### HDR of Nicolas Bonneel

Subject:
Optimal Transport for Computer Graphics and Temporal Coherence of Image Processing Algorithms

Summary:

This document summarizes my main contributions to computer graphics in the last nine years, since I defended my PhD in 2009. These contributions have spanned two distinct areas of computer graphics – Optimal Transport and Video Processing – but linked with the desire to provide numerical tools to the computer graphics community. Optimal transport is a trending tool with applications in computer graphics, including video processing, which I explore in a first chapter. As I explored different solutions to video processing problems that led to high impact contributions, I decided to expose these contributions in a separate chapter. Optimal Transport. The Optimal Transport problem seeks a way to warp one function (or more precisely a probability measure) towards another, by minimizing a certain cost function modeling the effort one would require to move the function as if it were a pile of sand. This framework is particularly attractive to computer graphics as it produces visually appealing deformations. I developed computationally efficient optimal transport algorithms (Sec. 2.1 and 2.2), formulated inverse problems making use of the optimal transport theory (Sec. 2.3) and applied these algorithms to computer graphics problems throughout my work. I became aware of optimal transport theory at the end of my PhD thesis, while working on a photograph-based reflectance acquisition method for hair, that made use of the so-called Earth Mover’s Distance [27]. I pursued the study of this fascinating theory during my post-docs and until now. Video Processing. The second problem I addressed in this manuscript is that of making image processing algorithms stable when applied to video frames. This came from the observation that most image processing algorithms, when applied to videos, tend to produce flickering artifacts. My first attempts at solving this problem were focusing on two specific but well studied image processing problems: color grading (Sec. 3.1) and intrinsic decomposition (Sec. 3.2). Faced to the colossal project of adapting each possible image processing algorithm to videos, I then developed an all-purpose blind solution that handles most image processing algorithms, and further extended it to the case of videos taken from multiple cameras (Sec. 3.3). I entered the area of video processing during my post-doc at Harvard University funded by an NSF grant on video processing, and continued this line of work afterwards thanks to a long-lasting collaboration with Adobe.

Defense date: friday, november 9, 2018

Jury:
 Delon Julie Professeur(e) Université Paris Descartes Rapporteur(e) Mérigot Quentin Professeur(e) Université Paris-Sud Rapporteur(e) Santambrogio Filippo Professeur(e) Université de Lyon Rapporteur(e) Courty Nicolas Professeur(e) Université de Bretagne Sud Président(e) Solomon Justin Maître de conférence Massachusetts Institute of Technology Examinateur​(trice)