This thesis presents a technique for face recognition that is based on image registration. The image registration technique is based on finding a set of feature points in the two images and using these feature points for registration. This is done in four steps. In the first, images are filtered with the Mexican hat wavelet to obtain the feature point locations. In the second, the Zernike moments of neighbourhoods around the feature points are calculated and compared in the third step to establish correspondence between feature points in the two images and in the fourth the transformation parameters between images are obtained using an iterative weighted least squares technique. The face recognition technique consists of three parts, a training part, an image registration part and a post-processing part. During training a set of images are chosen as the training images and the Zernike moments for the feature points of the training images are obtained and stored. In the registration part, the transformation parameters to register the training images with the images under consideration are obtained. In the post-processing, these transformation parameters are used to determine whether a valid match is found or not. The performance of the proposed method is evaluated using various face databases and it is compared with the performance of existing techniques. Results indicate that the proposed technique gives excellent results for face recognition in conditions of varying pose, illumination, background and scale. These results are comparable to other well known face recognition techniques.

Inspection of optical components is essential to assure the quality and performance of optical systems. Evaluation of optical components includes metrology measurements of surface topography. It also requires optical measurements including refractive index, thin film thickness, reflectivity and transmission. The dispersion characteristics of optical constants including refractive index are also required. Hence, various instruments are used to make these measurements in research laboratories and for quality assurance. Clearly, it would be a significant advantage and cost saving if a technique was developed that could combine surface metrology with optical measurements. {Coherence Scanning Interferometry} (CSI) (also referred to as {Scanning White Light Interferometry} (SWLI)) has been used widely to measure surface topography with sub-nanometre vertical resolution. One of the benefits of the CSI is that the technique is non-contacting and hence non-destructive. Thus the test surfaces are not affected by the measurement using a CSI instrument whereas damage to the surfaces can occur when using traditional contact methods such as stylus profilometry. However use of CSI is geometrically limited to small areas ($\lesssim 10 \times 10$ mm) with gentle slopes ($\lesssim \ang{40}$) because of the numerical aperture of objective lens whereas stylus profilometry works well with larger areas and higher slopes due to the range of motion of the gauge and the traverse unit. Since the CSI technique is optical and involves light reflection and interference it is possible to extend the technique for the measurement of the thickness of transparent films, the roughness of surfaces buried beneath thin films or interfacial surfaces. It may also be used to determine spectral complex refractive index. This thesis provides an analytical framework of new methods to obtain complex refractive index in a visible light domain and interfacial surface roughness (ISR). It also provides experimental verification of these new capabilities using actual thin film model systems. The original Helical Complex Field (HCF) function theory is presented followed by its existing extensions that enable determination of complex refractive index and interfacial surface roughness. Further theoretical extensions of the HCF theory are also provided: A novel theory to determine the refractive index of a (semi-)transparent film is developed to address the constraint of the current HCF theory that restricted its use to opaque materials; Another novel theory is provided to measure ISR with noise compensation, which avoids erroneous surface roughness caused by the numerical optimisation affected by the existence of noise. The effectiveness of the ISR measurement with noise compensation has been verified using a number of computer simulations. Stylus profilometry is a well established method to provide a profile and has been used extensively as a 'reference' for other techniques. It normally provides a profile on which the roughness and the waviness are computed. Extension of the stylus profilometry technique to areal measurement of asymmetrical surfaces, namely raster scan measurement, requires a system to include error compensation between each traverse. The system errors and the random errors need to be separately understood particular when the measurement of a surface with nanometre-order accuracy is required. In this thesis a mathematical model to locate a stylus tip considering five mechanical errors occurring in a common raster scan profilometer is provided. Based on the model, the simulator which provides an areal measurement of a sphere was developed. The simulator clarified the relationship between the Zernike coefficients obtained from the form residual and the size of the errors in the form of partial derivatives of Zernike coefficients with respect to the errors. This provides theoretical support to the empirical knowledge of the relationship between the coefficients and the errors. Furthermore, a method to determine the size of errors directly from Zernike coefficients is proposed supported by simulations. Some of the error parameters were accurately determined avoiding iterative computation with this method whereas the errors are currently being determined by iterative computation.

La synthèse d'ouverture est une technique interférométrique similaire à la synthèse par rotation de la terre utilisée en radioastronomie où les signaux reçus par une paire de petites antennes sont traités de telle manière à synthétiser une seule grande antenne. Le concept de synthèse d'ouverture a été réadapté pour l'observation de la terre dans le cas de la télédétection de sources étendues de température. L'utilisation de cette technique pour l'observation de la terre a permis de contourner les limitations sur la taille d'antenne en télédétection passive. La fonction de corrélation, ou de visibilité, obtenue en inter-corrélant les signaux reçus par les an- tennes d'un système interférométrique employant une synthèse d'ouverture est définie comme étant la transformée de Fourier de la carte des températures de bril lance de la scène observée. Cette relation est connue sous le nom du théorème de Van Cittert-Zernike pour des observateurs en repos par rapport aux sources de température. La forme classique de ce théorème a été dérivée en inter-corrélant les échantillons temporels instantanés du champ électrique mesurés par différentes antennes. Un nouveau concept basé une interférométrie spatio-temporelle passive a été proposé comme étant la nouvelle génération qui succédera à la mission SMOS (Soil Moisture and Ocean Salinity) opérant dans l'espace depuis Novembre 2009. Celui-ci a pour objectif principal l'amélioration de la résolution spatiale à des ordres pouvant répondre aux applications hydrologiques à l'échelle locale où des résolutions kilométriques sont exigées. Ce concept interférométrique se base sur l'idée d'intégrer le déplacement de l'observateur (l'antenne) et ainsi la variable temps dans le calcul de la fonction de corrélation. Ceci engendre la création de nouvelles lignes de base virtuelles entre les positions des antennes à des instants différents, en plus des lignes de base physiques formées entres les positions des antennes instantanées. L'étude de ce concept de corrélation a malheureusement démontré la suppression exacte de l'information additionnelle due aux lignes de base virtuelles par le décalage Doppler induit par le déplacement. Une seconde étude du concept d'interférométrie spatio-temporelle combinée à une nouvelle procé- dure d'imagerie par corrélation dans l'espace fréquentiel, accomplie en inter-corrélant les spectres fréquentiels des champs électriques mesurés par une paire d'antennes séparées d'une distance Δr à bord d'un satellite à une hauteur h, a démontré l'obtention d'une information en 2D en températures de brillance de la scène observée. En plus, le développement théorique de la fonction de corrélation a mis en évidence une relation liant les visibilités aux températures de brillance par l'intermédiaire d'un noyau hautement oscillatoire. L'élément nouveau apporté par la corrélation dans l'espace fréquentiel consiste à exploiter l'informati- on de corrélation acquise par les antennes du satellite pour des fréquences présentant de petites dif- férences et pas seulement l'auto-corrélation. Cette propriété permet une reconstruction en 2D des températures de brillance avec seulement deux antennes / Aperture synthesis is an interferometric technique similar to Earth rotation synthesis employed in radio astronomy in which the signals received by a pair of small antennas are processed in a way to synthesize a single large antenna. The aperture synthetic concept used in radioastronomy was readapted to Earth remote sensing for large thermal sources. Thanks to this technique, limitations on antenna size in passive microwave remote sensing have been overcome. The correlation, or visibility, function obtained by cross-correlating the signals received by the antennas of an interferometric system using aperture synthesis is linked to the brightness temperature map of the observed scene by means of a Fourier-transform law. This is know as the standard form of the Van Cittert-Zernike theorem for fixed observers with respect to sources of temperature. This stan- dard formulation is derived by cross-correlating the instantaneous temporal components of the measured electric fields by different antennas. A new concept based on a passive spatio-temporal interferometry was proposed as the new generation to follow the well-known SMOS (Soil Moisture and Ocean Salinity) mission successfully operating since November 2, 2009. The aim of the proposed concept is a jump in the current achieved geometric resolution to orders capable of meeting the stringent users' needs for the study of hydrological applications in the local scale where sub-kilometric resolutions are required. This interferometric concept is based on the idea of integrating the displacement of the observer (satellite's antenna), and hence the time variable, in the calculation of the correlation function, which yields the creation of virtual baselines between the positions of antennas at different instants, in addition to the physical ones formed between the instantaneous antennas' spatial positions. Sadly, the additional information due to the virtual baseline was shown to be exactly canceled by the induced Doppler shift due to the observer's motion. We show furthermore that when using the aforementioned spatio-temporal interferometric system combined with a revolutionary Fourier Correlation Imaging (FouCoIm) procedure, consisting in cross-correlating, at slightly different frequencies, the Fourier components of the fluctuations of the re- ceived electric fields by a pair of antennas separated by a distance Δr on board of a satellite flying at height h, the 2D position-dependent brightness temperature can be reconstructed. Besides, the analytical derivation of the correlation function gives rise to a relationship linking the measured cor- relations to the position-dependent brightness temperatures by means of a Highly Oscillatory Integral (HOI) kernel. Interestingly, the analytical study of the HOI kernel showed the remarkable property that a corre- lation between both antenna-signals remains within a small frequency interval (different frequencies) outside the simple auto-correlation (same frequency). As a matter of fact, while existing systems had, until now, only considered the simple 1D information contained in the auto-correlation, it appears that the resulting correlation function from this concept bears a 2D information for the measurement of the position-dependent brightness temperature. Based on this, one is capable of reconstructing 2D bright- ness temperatures starting from a simple 1D geometry (two antennas arranged perpendicularly to the flight direction)

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<p>Imaging at range for the purposes of biometric, scientific, or militaristic applications often suffer due to degradations by the atmosphere. These degradations, due to the non-uniformity of the atmospheric medium, can be modeled as being caused by turbulence. Dating back to the days of Kolmogorov in the 1940’s, the field has had many successes in modeling and some in mitigating the effects of turbulence in images. Today, modern restoration methods are often in the form of learning-based solutions which require a large amount of training data. This places atmospheric turbulence mitigation at an interesting point in its history; simulators which accurately capture the effects of the atmosphere were developed without any consideration of deep learning methods and are often missing critical requirements for today’s solutions.</p><p><br></p><p>In this work, we describe a simulator which is not only fast and accurate but has the additional property of being end-to-end differentiable, allowing for end-to-end training with a reconstruction network. This simulation, which we refer to as Zernike-based simulation, performs at a similar level of accuracy as its purely optics-based simulation counterparts while being up to 1000x faster. To achieve this we combine theoretical developments, engineering efforts, and learning-based solutions. Our Zernike-based simulation not only aids in the application of modern solutions to this classical problem but also opens the field to new possibilities with what we refer to as computational image formation.chimi</p>

Frequency domain photon migration (FDPM) measurements are used to study the properties of dense colloidal dispersions with hard sphere and electrostatic interactions, which are otherwise difficult to analyze due to multiple scattering effects. Hard sphere interactions were studied using a theoretical model based upon a polydisperse mixture of particles using the hard sphere Percus Yevick theory. The particle size distribution and volume fraction were recovered by solving a non linear inverse problem using genetic algorithms. The mean sizes of the particles of 144 and 223 nm diameter were recovered within an error range of 0-15.53% of the mean diameters determined from dynamic light scattering measurements. The volume fraction was recovered within an error range of 0-24% of the experimentally determined volume fractions. At ionic strengths varying between 0.5 and 4 mM, multiple wavelength (660, 685, 785 and 828 nm) FDPM measurements of isotropic scattering coefficients were made of 144 and 223 nm diameter, monodisperse dispersions varying between 15% - 22% volume fraction, as well as of bidisperse mixtures of 144 and 223 nm diameter latex particles in 1:3, 1:1 and 3:1 mixtures varying between volume fractions of 15% - 24%. Structure factor models with Yukawa potential were computed by Monte Carlo (MC) simulations and numerical solution of the coupled Ornstein Zernike equations. In monodisperse dispersions of particle diameter 144 nm the isotropic scattering coefficient versus ionic strength show an increase with increasing ionic strength consistent with model predictions, whereas there was a reversal of trends and fluctuations for the particle diameter of 223 nm. In bidisperse mixtures for the case of maximum number of smaller particles, the isotropic scattering coefficient increased with increasing ionic strength and the trends were in conformity with MC simulations of binary Yukawa potential models. As the number of larger diameter particles increased in the dispersions, the isotropic scattering coefficients depicted fluctuations, and no match was found between the models and measurements for a number ratio of 1:3. The research lays the foundation for the determination of particle size distribution, volume fractions and an estimate of effective charge for high density of particles.

In this dissertation, we describe a novel method that we call Diffusing Colloidal Probe Microscopy (DCPM), which integrates Total Internal Reflection Microscopy (TIRM) and Video Microscopy (VM) methods to monitor three dimensional trajectories in colloidal ensembles levitated above macroscopic surfaces. TIRM and VM are well established optical microscopy techniques for measuring normal and lateral colloidal excursions near macroscopic planar surfaces. The interactions between particle-particle and particle-substrate in colloidal interfacial systems are interpreted by statistical analyses from distributions of colloidal particles; dynamic properties of colloidal assembly are also determined from particle trajectories. Our studies show that DCPM is able to detect many particle-surface interactions simultaneously and provides an ensemble average measurement of particle-surface interactions on a homogeneous surface to allow direct comparison of distributed and average properties. A benefit of ensemble averaging of many particles is the diminished need for time averaging, which can produce orders of magnitude faster measurement times at higher interfacial particle concentrations. The statistical analyses (Ornstein- Zernike and three dimensional Monte Carlo analyses) are used to obtain particle-particle interactions from lateral distribution functions and to understand the role of nonuniformities in interfacial colloidal systems. An inconsistent finding is the observation of an anomalous long range particle-particle attraction and recovery of the expected DLVO particle-wall interactions for all concentrations examined. The possible influence of charge heterogeneity and particle size polydispersity on measured distribution functions is discussed in regard to inconsistent particle-wall and particle-particle potentials. In the final part of this research, the ability of DCPM is demonstrated to map potential energy landscapes on patterned surfaces by monitoring interactions between diffusing colloidal probes with Au pattern features. Absolute separation is obtained from theoretical fits to measured potential energy profiles and direct measurement by sticking silica colloids to Au surfaces via electrophoretic deposition. Initial results indicate that, as colloidal probe and pattern feature dimensions become comparable, measured potential energy profiles suffer some distortion due to the increased probability of probes interacting with surfaces at the edges of adjacent pattern features. Measurements of lateral diffusion via analysis of mean square displacements also indicated lateral diffusion coefficients in excellent agreement with rigorous theoretical predictions.

Made available in DSpace on 2015-04-09T12:28:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-10-24Bitstream added on 2015-04-09T12:47:21Z : No. of bitstreams: 1 000812794.pdf: 1525344 bytes, checksum: b68f6da113153c038916e9bd3f57c375 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta pesquisa foi estudado um m etodo de reconhecimento de contornos de telhado de edif cios em imagens digitais de alta resolu c~ao, que classi ca-os com rela c~ao a sua forma. O m etodo baseia-se nos momentos de Zernike, que s~ao baseados nos polin omios ortogonais de Zernike, em que cria-se um vetor de caracter sticas para cada regi~ao da imagem, que deve ser previamente segmentada de maneira que seus objetos sejam divididos em diferentes regi~oes. Este m etodo para a descri c~ao de forma baseia-se na area do objeto de interesse e possui a caracter stica dos momentos serem invariantes em rela c~ao as transforma c~oes geom etricas de rota c~ao, transla c~ao e escala, que o torna atrativo para o problema de an alise de imagem proposto. Desse modo, foi criada uma base de dados contendo esbo cos (ou modelos) de poss veis apari c~oes de contornos de telhado de edif cio numa dada cena, para que seja associado tamb em um vetor de caracter sticas de Zernike para estes esbo cos. Assim, a dist ancia euclidiana entre este vetor e o vetor de caracter sticas calculado a partir de uma regi~ao segmentada na imagem, permite dizer se a regi~ao dada corresponde a um contorno de edif cio ou a outro objeto. A capacidade de discrimina c~ao do m etodo proposto entre diferentes formas de edif cios, e tamb em entre formas de edif cios e n~ao edif cios foi avaliada experimentalmente e mostrou resultados positivos. / In this research, a method of recognition of building roof contours in high-resolution digital images which classi es them with respect to their form was studied. The method is based on Zernike moments, which are based on orthogonal Zernike polynomials and it creates a feature vector for each image region. The image segmentation has to be made rst to de ne di erent regions for its objects. This method for shape analysis is based on the object area of interest and the moments has the characteristic of being invariant under geometric transformations of rotation, translation and scaling, this makes it attractive to the proposed image analysis problem. Thus, a database containing sketches (or models) of possible appearances of building roof contours in a given scene was created, so a Zernike feature vector was also associated for these sketches. Therefore, the Euclidean distance between this vector and the feature vector calculated from a segmented region in the image lets say if the given region corresponds to a building contour or other object. The capacity of the proposed method in discriminating di erent building shapes and also in discriminating building shapes from non-building shapes was evaluated experimentally and it showed positive results.

The wavefront reconstruction of a light wave transformed by a microscope objective is the main subject of this diploma thesis together with the design and assembly of a~measuring device and the development of a computational algorithm. The purpose is to determine optical aberrations and to compare a quality of objectives with identical parameters. The term wavefront is explained and its description using Zernike polynomials is introduced in the first part of the thesis. The following part summarizes possible methods for wavefront reconstrucion. Two methods were chosen for experimental determination of a wavefront shape – shearing interferometry and solution of the transport of intensity equation. For each method a brief characteristic is provided together with possible applications, mathematical apparatus, image processing, computational procedure, setup description and proposition and results of experiments. The suitability of both methods for optical aberration determination and microscope objective comparison is discussed. Based on the obtained results, both methods were found to be suitable for comparison of microscope objectives. The suitability for optical aberration determination is possible with certain restrictions.

Proteins are involved in almost all functions in a living cell, and functions of proteins are realized by their tertiary structures. Protein three-dimensional structures can be solved by multiple experimental methods, but computational approaches serve as an important complement to experimental methods for comparing and analyzing protein structures. Protein structure comparison allows the transfer of knowledge about known proteins to a novel protein and plays an important role in function prediction. Obtaining a global perspective of the variety and distribution of protein structures also lays a foundation for our understanding of the building principle of protein structures. This dissertation introduces our computational method to compare protein 3D structures and presents a novel mapping of protein shapes that represents the variety and the similarities of 3D shapes of proteins and their assemblies. The methods developed in this work can be applied to obtain new biological insights into protein atomic structures and electron density maps.