We developed a QR decomposition algorithm, based on the orthogonalisation process of Gram-Schmidt in a series of posts here, here, here, and here. Let’s have a look how good this algorithm performs against built-in implementations from julia and other programming languages.
Problem Formulation We already discussed QR decompositions and showed that using the modified formulation of Gram Schmidt significantly improves the accuracy of the results. However, there is still an error of about $10^3 M_\varepsilon$ (where $M_\varepsilon$ is the machine epsilon) when using the modified Gram Schmidt as base algorithm for the orthogonalisation.
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.
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 …
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’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.