With the advances in computer technology and the changing needs of people&rsquo / s daily lives, robots start to offer alternative solutions. As one of these solutions, the branch of humanoid robots emerged as advanced robots that can interact with people. Robot faces are one of the most effective means of interacting with people / since they can express their emotions and reactions through facial mimics. However, the development of realistic robot faces necessitates the knowledge of the trajectories and displacements of actual face mimics. In this study, a setup (both hardware and software), that can be used for tracking critical points on human face while exhibiting mimics, is developed. From the outputs of this setup, the mimic trajectories are going to be extracted. The setup is designed and manufactured to be durable to external effects so that with a single camera calibration procedure the 3D reconstruction can be carried out several times. The setup consists of two webcams that are specially oriented for mimic tracking. The images taken from the cameras are corrected / their features are extracted using image processing algorithms / the centroids of the features are found / correspondence is carried out and the reconstruction is made. This system can also be used for any special point tracking or volumetric measurement purposes.

The current paradigm in the lens distortion characterization industry is to use simple radial distortion models with only one or two radial terms. Tangential terms and the optimal distortion centre are also seldom determined. Inherent in the models currently used is the assumption that lens distortion is radially symmetrical. The reason for the use of these models is partly due to the perceived instability of more complex lens distortion models. This dissertation shows, in the first of its three hypotheses, that higher order models are indeed beneficial, when their parameters are determined using modern numerical optimization techniques. They are both stable and provide superior characterization. Although it is true that the first two radial terms dominate the distortion characterization, this work proves superior characterization is possible for those applications that may require it. The third hypothesis challenges the assumption of the radial symmetry of lens distortion. Building on the foundation provided by the first hypothesis, a sample of lens distortion models of similar and greater complexity to those found in literature are modified to have a radial gain, allowing the distortion corrections to vary both with polar angle and distance from the distortion centre. Four angular gains are evaluated, and two provide better characterization. The elliptical gain was the only method to both consistently improve the characterization and not ‘skew’ the corrected images. This gain was shown to improve characterization by as much as 50% for simple (single radial term) models and by 7% for even the most complex models. To create an undistorted image from a distorted image captured through a lens which has had its distortion characterized, one needs to find the corresponding distorted pixel for each undistorted pixel in the corrected image. This is either done iteratively or using a simplified model typically based on the Taylor expansion of a simple (one or two radial coefficients) distortion model. The first method is accurate yet slow and the second, the opposite. The second hypothesis of this research successfully combines the advantages of both methods without any of their disadvantages. It was shown that, using the superior characterization of high order radial models (when fitted with modern numerical optimization methods) together with the ‘side-effect’ undistorted image points created in the lens distortion characterization, it is possible to fit a ‘reverse’ model from the undistorted to distorted domains. This reverse characterization is of similar complexity to the simplified models yet provides characterization equivalent to the iterative techniques. Compared to using simplified models the reverse mapping yields an improvement of more than tenfold - from the many tenths of pixels to a few hundredths. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

Lens distortions appear in almost all digital images and cause straight lines to appear curved in the image. This can contribute to errors in position estimations and 3D reconstruction and it is therefore of interest to correct for the distortion. If the camera is available, the distortion parameters can be obtained when calibrating the camera. However, when the camera is unavailable the distortion parameters can not be found with the standard camera calibration technique and other approaches must be used. Recently, variants of Perspective-n-Point (PnP) extended with lens distortionand focal length parameters have been proposed. Given a set of 2D-3D point correspondences, the PnP-based methods can estimate distortion parameters without the camera being available or with modified settings. In this thesis, the performance of PnP-based methods is compared to Zhang’s camera calibration method. The methods are compared both quantitatively, using the errors in reprojectionand distortion parameters, and qualitatively by comparing images before and after lens distortion correction. A test set for the comparison was obtained from a camera and a 3D laser scanner of an indoor scene.The results indicate that one of the PnP-based models can achieve a similar reprojection error as the baseline method for one of the cameras. It could also be seen that two PnP-based models could reduce lens distortion when visually comparing the test images to the baseline. Moreover, it was noted that a model can have a small reprojection error even though the distortion coefficient error is large and the lens distortion is not completely removed. This indicates that it is important to include both quantitative measures, such as reprojection error and distortion coefficient errors, as well as qualitative results when comparing lens distortion correction methods. It could also be seen that PnP-based models with more parameters in the estimation are more sensitive to noise.

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In recent years, researchers have increasingly used magnetic resonance imaging (MRI) to study temporal skeletal muscle changes using gradient echo (GRE) echo planar imaging (EPI). These studies, typically involving exercise or ischemic challenges, have differentiated healthy subjects from athletic or unhealthy populations, such as those with peripheral vascular disease. However, the analysis methodologies have been lacking. In this thesis, two sessions of post-exercise GRE EPI data were collected from six subjects' lower legs using a 3 Tesla MRI scanner and a custom built ergometer. Past studies used common medical imaging software for motion correction. This work shows that such tools degrade leg image data by introducing motion, increasing root mean squared error in rest data by 22%. A new approach decreased it by 12%. EPI distortion correction in muscle images was also achieved, with the correlation ratio of functional and structural images increasing by up to 8%. In addition, a brief but intense artifact in GRE EPI muscle images results from muscle tissue moving in and out of the imaged volume. This through-plane artifact was successfully modelled as a mono-exponential decay for regression analysis, increasing the utility of the residual signal. The regression parameters were also leveraged to produce muscle displacement maps, identifying 44% of voxels as displaced. The maps were validated in a motion phantom and in-vivo using ultrasound. Finally, independent component analysis (ICA) was applied to post-exercise GRE EPI images to detect features in a data-driven, multivariate way and improve on conventional ROI selection methods. ICA produced parametric maps that were spatially correlated to working muscles from every trial (most with |R| > 0.4). The components were also separated from the susceptibility, motion, and blood vessel signals, and temporally reliable within individuals. These methodological advances represent increased rigour in the analysis of muscle GRE EPI images. / Thesis / Doctor of Philosophy (PhD) / Adequate blood circulation to muscles is important for good health. Researchers have used magnetic resonance imaging (MRI) techniques to assess blood and oxygen supply to muscles. The work in this thesis improves upon the analysis methods in prior work, especially in the areas of motion correction of the images and selection of individual muscle regions for analysis. Previous techniques could sometimes make motion in muscle images worse. This work provides valuable motion and distortion correction for muscle imaging, ensuring that measurements truly reflect muscle physiology. It also describes a method to remove an unwanted signal from post-exercise muscle data, and create a map of the internal muscle motion that occurred. Finally, an advanced mathematical technique was used to extract signals of interest and important spatial features from muscle image data automatically. The technique produced reliable results within and among subjects.

Liquid water formation and flooding in PEM fuel cell gas distribution channels can significantly degrade fuel cell performance by causing substantial pressure drop in the channels and by inhibiting the transport of reactants to the reaction sites at the catalyst layer. A better understanding of the mechanisms of discrete water droplet transport by air flow in such small channels may be developed through the application of quantitative flow visualization techniques. This improved knowledge could contribute to improved gas channel design and higher fuel cell efficiencies. An experimental investigation was undertaken to gain better understanding of the relationships between air velocity in the channel, secondary rotational flows inside a droplet, droplet deformation, and threshold shear, drag, and pressure forces required for droplet removal. Micro-digital-particle-image-velocimetry (micro-DPIV) techniques were used to provide quantitative visualizations of the flow inside the liquid phase for the case of air flow around a droplet adhered to the wall of a 1 mm x 3 mm rectangular gas channel model. The sidewall against which the droplet was adhered was composed of PTFE treated carbon paper to simulate the porous GDL surface of a fuel cell gas channel. Visualization of droplet shape, internal flow patterns and Velocity measurements at the central cross-sectional plane of symmetry in the droplet were obtained for different air flow rates. A variety of rotational secondary flow patterns within the droplet were observed. The nature of these flows depended primarily on the air flow rate. The peak velocities of these secondary flow fields were observed to be around two orders of magnitude below the calculated channel-averaged driving air velocities. The resulting flow fields show in particular that the velocity at the air-droplet interface is finite. The experimental data collected from this study may be used for validation of numerical simulations of such droplet flows. Further study of such flow scenarios using the techniques developed in this experiment, including the general optical distortion correction algorithm developed as part of this work, may provide insight into an improved force balance model for a droplet exposed to an air flow in a gas channel.

Liquid water formation and flooding in PEM fuel cell gas distribution channels can significantly degrade fuel cell performance by causing substantial pressure drop in the channels and by inhibiting the transport of reactants to the reaction sites at the catalyst layer. A better understanding of the mechanisms of discrete water droplet transport by air flow in such small channels may be developed through the application of quantitative flow visualization techniques. This improved knowledge could contribute to improved gas channel design and higher fuel cell efficiencies. An experimental investigation was undertaken to gain better understanding of the relationships between air velocity in the channel, secondary rotational flows inside a droplet, droplet deformation, and threshold shear, drag, and pressure forces required for droplet removal. Micro-digital-particle-image-velocimetry (micro-DPIV) techniques were used to provide quantitative visualizations of the flow inside the liquid phase for the case of air flow around a droplet adhered to the wall of a 1 mm x 3 mm rectangular gas channel model. The sidewall against which the droplet was adhered was composed of PTFE treated carbon paper to simulate the porous GDL surface of a fuel cell gas channel. Visualization of droplet shape, internal flow patterns and Velocity measurements at the central cross-sectional plane of symmetry in the droplet were obtained for different air flow rates. A variety of rotational secondary flow patterns within the droplet were observed. The nature of these flows depended primarily on the air flow rate. The peak velocities of these secondary flow fields were observed to be around two orders of magnitude below the calculated channel-averaged driving air velocities. The resulting flow fields show in particular that the velocity at the air-droplet interface is finite. The experimental data collected from this study may be used for validation of numerical simulations of such droplet flows. Further study of such flow scenarios using the techniques developed in this experiment, including the general optical distortion correction algorithm developed as part of this work, may provide insight into an improved force balance model for a droplet exposed to an air flow in a gas channel.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Images captured in endoscopy examinations show some distortion, the radial is the most visible. The radial distortion appears in images due to lens used in endoscopes. When a doctor or researcher is analyzing a distorted image, he can not see the exact size of an organ, tumor or lesion, due the magnification in the center of the image and a contraction in the peripheral regions caused by such distortion. This paper aims to propose a new method for correction of radial distortion in endoscopic images. The proposed method is based on concepts of Morphing and Warping, which are techniques widely used in computer graphics to transform the image of one person to another or to cause objects deformations. The system presents the advantage of automatic application of these techniques, since the vast majority of correction algorithms need user interaction. The proposed method uses a pattern image, created for the calibration of the transformations that are applied to the images of endoscopy. The developed system receives the pattern image captured by endoscope, divides the image into a triangular mesh, make the matching of each triangle of the meshes and store the affine transformations of each triangular region of the mesh separately. After calibration, the affine transformations of each triangular region are used in real image of endoscopic examinations performed by the same endoscope used for calibration to correct the images. Finally, the method was compared with others in the literature and has been made quantitative and qualitative analysis with the results. / Imagens capturadas em exames de endoscopia apresentam algumas distorções, sendo a distorção radial a principal. A distorção radial surge na imagem devido ao sistema de lentes utilizado nos endoscópios. Quando um médico ou pesquisador está analisando uma imagem distorcida, não consegue perceber qual o tamanho exato de um órgão, lesão ou tumor, pois tal distorção causa uma ampliação no centro da imagem e uma contração nas regiões periféricas. Este trabalho tem como objetivo propor um novo método para a correção de distorções radiais em imagens de endoscopia. O método proposto baseia-se em conceitos de Morphing e Warping, que são técnicas bastante utilizadas em computação gráfica para transformar a imagem de uma pessoa em outra ou para causar deformações em objetos. O sistema apresentado tem como diferencial a aplicação automática destas técnicas, visto que a grande maioria de algoritmos que fazem uso delas funciona com interação do usuário. O método proposto utiliza uma imagem padrão, criada para a calibração das transformações que serão aplicadas nas imagens de exames de endoscopia. O sistema desenvolvido recebe a imagem padrão capturada por endoscópio, divide a imagem em uma malha triangular, faz a correspondência de cada triângulo desta malha com a malha da imagem padrão original e armazena as transformações afins em cada região da malha separadamente, transformando assim a imagem capturada na imagem original. Após a calibração, as mesmas transformações afins armazenadas para cada elemento triangular da malha são utilizadas em imagem reais de exames endoscópicos feitos pelo mesmo endoscópio utilizado na calibração, para corrigir a deformação. Por fim, o método desenvolvido foi comparado com outros da literatura e foram feitas análises quantitativas e qualitativas dos resultados obtidos.

Cette thèse se concentre sur le sujet de la calibration de la camera interne et, en particulier, sur les aspects de haute précision. On suit et examine deux fils principaux: la correction d'une aberration chromatique de lentille et l'estimation des paramètres intrinsèques de la caméra. Pour la problème de l'aberration chromatique, on suit un chemin de post-traitement numérique de l'image, afin de se débarrasser des artefacts de couleur provoqués par le phénomène de dispersion du système d'objectif de la caméra, ce qui produit une désalignement perceptible des canaux couleur. Dans ce contexte, l'idée principale est de trouver un modèle de correction plus général pour réaligner les canaux de couleur que ce qui est couramment utilisé - différentes variantes du polynôme radial. Celui-ci ne peut pas être suffisamment général pour assurer la correction précise pour tous les types de caméras. En combinaison avec une détection précise des points clés, la correction la plus précise de l'aberration chromatique est obtenue en utilisant un modèle polynomial qui est capable de capter la nature physique du décalage des canaux couleur. Notre détection de points clés donne une précision allant jusqu'à 0,05 pixels, et nos expériences montrent sa grande résistance au bruit et au flou. Notre méthode de correction de l’aberration, par opposition aux logiciels existants, montre une géométrique résiduelle inférieure à 0,1 pixels, ce qui est la limite de la perception de la vision humaine. En ce qui concerne l'estimation des paramètres intrinsèques de la caméra, la question est de savoir comment éviter la compensation d'erreur résiduelle qui est inhérent aux méthodes globales d'étalonnage, dont le principe fondamental consiste à estimer tous les paramètres de la caméra ensemble - l'ajustement de faisceaux. Détacher les estimations de la distorsion de la caméra et des paramètres intrinsèques devient possible lorsque la distorsion est compensée séparément. Cela peut se faire au moyen de la harpe d'étalonnage, récemment développée, qui calcule le champ de distorsion en utilisant la mesure de la rectitude de cordes tendues dans différentes orientations. Une autre difficulté, étant donnée une image déjà corrigée de la distorsion, est de savoir comment éliminer un biais perspectif. Ce biais dû à la perspective est présent quand on utilise les centres de cibles circulaires comme points clés, et il s'amplifie avec l'augmentation de l'angle de vue. Afin d'éviter la modélisation de chaque cercle par une fonction conique, nous intégrons plutôt fonction de transformation affine conique dans la procédure de minimisation pour l'estimation de l'homographie. Nos expériences montrent que l'élimination séparée de la distorsion et la correction du biais perspectif sont efficaces et plus stables pour l'estimation des paramètres intrinsèques de la caméra que la méthode d'étalonnage globale / This dissertation focuses on internal camera calibration and, especially, on its high-precision aspects. Two main threads are followed and examined: lens chromatic aberration correction and estimation of camera intrinsic parameters. For the chromatic aberration problem, we follow a path of digital post-processing of the image in order to get rid from the color artefacts caused by dispersion phenomena of the camera lens system, leading to a noticeable color channels misalignment. In this context, the main idea is to search for a more general correction model to realign color channels than what is commonly used - different variations of radial polynomial. The latter may not be general enough to ensure stable correction for all types of cameras. Combined with an accurate detection of pattern keypoints, the most precise chromatic aberration correction is achieved by using a polynomial model, which is able to capture physical nature of color channels misalignment. Our keypoint detection yields an accuracy up to 0.05 pixels, and our experiments show its high resistance to noise and blur. Our aberration correction method, as opposed to existing software, demonstrates a final geometrical residual of less than 0.1 pixels, which is at the limit of perception by human vision. When referring to camera intrinsics calculation, the question is how to avoid residual error compensation which is inherent for global calibration methods, the main principle of which is to estimate all camera parameters simultaneously - the bundle adjustment. Detachment of the lens distortion from camera intrinsics becomes possible when the former is compensated separately, in advance. This can be done by means of the recently developed calibration harp, which captures distortion field by using the straightness measure of tightened strings in different orientations. Another difficulty, given a distortion-compensated calibration image, is how to eliminate a perspective bias. The perspective bias occurs when using centers of circular targets as keypoints, and it gets more amplified with increase of view angle. In order to avoid modelling each circle by a conic function, we rather incorporate conic affine transformation function into the minimization procedure for homography estimation. Our experiments show that separate elimination of distortion and perspective bias is effective and more stable for camera's intrinsics estimation than global calibration method