Frequency Domain Decomposition of Digital Video Containing Multiple Moving Objects

Motion estimation has been dominated by time domain methods such as block matching and optical flow. However, these methods have problems with multiple moving objects in the video scene, moving backgrounds, noise, and fractional pixel/frame motion. This dissertation proposes a frequency domain method (FDM) that solves these problems. The methodology introduced here addresses multiple moving objects, with or without a moving background, 3-D frequency domain decomposition of digital video as the sum of locally translational (or, in the case of background, a globally translational motion), with high noise rejection. Additionally, via a version of the chirp-Z, fractional pixel/frame motion detection and quantification is accomplished. Furthermore, images of particular moving objects can be extracted and reconstructed from the frequency domain. Finally, this method can be integrated into a larger system to support motion analysis. The method presented here has been tested with synthetic data, realistic, high fidelity simulations, and actual data from established video archives to verify the claims made for the method, all presented here. In addition, a convincing comparison with an up-and-coming spatial domain method, incremental principal component pursuit (iPCP), is presented, where the FDM performs markedly better than its competition

Multimodal retinal imaging: Improving accuracy and efficiency of image registration using Mutual Information

This thesis addresses the challenging task of multi-modal image registration. Registration is often required in a number of applications, whereby two images are aligned to give matching correspondence between the features in each image. Such techniques have become popular in many different fields, especially in medical imaging. Multi-modal registration would allow for anatomical structure to be studied concurrently in both modalities, providing the clinician with a greater insight of the patient's condition. Glaucoma is a serious condition that damages the optic nerve progressively, leading to irreversible blindness. The disease can be treated so to prevent any further infection, however it can not be reversed. Therefore it is paramount that the disease is detected in the early stages so to minimise the affect of the condition. The work in this thesis focuses on two particular imaging modalities: colour fundus photographs and scanning laser ophthalmoscope images. Both images are captured from the human eye and show the appearance and reflectivity of the retina respectively. Registration of these two modalities would significantly improve demarcation and monitoring of the optic nerve head, a crucial stage for glaucoma diagnosis. In recent years, Mutual Information has become a popular technique used to perform multi-modal registration. This thesis provides a comprehensive overview of the algorithm. Firstly, an investigation is performed that shows how probability estimation can improve the algorithm performance. Secondly, the weaknesses of the current technique are revealed and so a novel solution is proposed that overcomes these problems. Finally, the proposed solution is incorporated in a non-rigid registration scheme that provides excellent registration accuracy for our intended application

Analyzing Image Structure by Multidimensional Frequency Modulation

We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the IFGT. Using the IFGT, we derive the ordinary differential equations (ODEs) that describe image flowlines. We study the diagonalization of the ODEs of multidimensional frequency modulation on the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. We illustrate these new methods of image pattern analysis on textured and fingerprint images. We envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity. Examples of such textures abound in nature

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1 Analyzing Image Structure By Multidimensional Frequency Modulation

We develop a mathematical framework for quantifying and understanding multidimensional fre-quency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase, and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are derived and interpreted in terms of the eigen decomposition of the IFGT. Using the IFGT, we derive the ordinary differential equations (ODEs) that describe image flowlines. We study the diagonalization of the ODEs of multidimensional frequency modulation on the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. We illustrate these new methods of image pattern analysis on textured and fingerprint images. We envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity. Examples of such textures abound in nature