Principled Design and Implementation of Steerable Detectors

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown position and orientation. We propose a continuous-domain additive image model, where the analyzed image is the sum of the template and an isotropic background signal with self-similar isotropic power-spectrum. The method is able to learn an optimal steerable filter fulfilling the SNR criterion based on one single template and background pair, that therefore strongly responds to the template, while optimally decoupling from the background model. The proposed filter then allows for a fast detection process, with the unknown orientation estimation through the use of steerability properties. In practice, the implementation requires to discretize the continuous-domain formulation on polar grids, which is performed using radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments

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

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with version accepted by PRD. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchange

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Powellsnakes II: a fast Bayesian approach to discrete object detection in multi-frequency astronomical data sets

Powellsnakes is a Bayesian algorithm for detecting compact objects embedded in a diffuse background, and was selected and successfully employed by the Planck consortium in the production of its first public deliverable: the Early Release Compact Source Catalogue (ERCSC). We present the critical foundations and main directions of further development of PwS, which extend it in terms of formal correctness and the optimal use of all the available information in a consistent unified framework, where no distinction is made between point sources (unresolved objects), SZ clusters, single or multi-channel detection. An emphasis is placed on the necessity of a multi-frequency, multi-model detection algorithm in order to achieve optimality

Deformable shape matching

Deformable shape matching has become an important building block in academia as well as in industry. Given two three dimensional shapes A and B the deformation function f aligning A with B has to be found. The function is discretized by a set of corresponding point pairs. Unfortunately, the computation cost of a brute-force search of correspondences is exponential. Additionally, to be of any practical use the algorithm has to be able to deal with data coming directly from 3D scanner devices which suffers from acquisition problems like noise, holes as well as missing any information about topology. This dissertation presents novel solutions for solving shape matching: First, an algorithm estimating correspondences using a randomized search strategy is shown. Additionally, a planning step dramatically reducing the matching costs is incorporated. Using ideas of these both contributions, a method for matching multiple shapes at once is shown. The method facilitates the reconstruction of shape and motion from noisy data acquired with dynamic 3D scanners. Considering shape matching from another perspective a solution is shown using Markov Random Fields (MRF). Formulated as MRF, partial as well as full matches of a shape can be found. Here, belief propagation is utilized for inference computation in the MRF. Finally, an approach significantly reducing the space-time complexity of belief propagation for a wide spectrum of computer vision tasks is presented.Anpassung deformierbarer Formen ist zu einem wichtigen Baustein in der akademischen Welt sowie in der Industrie geworden. Gegeben zwei dreidimensionale Formen A und B, suchen wir nach einer Verformungsfunktion f, die die Deformation von A auf B abbildet. Die Funktion f wird durch eine Menge von korrespondierenden Punktepaaren diskretisiert. Leider sind die Berechnungskosten für eine Brute-Force-Suche dieser Korrespondenzen exponentiell. Um zusätzlich von einem praktischen Nutzen zu sein, muss der Suchalgorithmus in der Lage sein, mit Daten, die direkt aus 3D-Scanner kommen, umzugehen. Bedauerlicherweise leiden diese Daten unter Akquisitionsproblemen wie Rauschen, Löcher sowie fehlender Topologieinformation. In dieser Dissertation werden neue Lösungen für das Problem der Formanpassung präsentiert. Als erstes wird ein Algorithmus gezeigt, der die Korrespondenzen mittels einer randomisierten Suchstrategie schätzt. Zusätzlich wird anhand eines automatisch berechneten Schätzplanes die Geschwindigkeit der Suchstrategie verbessert. Danach wird ein Verfahren gezeigt, dass die Anpassung mehrerer Formen gleichzeitig bewerkstelligen kann. Diese Methode ermöglicht es, die Bewegung, sowie die eigentliche Struktur des Objektes aus verrauschten Daten, die mittels dynamischer 3D-Scanner aufgenommen wurden, zu rekonstruieren. Darauffolgend wird das Problem der Formanpassung aus einer anderen Perspektive betrachtet und als Markov-Netzwerk (MRF) reformuliert. Dieses ermöglicht es, die Formen auch stückweise aufeinander abzubilden. Die eigentliche Lösung wird mittels Belief Propagation berechnet. Schließlich wird ein Ansatz gezeigt, der die Speicher-Zeit-Komplexität von Belief Propagation für ein breites Spektrum von Computer-Vision Problemen erheblich reduziert

Probing gravitational wave polarizations with signals from compact binary coalescences

In this technical note, we study the possibility of using networks of ground-based detectors to directly measure gravitational-wave polarizations using signals from compact binary coalescences. We present a simple data analysis method to partially achieve this, assuming presence of a strong signal well-captured by a GR template.Comment: Technical not

Visual Speech Recognition

Lip reading is used to understand or interpret speech without hearing it, a technique especially mastered by people with hearing difficulties. The ability to lip read enables a person with a hearing impairment to communicate with others and to engage in social activities, which otherwise would be difficult. Recent advances in the fields of computer vision, pattern recognition, and signal processing has led to a growing interest in automating this challenging task of lip reading. Indeed, automating the human ability to lip read, a process referred to as visual speech recognition (VSR) (or sometimes speech reading), could open the door for other novel related applications. VSR has received a great deal of attention in the last decade for its potential use in applications such as human-computer interaction (HCI), audio-visual speech recognition (AVSR), speaker recognition, talking heads, sign language recognition and video surveillance. Its main aim is to recognise spoken word(s) by using only the visual signal that is produced during speech. Hence, VSR deals with the visual domain of speech and involves image processing, artificial intelligence, object detection, pattern recognition, statistical modelling, etc.Comment: Speech and Language Technologies (Book), Prof. Ivo Ipsic (Ed.), ISBN: 978-953-307-322-4, InTech (2011