MSc Thesis Defence: Artem Chupryn

Title

Convolution operator on Riemannian 2-manifold using parallel transport

Abstract

In the last years, the volumes of non-Euclidian data became bigger and bigger. In order to addess such a problem, researchers came up with different methods. This thesis will explore one such method, called a geodesic convolutional neural network (GCNN). At the core of this method lie patch operators. Unfortunately the patch operators suffer from angular ambiguity. We suggest a new approach in providing a reference direction for patch operators. We create a discrete version of such a construction, and, evaluate it on the dataset that consists of textured speheres. After implementing and benchmarking the new method in a simplified setting, we conclude that there are no major differences from the original one. We also provide a discussion about possible reasons behind this lack of improvements and suggest directions for future research on the topic.

Vejleder: Stefan Sommer
Censor: Morten Pol Engell-Nørregård