Abstract
The method of Dynamic Mode Decomposition (DMD) was introduced originally in the area of Computatational Fluid Dynamics (CFD) for extracting coherent structures from spatio-temporal complex fluid flow data. DMD takes in time series data and computes a set of modes, each of which is associated with a complex eigenvalue. DMD analysis is closely associated with spectral analysis of the Koopman operator, which provides linear but infinite-dimensional representation of nonlinear dynamical systems. Therefore, by using DMD a nonlinear system could be described by a superposition of modes whose dynamics are governed by the eigenvalues. The key advantage of DMD is its data-driven nature which does not rely on any prior assumptions except the inherent dynamics which are observed over time. Its capability for extracting relevant modes from complex fluid flows has seen significant application across multiple fields, including computer vision, robotics and neuroscience. This thesis, in order to expand DMD to other applications, advances the original formulation so that it can be used to solve novel problems in the fields of signal processing and computer vision. In signal processing this thesis introduces the method of using DMD for decomposing a univariate time series into a number of interpretable elements with different subspaces, such as noise, trends and harmonics. In addition, univariate time series forecasting is shown using DMD. The computer vision part of this thesis focuses on innovative applications pertaining to the areas of medical imaging, biometrics and background modelling. In the area of medical imaging a novel DMD framework is proposed that introduces windowed and reconstruction variants of DMD for quantifying kidney function in Dynamic Contrast Enhanced Magnetic Resonance imaging (DCE-MRI) sequences, through movement correction and functional segmentation of the kidneys. The biometrics portion of this thesis introduces a DMD based classification pipeline for counter spoofing 2D facial videos and static finger vein images. The finger vein counter spoofing makes use of a novel atemporal variant of DMD that captures micro-level artefacts that can differentiate the quality and light reflection properties between a live and a spoofed finger vein image, while the DMD on 2D facial image sequences distinguishes attack specific cues from a live face by capturing complex dynamics of head movements, eye-blinking and lip-movements in a data driven manner. Finally, this thesis proposes a new technique using DMD to obtain a background model of a visual scene in the colour domain. These aspects form the major contributions of this thesis. The results from this thesis present DMD as a promising approach for applications requiring feature extraction including: (i) trends and noise from signals, (ii) micro-level texture descriptor from images, and (iii) coherent structures from image sequences/videos, as well as applications that require suppression of movements from dynamical spatio-temporal image sequences.