IAM

TAG»MATHEMATICS«

ARTICLE

The Mathematics of Variational Auto-Encoders

As part of my master thesis, I made heavy use of variational auto-encoders in order to learn latent spaces of shapes — to later perform shape completion. Overall, I invested a big portion of my time in understanding and implementing different variants of variational auto-encoders. This article, a first in a small series, will deal with the mathematics behind variational auto-encoders. The article covers variational inference in general, the concrete case of variational auto-encoder as well as practical considerations.

More ...

DECEMBER2017

PROJECT

The Simplex algorithm for solving linear programs implemented in PHP.

More ...

DECEMBER2017

PROJECT

Common matrix decompositions, including LU, Cholesky and QR decompositions, implemented in PHP; also includes an interactive application to demonstrate and explain the material.

More ...

ARTICLE

Seminar Paper “iPiano: Inertial Proximal Algorithms for Non-Convex Optimization”

In the course of a seminar on “Selected Topics in Image Processing”, I worked on iPiano, an algorithm for non-convex and non-smooth optimization proposed by Ochs et al. [1]. iPiano combines forward-backward splitting with an inertial force. This article presents the corresponding seminar paper including an implementation in C++ with applications to image denoising, image segmentation and compressed sensing.

More ...

MAY2016

PROJECT

Efficient C++ implementation of iPiano, a proximal algorithm with inertial force for non-convex and non-smooth optimization; including applications to image segmentation.

More ...

ARTICLE

Implementation of iPiano for Non-Convex and Non-Smooth Optimization

Ochs et al. proposed iPiano, a proximal algorithm with inertial force for non-convex and non-smooth optimization. This article presents a C++ implementation which was written as part of a seminar on “Selected Topics in Image Processing”.

More ...