Application of the Monge-Kantorovich Transportation Metric in the Analysis of Video Sequences

Student: Lukashkin Pavel

Educational Programme: Mathematical Methods of Optimization and Stochastics (Master)

Final Grade: 7

Year of Graduation: 2017

In this paper, we present an algorithm for finding optimal transport plans for successive images from a video sequence in which there is an assembly gluing or, as in our experiments, a sharp change in the frame at some point in time. In this case, the hypothesis was tested that at that moment the optimal transport plan calculated for a pair of images and being a histogram shift by some amount will differ substantially from the others. It should be noted that the computed values of transport plans come from the task of optimally transferring the values of the tone of one picture to another while preserving the values of brightness and lightness. His theoretical justification is given in another paper and is based on the Monge-Kantorovich transport optimization problem on the circle. All computer experiments were conducted in Python.

Full text (added May 31, 2017)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses