Researcher, Engineer, Tinkerer, Scholar, and Philosopher.
PhD in Applied Mathematics, 2015
MSc in Applied Mathematics, 2010
BSc in Pure Mathematics, 2008
University of Luxembourg
A collection of notes and investigations on numerical linear algebra and optimization related topics.
Recently I acquired a Raspberry Pi 4 and decided to build a tiny computer cluster out of it. The goal is to do play around a bit with parallel computing technology.
Besides my research in computer vision related tasks such as optical flow, photometric stereo, and shape matching and my focus on PDE-based compression, I have also ventured in other image processing tasks.
I have used machine learning techniques in various projects. Our most successful applications were in the context of quantizing colour values for optimized inpainting and in accoustic source characterizations. Source Code The source code for clustering methods used for quantizing optimal masks can be found here.
Let us consider a microphone array comprising $n$ microphones at known locations (see figure above). These microphones register the sound that is emitted by a number of sources with unknown locations.
Floating point computations on computers may behave differently than one might expect. Every software developer should be aware of these since computed results may be off by orders of magnitude in the worst case.
I develop a small toy setup with a pair of Arduinos and some ultrasound sensors to do object localization. The goal is to have at least 4 echo distances in each measurement to assert a unique solution of the localization equations.
We have investigated high performing optimization algorithms and matrix differential calculus technique in the context of Photometric Stereo and presented the results at the BMVC 2016 Source Code A github repository with the code is maintained by Yvain Quéau.
I have been using emacs since about 2008. My current configuration is stored in an org file. The git repository is available here. A webpage containing all settings is accessible here.
I’ve developed optimization algorithms for variational optical flow models based on the split Bregman algorithm in my Master thesis. A follow-up investigation on the necessity of certain intermediate filtering steps was published at the EMMCVPR 2011.
The main task in three-dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three-dimensional objects. We analysed how well partial differential equations may be used to solve this problem.
This is a complete theme for the beamer package for LaTeX. I have used in on for regularly for several years now. The theme includes an outer, inner, font and colour theme.
It is possible to compress/inpaint images from very little data. In order to obtain reconstructions that are comparable to the original image it is necessary to optimize the underlying interpolation data.
Lossy image compression methods based on partial differential equations have received much attention in recent years. They may yield high-quality results but rely on the computationally expensive task of finding an optimal selection of data. For the possible extension to video compression, this data selection is a crucial issue. In this context, one could either analyse the video sequence as a whole or perform a frame-by-frame optimisation strategy. Both approaches are prohibitive in terms of memory and run time. In this work, we propose to restrict the expensive computation of optimal data to a single frame and to approximate the optimal reconstruction data for the remaining frames by prolongating it by means of an optic flow field. In this way, we achieve a notable decrease in the computational complexity. As a proof-of-concept, we evaluate the proposed approach for multiple sequences with different characteristics. In doing this, we discuss in detail the influence of possible computational setups. We show that the approach preserves a reasonable quality in the reconstruction and is very robust against errors in the flow field.
We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances.
Estimating the shape and appearance of a three dimensional object from flat images is a challenging research topic that is still actively pursued. Among the various techniques available, Photometric Stereo is known to provide very accurate local shape recovery, in terms of surface normals. In this work, we propose to minimise non-convex variational models for Photometric Stereo that recover the depth information directly. We suggest an approach based on a novel optimisation scheme for non-convex cost functions. Experiments show that our strategy achieves more accurate results than competing approaches.
This work analyses several approaches for determining optimal sparse data sets for image reconstructions by means of linear homogeneous diffusion. Two optimisation strategies for finding optimal data locations are presented. The first one impresses through its simplicity and is based on results from spline interpolation theory. However, this approach can only be applied to one dimensional strictly convex and differentiable functions. Due to these restrictions we derive an alternative approach which uses findings from optimal control theory. This new algorithm can be applied on arbitrary signals. Both approaches are analysed for their convergence behaviour. Further, we discuss the problem of selecting good data values for fixed data positions. This problem can be analysed as a least squares problem. An important relationship between the optimal data locations and the data values is derived and we present efficient numerical schemes to obtain these values. Finally, we present a image compression approach based on the findings from this work. Experiments show that is possible to outperform popular compression algorithms.