Project

Optimal Transport for Computer Graphics

Publisher

Supervisor

Location

Greater Copenhagen area

Given two distributions of material, probability, or whatnot, we might often be interested in computing the distance between the distributions. Our initial idea might be to consider the distributions to be vectors and simply compute the Euclidean distance. However, this does not tell us how we would have to move around "stuff" in order to transform one distribution into the other. 

Computing the Wasserstein distance on the other hand requires us to find a coupling, i.e. a least-work plan for moving material from one distribution such that it turns into the other distribution.

Unfortunately, the Wasserstein distance, also known as Earth-Mover's Distance, is expensive to compute, but, recently, efficient algorithms to approximate this distance have emerged.

For a somewhat deeper discussion, please see:

http://www2.compute.dtu.dk/~janba/w2.html

The Wasserstein distance and associated coupling have many applications. In computer graphics we could potentially use it to turn a shape into another shape, or an image into another image. It could be used to change color histograms, or compute motion blur or possibly speed up rendering.

The goal of the project is to implement one or more efficient methods for computing the Wasserstein distance (also known as Earth Movers Distance) and then explore applications such as those outlined above.

Requirements

Solid math skills and reasonably good programming skills

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Contact

Company / Organization

DTU Compute

Name

Jakob Andreas Bærentzen

Position

Lektor

Mail

janba@dtu.dk

Supervisor info

MSc in Mathematical Modelling and Computation

Supervisor

Jakob Andreas Bærentzen

ECTS credits

30 - 35

Type

MSc thesis

Technical University of Denmark

For almost two centuries DTU, Technical University of Denmark, has been dedicated to fulfilling the vision of H.C. Ørsted – the father of electromagnetism – who founded the university in 1829 to develop and create value using the natural sciences and the technical sciences to benefit society.


Today, DTU is ranked as one of the foremost technical universities in Europe, continues to set new records in the number of publications, and persistently increases and develops our partnerships with industry, and assignments accomplished by DTU’s public sector consultancy.

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Denmark



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CVR-nr. 30 06 09 46

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