# Mathematics

## Gram-Schmidt vs. Modified Gram-Schmidt

We compare the accuracy of the classical Gram-Schmidt algorithm to the modified Gram-Schmidt algorithm.

## Image processing

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.

## Towards PDE-Based Video Compression with Optimal Masks Prolongated by Optic Flow

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 …

## Photometric Stereo

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.

## Optical Flow Computation

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.

## Shape Matching

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.

## PDE-based image reconstruction and compression

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.

## Towards PDE-Based Video Compression with Optimal Masks and Optic Flow

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 optimal data. For the possible …

## Theoretical Foundation of the Weighted Laplace Inpainting Problem

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where …

## Sparse $l_{1}$ Regularisation of Matrix Valued Models for Acoustic Source Characterisation

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 …