Projekt

Optimal Transport for Computer Graphics

Udbyder

Vejleder

Sted

København og omegn

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.

Forudsætninger

Solid math skills and reasonably good programming skills

Søg i opslag
Kontakt

Virksomhed/organisation

DTU Compute

Navn

Jakob Andreas Bærentzen

Stilling

Lektor

Mail

janba@dtu.dk

Vejleder-info

Kandidatuddannelsen i Matematisk Modellering og Computing

Vejleder

Jakob Andreas Bærentzen

ECTS-point

30 - 35

Type

Kandidatspeciale

OM DTU

DTU er et teknisk eliteuniversitet med international rækkevidde og standard. Vores mission er at udvikle og nyttiggøre naturvidenskab og teknisk videnskab til gavn for samfundet. 10.000 studerende uddanner sig her til fremtiden, og 5.700 medarbejdere har hver dag fokus på uddannelse, forskning, myndighedsrådgivning og innovation, som bidrager til øget vækst og velfærd.

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Anker Engelunds Vej 1
Bygning 101A
2800 Kgs. Lyngby


45 25 25 25

dtu@dtu.dk

CVR-nr. 30 06 09 46

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