Similarity measures for plane curves

Goal:

The goal of the project is to obtain efficient implementations of "similarity measures" for curves, focusing in particular on the Fréchet distance.

Consider a large family of planed curves. How to define when two such curves are "similar" or "close"? A possible solution is to rely on a distance function defined on the family of curves, such as the Hausdorff or the Fréchet distance.

To implement these solutions, some extra assumptions must be made to simplify computations.

The group of students in charge of the project will have to harvest relevant results in the literature and implement the solutions from scratch, ideally in a fast language such as C, C++, Go, Rust... but any other possibility can be considered. A first phase of data transformations will have to be conducted, in order to transform the .svg curve files into usable data.

During the summer semester, we will have a large data set of curves produced by humans as part of a Esch 2022 collaborative art project on which running the solutions implemented by the students.

Supervisors: Hugo Parlier and Bruno Teheux. Interested students should contact supervisors before asking for the topic.

Difficulty level: For master students who are confortable with coding. The topic is eligible for a master student thesis. Students must have a high degree of autonomy.

FSTM -- University of Luxembourg