Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

DragonflEYE: a passive approach to aerial collision sensing

"This dissertation describes the design, development and test of a passive wide-field optical aircraft collision sensing instrument titled 'DragonflEYE'. Such a ""sense-and-avoid"" instrument is desired for autonomous unmanned aerial systems operating in civilian airspace. The instrument was configured as a network of smart camera nodes and implemented using commercial, off-the-shelf components. An end-to-end imaging train model was developed and important figures of merit were derived. Transfer functions arising from intermediate mediums were discussed and their impact assessed. Multiple prototypes were developed. The expected performance of the instrument was iteratively evaluated on the prototypes, beginning with modeling activities followed by laboratory tests, ground tests and flight tests. A prototype was mounted on a Bell 205 helicopter for flight tests, with a Bell 206 helicopter acting as the target. Raw imagery was recorded alongside ancillary aircraft data, and stored for the offline assessment of performance. The ""range at first detection"" (R0), is presented as a robust measure of sensor performance, based on a suitably defined signal-to-noise ratio. The analysis treats target radiance fluctuations, ground clutter, atmospheric effects, platform motion and random noise elements. Under the measurement conditions, R0 exceeded flight crew acquisition ranges. Secondary figures of merit are also discussed, including time to impact, target size and growth, and the impact of resolution on detection range. The hardware was structured to facilitate a real-time hierarchical image-processing pipeline, with selected image processing techniques introduced. In particular, the height of an observed event above the horizon compensates for angular motion of the helicopter platform.

Statistical and Graph-Based Signal Processing: Fundamental Results and Application to Cardiac Electrophysiology

The goal of cardiac electrophysiology is to obtain information about the mechanism, function, and performance of the electrical activities of the heart, the identification of deviation from normal pattern and the design of treatments. Offering a better insight into cardiac arrhythmias comprehension and management, signal processing can help the physician to enhance the treatment strategies, in particular in case of atrial fibrillation (AF), a very common atrial arrhythmia which is associated to significant morbidities, such as increased risk of mortality, heart failure, and thromboembolic events. Catheter ablation of AF is a therapeutic technique which uses radiofrequency energy to destroy atrial tissue involved in the arrhythmia sustenance, typically aiming at the electrical disconnection of the of the pulmonary veins triggers. However, recurrence rate is still very high, showing that the very complex and heterogeneous nature of AF still represents a challenging problem. Leveraging the tools of non-stationary and statistical signal processing, the first part of our work has a twofold focus: firstly, we compare the performance of two different ablation technologies, based on contact force sensing or remote magnetic controlled, using signal-based criteria as surrogates for lesion assessment. Furthermore, we investigate the role of ablation parameters in lesion formation using the late-gadolinium enhanced magnetic resonance imaging. Secondly, we hypothesized that in human atria the frequency content of the bipolar signal is directly related to the local conduction velocity (CV), a key parameter characterizing the substrate abnormality and influencing atrial arrhythmias. Comparing the degree of spectral compression among signals recorded at different points of the endocardial surface in response to decreasing pacing rate, our experimental data demonstrate a significant correlation between CV and the corresponding spectral centroids. However, complex spatio-temporal propagation pattern characterizing AF spurred the need for new signals acquisition and processing methods. Multi-electrode catheters allow whole-chamber panoramic mapping of electrical activity but produce an amount of data which need to be preprocessed and analyzed to provide clinically relevant support to the physician. Graph signal processing has shown its potential on a variety of applications involving high-dimensional data on irregular domains and complex network. Nevertheless, though state-of-the-art graph-based methods have been successful for many tasks, so far they predominantly ignore the time-dimension of data. To address this shortcoming, in the second part of this dissertation, we put forth a Time-Vertex Signal Processing Framework, as a particular case of the multi-dimensional graph signal processing. Linking together the time-domain signal processing techniques with the tools of GSP, the Time-Vertex Signal Processing facilitates the analysis of graph structured data which also evolve in time. We motivate our framework leveraging the notion of partial differential equations on graphs. We introduce joint operators, such as time-vertex localization and we present a novel approach to significantly improve the accuracy of fast joint filtering. We also illustrate how to build time-vertex dictionaries, providing conditions for efficient invertibility and examples of constructions. The experimental results on a variety of datasets suggest that the proposed tools can bring significant benefits in various signal processing and learning tasks involving time-series on graphs. We close the gap between the two parts illustrating the application of graph and time-vertex signal processing to the challenging case of multi-channels intracardiac signals

Mitigating the effect of covariates in face recognition

Current face recognition systems capture faces of cooperative individuals in controlled environment as part of the face recognition process. It is therefore possible to control lighting, pose, background, and quality of images. However, in a real world application, we have to deal with both ideal and imperfect data. Performance of current face recognition systems is affected for such non-ideal and challenging cases. This research focuses on designing algorithms to mitigate the effect of covariates in face recognition.;To address the challenge of facial aging, an age transformation algorithm is proposed that registers two face images and minimizes the aging variations. Unlike the conventional method, the gallery face image is transformed with respect to the probe face image and facial features are extracted from the registered gallery and probe face images. The variations due to disguises cause change in visual perception, alter actual data, make pertinent facial information disappear, mask features to varying degrees, or introduce extraneous artifacts in the face image. To recognize face images with variations due to age progression and disguises, a granular face verification approach is designed which uses dynamic feed-forward neural architecture to extract 2D log polar Gabor phase features at different granularity levels. The granular levels provide non-disjoint spatial information which is combined using the proposed likelihood ratio based Support Vector Machine match score fusion algorithm. The face verification algorithm is validated using five face databases including the Notre Dame face database, FG-Net face database and three disguise face databases.;The information in visible spectrum images is compromised due to improper illumination whereas infrared images provide invariance to illumination and expression. A multispectral face image fusion algorithm is proposed to address the variations in illumination. The Support Vector Machine based image fusion algorithm learns the properties of the multispectral face images at different resolution and granularity levels to determine optimal information and combines them to generate a fused image. Experiments on the Equinox and Notre Dame multispectral face databases show that the proposed algorithm outperforms existing algorithms. We next propose a face mosaicing algorithm to address the challenge due to pose variations. The mosaicing algorithm generates a composite face image during enrollment using the evidence provided by frontal and semiprofile face images of an individual. Face mosaicing obviates the need to store multiple face templates representing multiple poses of a users face image. Experiments conducted on three different databases indicate that face mosaicing offers significant benefits by accounting for the pose variations that are commonly observed in face images.;Finally, the concept of online learning is introduced to address the problem of classifier re-training and update. A learning scheme for Support Vector Machine is designed to train the classifier in online mode. This enables the classifier to update the decision hyperplane in order to account for the newly enrolled subjects. On a heterogeneous near infrared face database, the case study using Principal Component Analysis and C2 feature algorithms shows that the proposed online classifier significantly improves the verification performance both in terms of accuracy and computational time

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide