Dans certains contextes, les méthodes classiques utilisées pour le calcul de champs rayonnés ou diffractés en présence d'obstacles de grande taille par rapport à la longueur d'onde, comme l'Optique Physique ou les méthodes de rayons, ne sont pas valides ou deviennent très lourdes en temps de calcul. La théorie des frames de Gabor fournit un cadre rigoureux permettant de décomposer une distribution de sources électromagnétiques, définie dans une ouverture équivalente plane, en une somme plus ou moins redondante de fenêtres gaussiennes. Cette décomposition peut servir de base à des algorithme de lancer de faisceaux gaussiens.Jusqu'à présent cette théorie était limitée à des décompositions dans un plan (rayonnement dans un demi-espace). L'objet de cette thèse est d'utiliser cette théorie pour décomposer des champs rayonnés ou diffractés dans toutes les directions de l'espace. Ce travail de thèse commence par une étude approfondie de l'influence des paramètres utilisés pour le calcul des coefficients de frame. La mise en oeuvre numérique permet de tester l'efficacité de techniques de troncation et de compression en termes de compromis précision/temps de calcul. Le coeur de la thèse consiste en une méthode originale de partitionnement spectral, utilisant des fonctions de partition de l'unité, qui permet d'utiliser le lancer de faisceaux gaussiens à partir de frames définis dans six plans, pour un rayonnement dans tout l'espace tridimensionnel. La formulation de la méthode est présentée. Elle est appliquée à la décomposition en faisceaux gaussiens du champ rayonné par des antennes théoriques omnidirectionnelles (réseau de dipôles et dipôle demi-onde). Une antenne réaliste sert enfin de cas test pour la mise en œuvre de la décomposition à partir de données expérimentales discrètes / In some contexts, conventional methods used for large problems involving radiated or diffracted field computations in the presence of obstacles, such as Physical Optics and ray based methods, become really inaccurate or prohibitively time-consuming. Gabor frame theory provides a rigorous framework for the initial decomposition of equivalent source distributions into a redundant set of Gaussian windows. Frame decomposition has been introduced as a first discretization step into Gaussian Beam Shooting (GBS) algorithms. Until now, frame decomposition has essentially been restricted to planar source distributions, radiating into one half space. The main goal of this thesis is to extend the application range of this theory to radiated or diffracted field decomposition into Gaussian beams propagating into the whole space. The thesis begins with a thorough study of influence of the parameters used for frame coefficient calculation. Numerical implementation is used to test the efficiency of truncation and compression techniques in terms of accuracy / computation time balance optimization. The core of the thesis consists of an original spectral domain partitioning method involving partition of unity functions, which allows to use Gaussian beam shooting from frames defined in six planes, for radiation into the whole three-dimensional space. The formulation of the method is presented and applied to the decomposition of fields radiated by theoretical omnidirectional antennas (dipole array and half-wave dipole) into Gaussian beams. A realistic antenna is used as a test case for the implementation of decompositions based on experimental discrete initial data

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This PhD work constitutes a series of inter-disciplinary studies that use biologically plausible computational techniques and experiments with human subjects in analyzing facial expressions. The performance of the computational models and human subjects in terms of accuracy and response time are analyzed. The computational models process images in three stages. This includes: Preprocessing, dimensionality reduction and Classification. The pre-processing of face expression images includes feature extraction and dimensionality reduction. Gabor filters are used for feature extraction as they are closest biologically plausible computational method. Various dimensionality reduction methods: Principal Component Analysis (PCA), Curvilinear Component Analysis (CCA) and Fisher Linear Discriminant (FLD) are used followed by the classification by Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA). Six basic prototypical facial expressions that are universally accepted are used for the analysis. They are: angry, happy, fear, sad, surprise and disgust. The performance of the computational models in classifying each expression category is compared with that of the human subjects. The Effect size and Encoding face enable the discrimination of the areas of the face specific for a particular expression. The Effect size in particular emphasizes the areas of the face that are involved during the production of an expression. This concept of using Effect size on faces has not been reported previously in the literature and has shown very interesting results. The detailed PCA analysis showed the significant PCA components specific for each of the six basic prototypical expressions. An important observation from this analysis was that with Gabor filtering followed by non linear CCA for dimensionality reduction, the dataset vector size may be reduced to a very small number, in most cases it was just 5 components. The hypothesis that the average response time (RT) for the human subjects in classifying the different expressions is analogous to the distance measure of the data points from the classification hyper-plane was verified. This means the harder a facial expression is to classify by human subjects, the closer to the classifying hyper-plane of the classifier it is. A bi-variate correlation analysis of the distance measure and the average RT suggested a significant anti-correlation. The signal detection theory (SDT) or the d-prime determined how well the model or the human subjects were in making the classification of an expressive face from a neutral one. On comparison, human subjects are better in classifying surprise, disgust, fear, and sad expressions. The RAW computational model is better able to distinguish angry and happy expressions. To summarize, there seems to some similarities between the computational models and human subjects in the classification process.

Based on the construction of Gabor feature space, which is important in applying pixel similarity computations, we formalize the space using rotation-invariant Gabor filter banks and apply optimizations in texture feature space. In image colorizations, the pixels that have similar Gabor features appear similar colors, our approach can colorize natural images globally, without the restriction of the disjoint regions with similar texture-like appearances. Our approach supports the two-pass colorization processes: coloring optimization in Gabor space and color detailing for progressive effects. We further work on the video colorization using the optimized Gabor flow computing, including coloring keyframes, color propagation by Gabor filtering, and optimized parallel computing over the video. Our video colorization is designed in a spatiotemporal manner to keep temporal coherence, and provides simple closed-form solutions in energy optimization that yield fast colonizations. Moreover, we develop parallel surface texturing of geometric models on GPU, generating spatially-varying visual appearances. We incorporate the Gabor feature space for the searching of 2D exemplars, to determine the k-coherence candidate pixels. The multi-pass correction in synthesis is applied to the local neighborhood for parallel processes. The iso/aniso-scale texture synthesis leverages the strengths of GPU computing, so to synthesize the iso/aniso-scale texturing appearance in parallel over arbitrary surfaces. Our experimental results showed that our approach produces simply controllable texturing effects of surface synthesis, generating texture-similar and spatially-varying visual appearances with GPU accelerated performance. / Texture feature similarity has long been crucial and important topic in VR/graphics applications, such as image and video colorizations, surface texture synthesis and geometry image applications. Generally, the image feature is highly subjective, depending on not only the image pixels but also interactive users. Existing colorization and surface texture synthesis pay little attention to the generation of conforming color/textures that accurately reflect exemplar structures or user's intension. Realistic surface synthesis remains a challenging task in VR/graphics researches. In this dissertation, we focus on the encoding of the Gabor filter banks into texture feature similarity computations and GPU-parallel surface rendering faithfully, including image/vodeo colorizations, parallel texturing of geometric surfaces, and multiresolution rendering on sole-cube maps (SCMs). / We further explore the GPU-based multiresolution rendering on solecube maps (SCMs). Our SCMs on GPU generate adaptive mesh surfaces dynamically, and are fully developed in parallelization for large-scale and complex VR environments. We also encapsulate the differential coordinates in SCMs, reflecting the local geometric characteristics for geometric modeling and interactive animation applications. For the future work, we will work on improving the image/ video feature analysis framework in VR/graphics applications. The further work lying in the surface texture synthesis includes the interactive control of texture orientations by surface vector fields using sketch editing, so to widen the gamut of interactive tools available for texturing artists and end users. / Sheng, Bin. / Adviser: Hanqin Sun. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 128-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis we study the short-time Fourier transform. The short-time Fourier transform of a function f(x) is obtained by restricting our function to a short time segment and take the Fourier transform of this restriction. This method gives information locally of f in both time and frequency simultaneously.To get a smooth frequency localization one wants to use a smooth window, whichmeans that the windows will overlap. The continuous short-time Fourier transform is not appropriate for practical purpose, therefore we want a discrete representation of f. Using Gabor theory, we can write a function f as a linear combination of time- and frequency shifts of a fixed window function g with integer parameters a; b > 0. We show that if the window function g has compact support, then g generates a Gabor frame G(g; a; b). We also show that for such a g there exists a dual frame such that both G(g; a; b) and its dual frame has compact support and decay fast in the Fourier domain. Based on [2], we show that B-splines generates a pair of Gabor frames.

A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show that all such frames are connected by transformations that are linear in the larger Hilbert space of square-integrable functions on the indexing space. We apply our results to frames on finite-dimensional Hilbert spaces and to the discretization of the Gabor frame with a band-limited window function.

Traditional remote sensing image classification has primarily relied on image spectral information and texture information was ignored or not fully utilized. Existing remote sensing software packages have very limited functionalities with respect to texture information extraction and utilization. This research focuses on the use of multi-scale image texture analysis techniques using Gabor filter banks and Wavelet transformations. Gabor filter banks model texture as irradiance patterns in an image over a limited range of spatial frequencies and orientations. Using Gabor filters, each image texture can be differentiated with respect to its dominant spatial frequency and orientation. Wavelet transformations are useful for decomposition of an image into a set of images based on an orthonormal basis. Dyadic transformations are applied to generate a multi-scale image pyramid which can be used for texture analysis. The analysis of texture is carried out using both artificial textures and remotely sensed image corresponding to natural scenes. This research has shown that texture can be extracted and incorporated in conventional classification algorithms to improve the accuracy of classified results. The applicability of Gabor filter banks and Wavelets is explored for classifying and segmenting remote sensing imagery for geographical applications. A qualitative and quantitative comparison between statistical texture indicators and multi-scale texture indicators has been performed. Multi-scale texture indicators derived from Gabor filter banks have been found to be very effective due to the nature of their configurability to target specific textural frequencies and orientations in an image. Wavelet transformations have been found to be effective tools in image texture analysis as they help identify the ideal scale at which texture indicators need to be measured and reduce the computation time taken to derive statistical texture indicators. A robust set of software tools for texture analysis has been developed using the popular .NET and ArcObjects. ArcObjects has been chosen as the API of choice, as these tools can be seamlessly integrated into ArcGIS. This will aid further exploration of image texture analysis by the remote sensing community.

Stages in Drosophila development denote the time after fertilization at which certain specific events occur in the developmental cycle. Stage information of a host embryo, as well as spatial information of a gene expression region is indispensable input for the discovery of the pattern of gene-gene interaction. Manual labeling of stages is becoming a bottleneck under the circumstance of high throughput embryo images. Automatic recognition based on the appearances of embryos is becoming a more desirable scheme. This problem, however, is very challenging due to severe variations of illumination and gene expressions. In this research thesis, we propose an appearance based recognition method using orientation histograms and Gabor filter. Furthermore, we apply Principal Component Analysis to reduce the dimension of the low-level features, aiming to accelerate the speed of recognition. With the experiments on BDGP images, we show the promise of the proposed method.

A new two-dimensional transform is derived and implemented that is able to discriminate with respect to angular and radial frequency. This octave-band directional filter bank (OBDFB) is maximally decimated, has a separable polyphase implmentation, provides perfect reconstruction, and can be implemented in a tree structure allowing for a somewhat arbitrary number of angular and radial divisions. This decomposition is based on the directional filter bank (DFB) and is compared to other transforms with similar properties. Additionally, the OBDFB is used in three applications. Texture segmentation results are provided with comparisons to both decimated and undecimated transforms. With hyperspectral data, the OBDFB is used to increase classification accuracy using texture augmentation and likelihood score combination. Finally, ultrasound despeckling is addressed with respect to real-time implementations, and subjective test results are presented. A non-uniform two-dimensional transform is also designed that is a modified version of the OBDFB. It is rationally sampled and maximally decimated, but it provides both angular and radial frequency passbands from the initial stage instead of making separate divisions like the OBDFB. It also does not create subband boundaries on the principal frequency axes and allows for further decomposition as well.

Traditional remote sensing image classification has primarily relied on image spectral information and texture information was ignored or not fully utilized. Existing remote sensing software packages have very limited functionalities with respect to texture information extraction and utilization. This research focuses on the use of multi-scale image texture analysis techniques using Gabor filter banks and Wavelet transformations. Gabor filter banks model texture as irradiance patterns in an image over a limited range of spatial frequencies and orientations. Using Gabor filters, each image texture can be differentiated with respect to its dominant spatial frequency and orientation. Wavelet transformations are useful for decomposition of an image into a set of images based on an orthonormal basis. Dyadic transformations are applied to generate a multi-scale image pyramid which can be used for texture analysis. The analysis of texture is carried out using both artificial textures and remotely sensed image corresponding to natural scenes. This research has shown that texture can be extracted and incorporated in conventional classification algorithms to improve the accuracy of classified results. The applicability of Gabor filter banks and Wavelets is explored for classifying and segmenting remote sensing imagery for geographical applications. A qualitative and quantitative comparison between statistical texture indicators and multi-scale texture indicators has been performed. Multi-scale texture indicators derived from Gabor filter banks have been found to be very effective due to the nature of their configurability to target specific textural frequencies and orientations in an image. Wavelet transformations have been found to be effective tools in image texture analysis as they help identify the ideal scale at which texture indicators need to be measured and reduce the computation time taken to derive statistical texture indicators. A robust set of software tools for texture analysis has been developed using the popular .NET and ArcObjects. ArcObjects has been chosen as the API of choice, as these tools can be seamlessly integrated into ArcGIS. This will aid further exploration of image texture analysis by the remote sensing community.