes to features on existing boundary meshes, as well as how to constrain implicit volumes within meshes that can be interactively edited.

Natural Language Generation (NLG) produces text from data, text or meaning representations. With the boom of AI and deep learning technology, the field of NLG has been growing at exponential speed. While NLG has many potential applications (summarization, data verbalisation, text simplification, robo-journalism, story telling, etc.), key research questions are still outstanding such as how to handle the lack of training data and how to allow for NLG into the many natural languages. Using state-of-the-art neural technologies (BERT language modelling, Encoder-Decoder architectures, multi-task and transfer learning), XNLG will (i) investigate techniques to compensate for the lack of training data and (ii) develop models for multi-lingual, multi-source generation i.e., generation into multiple languages and from either meaning representations (MR2T), text (T2T) or data (D2T). We will in particular investigate whether a single meaning representation (MR) can be used as input for generation into multiple languages and how it compares with generation from language dependent MRs; how well the models we’ll propose for MR2T generation extend to D2T and T2T generation; and whether MRs provide a better basis for MR2T generation than the powerful continuous representations currently created for sentences by neural models such as BERT and ELMO.

The central theme of this project is the study of geometric and combinatorial structures related to hyperbolic surfaces and their moduli from an algorithmic point of view. The needs for hyperbolic geometries are arising, e.g., in crystallography, in geometric modeling, neuromathematics, or physics. The generic need regarding computer science in all those examples is clearly stated in a very recent paper on Nature Communications~\cite{bullshit-2022}: "Spaces with negative curvature are difficult to realize and investigate experimentally". In order to solve this issue, our goal is to develop the study of hyperbolic surfaces in computational geometry and make our results readily available for users. We intend to design efficient and algorithms with precise data structures to compute geometrical characteristics of hyperbolic surfaces such as the systole, the diameter and optimal pants decompositions. We also want to study the regularity of the previous parameters while moving through the Teichmüller and moduli spaces. We plan to implement our algorithms and make them publicly available to users.