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The infinitesimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: vector fields and transport barriers from movies.

Santitissadeekorn, N and Bollt, EM (2007) The infinitesimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: vector fields and transport barriers from movies. Chaos, 17 (2).

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Abstract

In this paper, we present an approach to approximate the Frobenius-Perron transfer operator from a sequence of time-ordered images, that is, a movie dataset. Unlike time-series data, successive images do not provide a direct access to a trajectory of a point in a phase space; more precisely, a pixel in an image plane. Therefore, we reconstruct the velocity field from image sequences based on the infinitesimal generator of the Frobenius-Perron operator. Moreover, we relate this problem to the well-known optical flow problem from the computer vision community and we validate the continuity equation derived from the infinitesimal operator as a constraint equation for the optical flow problem. Once the vector field and then a discrete transfer operator are found, then, in addition, we present a graph modularity method as a tool to discover basin structure in the phase space. Together with a tool to reconstruct a velocity field, this graph-based partition method provides us with a way to study transport behavior and other ergodic properties of measurable dynamical systems captured only through image sequences.

Item Type: Article
Authors :
NameEmailORCID
Santitissadeekorn, Nn.santitissadeekorn@surrey.ac.ukUNSPECIFIED
Bollt, EMUNSPECIFIEDUNSPECIFIED
Date : June 2007
Identification Number : 10.1063/1.2742932
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:19
Last Modified : 17 May 2017 15:10
URI: http://epubs.surrey.ac.uk/id/eprint/838753

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