As coursework for my computer vision class in Leuven I looked into support vector machines on medical data. The task was to locate incisor teeth. For every window the svm generates the probabilities for a miss and hit. In this example the frame with the largest hit probability was chosen, as all images where known …

# Author Archives: moritz

## Linear Algebra

One of the most interesting things I have encountered in linear algebra are pseudospectra and their relation to toeplitz symbol functions, as well as their associated circulant matrix eigenvalues. Below I have included plots which illustrate this beautiful relation (click to enlarge in new tab): Shown on the left are the Symbol functions (yellow), Toeplitz …

## PDEs and iGem

One of the first equations I discretized and simulated was the wave equation using a finite difference scheme. I ended up with a simulation, which is quite pretty: The biggest PDE project I have done so far was with the Leuven iGem-Team. We simulated the behavior of pattern forming bacteria using pure PDE and a …

## Ray Tracing

Ray tracing is a fascinating algorithm used for image synthesis. I have written a rudimentary ray tracer consisting of more then 5000 lines of code. The video below shows it render a high resolution triangle mesh representation of the Stanford dragon: Fast implementations depend on binary trees to reduce the number …