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Bart M.N. Smets

Applied Mathematician

Eindhoven University of Technology

Biography

I am a PhD student in applied mathematics at the TU Eindhoven under the supervision of dr.ir. R. Duits. I have a keen interest in both abstract mathematics and new techniques in the field of machine learning.

In my research I try to bridge neural networks with classic mathematical ideas from geometry and analysis, such as in the PDE-based G-CNN paper. Implementations of techniques I have developed are available as an open source extension to the popular PyTorch deep learning framework, named LieTorch.

Interests

  • Differential Geometry
  • Mathematical Image Analysis
  • Probability Theory
  • Machine Learning
  • Applied Analysis
  • Motorsport
  • History

Education

  • MSc in Applied Mathematics, 2019

    TU Eindhoven

  • BSc in Applied Mathematics, 2017

    TU Eindhoven

Publications

Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)

Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the …
DOI SSVM

Analysis of (sub-)Riemannian PDE-G-CNNs

Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs …
Project DOI Journal for Mathematical Imaging and Vision

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the 3D homogeneous space $\mathbb{M}_2$ of 2D positions and …
ArXiv

PDE-based Group Equivariant Convolutional Neural Networks

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a …

PDF Project DOI Journal for Mathematical Imaging and Vision ArXiv

Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations (JMIV)

Two key ideas have greatly improved techniques for image enhancement and denoising: the lifting of image data to multi-orientation …

PDF Code DOI Journal of Mathematical Imaging and Vision
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Talks

PDE-based CNNs with Morphological Convolutions

Convolutional neural networks have found wide adoption and great success in image processing yet have drawbacks such as needing huge …

Nov 5, 2019 16:20 Science Centre Delft
PDF Slides