Nous proposons de construire un atlas numérique 3D contenant les caractéristiques moyennes et les variabilités de la morphologie d’un organe. Nos travaux seront appliqués particulièrement à la construction d'un atlas numérique 3D de la totalité de la cornée humaine incluant la surface antérieure et postérieure à partir des cartes topographiques fournies par le topographe Orbscan II. Nous procédons tout d'abord par normalisation de toute une population de cornées. Dans cette étape, nous nous sommes basés sur l'algorithme de recalage ICP (iterative closest point) pour aligner simultanément les surfaces antérieures et postérieures d'une population de cornée vers les surfaces antérieure et postérieure d'une cornée de référence. En effet, nous avons élaboré une variante de l'algorithme ICP adapté aux images (cartes) de cornées qui tient compte de changement d'échelle pendant le recalage et qui se base sur la recherche par voisinage via la distance euclidienne pour établir la correspondance entre les points. Après, nous avons procédé pour la construction de l'atlas cornéen par le calcul des moyennes des élévations de surfaces antérieures et postérieures recalées et leurs écarts-types associés. Une population de 100 cornées saines a été utilisée pour construire l'atlas cornéen normal. Pour visualiser l’atlas, on a eu recours à des cartes topographiques couleurs similairement à ce qu’offrent déjà les systèmes topographiques actuels. Enfin, des observations ont été réalisées sur l'atlas cornéen reflétant sa précision et permettant de développer une meilleure connaissance de l’anatomie cornéenne. / We propose to build a 3D digital atlas which contains the average characteristics and variability of the morphology of an organ. In particular our work consists in the construction of a 3D digital atlas of the entire human cornea including anterior and posterior surfaces. The atlas was built using topographies provided by the Orbscan II system. First, we normalized the given population of corneas using a variant of the ICP (iterative closest point) algorithm for shape registration to fit simultaneously the anterior and posterior surfaces with the anterior and posterior surfaces of a reference cornea. Indeed, we developed a specific algorithm for corneas topographies that considers scaling during registration and which is based on neighborhood search via the Euclidean distance to find the correspondence between points. After that, we built the corneal atlas by averaging elevations of anterior and posterior surfaces and by calculating their associated standard deviations. A population of 100 healthy corneas was used to construct the normal corneal atlas. To illustrate the atlas, we used topographic color maps like those already offered by existing topographic systems. Finally, observations were made on the corneal atlas that reflects its precision and allows to develop a better understanding of corneal anatomy.

The plumage colour and patterns of birds have interested biologists for a long time.Why are some bird species all black while others have a multitude of colours? Does ithave anything to do with sexual selection, predator avoidance or social signalling?Many questions such as these have been asked and as many hypotheses about thefunctional role of the plumage have been formed. The problem, however, has been toprove any of these. To test these hypotheses you need to analyse the bird plumagesand today such analyses are still rather subjective. Meaning the results could varydepending on the individual performing the analysis. Another problem that stemsfrom this subjectiveness is that it is difficult to make quantitative measurements of theplumage colours. Quantitative measurements would be very useful since they couldbe related to other statistical data like speciation rates, sexual selection and ecologicaldata. This thesis aims to assist biologists with the analysis and measurement of birdplumages by developing a MATLAB toolbox for this purpose. The result is a wellstructured and user friendly toolbox that contains functions for segmenting, resizing,filtering and warping, all used to prepare the images for analysis. It also containsfunctions for the actual analysis such as basic statistical measurements, principalcomponent analysis and eigenvector projection.

At present, the medical industry rapidly develops new imaging techniques and improves the imaging methods. Simultaneously also are developed new methods for processing data acquired by these methods. Especially in the past few years has become very used method of registration data, which leads to image transformations of the same scene so that the condition as possible. The work deals with the method of processing data that provides detailed information to individual structures, developments of individual structures over time, allows to simultaneously displayanatomical and physiological information or preprocessing data for further processing.

This thesis is dealing with problem of brain images registration aquired by computed tomography. At the beginning is explanation of image geometrical transformation methods, notably affine transformation. Following part of text the is dealing with interpolation methods issues, calculation of similarity criterion and subsequent optimalization. All issues are handled especially for three-dimensional data. Second part of this work is practical sample of MatLab® program enviroment for registration of acquired frames by affine tranformation. In this program is algorithm for removement of stair-step artefact, under head pillow and patient’s desk, too. As an optimalization algorithm is used control random search (CRS) methode. Due to medical images type, which are distributed in DICOM format, is included process for their load and save at this work.

Dans ce mémoire, on s'intéresse à l'action du groupe des transformations affines et des homothéties sur l'axe du temps des systèmes différentiels quadratiques à foyer faible d'ordre trois, dans le plan. Ces systèmes sont importants dans le cadre du seizième problème d'Hilbert. Le diagramme de bifurcation a été produit à l'aide de la forme normale de Li dans des travaux de Andronova [2] et Artès et Llibre [4], sans utiliser le plan projectif comme espace des paramètres ni de méthodes globales. Dans [7], Llibre et Schlomiuk ont utilisé le plan projectif comme espace des paramètres et des notions à caractère géométrique global (invariants affines et topologiques). Ce diagramme contient 18 portraits de phase et certains de ces portraits sont répétés dans des parties distinctes du diagramme. Ceci nous mène à poser la question suivante : existe-t-il des systèmes distincts, correspondant à des valeurs distinctes de paramètres, se trouvant sur la même orbite par rapport à l'action du groupe? Dans ce mémoire, on prouve un résultat original : l'action du groupe n'est pas triviale sur la forme de Li (théorème 3.1), ni sur la forme normale de Bautin (théorème 4.1). En utilisant le deuxième résultat, on construit l'espace topologique quotient des systèmes quadratiques à foyer faible d'ordre trois par rapport à l'action de ce groupe. / We are interessed here in the action of the group of affine transformations and time homotheties on quadratic differential systems which have a weak focus of third order. These systems are important for Hilbert sixteenth problem. The bifurcation diagram was produced using Li's normal form in the articles of Andronova [2], and Artès and Llibre [4], without using the projective plane as parameter space, and without using global methods. In [7], Llibre and Schlomiuk used the projective plane as parameter space and global geometric methods (affine and topological invariants). This diagram contains 18 phase portraits and some of these portraits are repeated in distinct parts of the diagram. This led us to ask the following question : do there exist distinct differential systems, corresponding to distinct values of the parameter, which are on the same orbit of the group action? In this master's thesis, we prove an original result : the action of the group is not trivial on Li's normal form (theorem 3.1), neither is it trivial on Bautin's normal form (theorem 4.1). Using the second result, we construct the quotient topological space of these systems with a weak focus of third order, with respect to the group action.

Scale-invariant interest points have found several highly successful applications in computer vision, in particular for image-based matching and recognition. This paper presents a theoretical analysis of the scale selection properties of a generalized framework for detecting interest points from scale-space features presented in Lindeberg (Int. J. Comput. Vis. 2010, under revision) and comprising: an enriched set of differential interest operators at a fixed scale including the Laplacian operator, the determinant of the Hessian, the new Hessian feature strength measures I and II and the rescaled level curve curvature operator, as well as an enriched set of scale selection mechanisms including scale selection based on local extrema over scale, complementary post-smoothing after the computation of non-linear differential invariants and scale selection based on weighted averaging of scale values along feature trajectories over scale. A theoretical analysis of the sensitivity to affine image deformations is presented, and it is shown that the scale estimates obtained from the determinant of the Hessian operator are affine covariant for an anisotropic Gaussian blob model. Among the other purely second-order operators, the Hessian feature strength measure I has the lowest sensitivity to non-uniform scaling transformations, followed by the Laplacian operator and the Hessian feature strength measure II. The predictions from this theoretical analysis agree with experimental results of the repeatability properties of the different interest point detectors under affine and perspective transformations of real image data. A number of less complete results are derived for the level curve curvature operator. / <p>QC 20121003</p> / Image descriptors and scale-space theory for spatial and spatio-temporal recognition

Made available in DSpace on 2016-03-15T19:37:38Z (GMT). No. of bitstreams: 1 Glauco dos Santos Reis.pdf: 1334999 bytes, checksum: d2d72d3f95a449c19482f55f82b7f61e (MD5) Previous issue date: 2011-08-22 / Fundo Mackenzie de Pesquisa / A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system (IFS). Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, the original image should be partitioned in regions, and each one of the active pixels are transformed by the AT. The new transformed set should be approximated to other image regions. This iterated execution to find ATs for the best set of areas might result in smaller storage space since the similar areas might be replaced by AT coefficients. Despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs that have to be searched for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, since the comparison is made point by point, instead of region by region. Experiments were made on a group of 10 images, representing a broad set of distinct features and resolutions. The proposed algorithm competes in terms of storage size, when compared to JPEG, mainly when the image size is small, and the number of colors are reduced, as currently happens for most images used in the Internet. Although the proposed method is faster than the traditional method for IFS compression, it is slower than common file formats like JPEG. / Uma nova técnica para compressão de imagens é proposta, baseada em conjuntos de transformações afins (affine transformations - ATs), normalmente conhecidos como sistemas de funções iteradas (iterated function system -IFS). Pesquisas anteriores mostraram que uma imagem poderia ser aproximada pela aplicação de um grupo de ATs em conjuntos de sub-regiões da imagem, de forma iterativa. Através deste processo, a imagem original seria subdividida em regiões e sobre a coordenada de cada ponto habilitado de cada região seria aplicada uma transformação afim. O resultado representaria um novo conjunto de pontos similares a outras regiões da imagem. A execução de forma iterada deste processo de identificação das ATs para o maior conjunto de regiões similares de uma determinada imagem permitiria uma redução no armazenamento, já que as regiões similares poderiam ser armazenadas como os coeficientes das transformações afins. Apesar desta vantagem em termos de compressão, a técnica é computacionalmente intensiva, pela busca exaustiva de sub-regiões e das ATs geradoras, de forma a proporcionar o melhor preenchimento em outras regiões da imagem. Esta pesquisa propõe uma nova forma de compressão baseada em ATs, utilizando a sequência de pontos gerada pela iteração das ATs. Entendendo uma AT como um sistema dinâmico em tempo discreto, cada novo ponto identificado é consequência direta da iteração da AT sobre o ponto anterior, permitindo a captura de similaridades nesta sequência de pontos. Através do salvamento dos coeficientes das ATs e das coordenadas iniciais, é possível a reconstrução da imagem pela iteração da AT a partir do ponto inicial. Isto pode resultar em menor esforço computacional, pois apenas comparações simples de pontos são necessárias, ao invés de comparações entre os pontos de regiões da imagem. Foram feitos experimentos em um conjunto de 10 classes de imagens, representando um espectro de diferentes características gerais e resoluções. O algoritmo proposto rivaliza em termos de armazenamento quando comparado ao formato JPEG, principalmente para imagens de pequeno tamanho e com número de cores reduzidas, como as utilizadas com frequência na Internet. Apesar de ser mais rápido para a compressão do que outros métodos baseados em IFS, ele é mais lento do que métodos clássicos como o JPEG.

Made available in DSpace on 2016-03-15T19:37:41Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-08-22 / Fundo Mackenzie de Pesquisa / A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system (IFS). Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, the original image should be partitioned in regions, and each one of the active pixels are transformed by the AT. The new transformed set should be approximated to other image regions. This iterated execution to find ATs for the best set of areas might result in smaller storage space since the similar areas might be replaced by AT coefficients. Despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs that have to be searched for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, since the comparison is made point by point, instead of region by region. Experiments were made on a group of 10 images, representing a broad set of distinct features and resolutions. The proposed algorithm competes in terms of storage size, when compared to JPEG, mainly when the image size is small, and the number of colors are reduced, as currently happens for most images used in the Internet. Although the proposed method is faster than the traditional method for IFS compression, it is slower than common file formats like JPEG. / Uma nova técnica para compressão de imagens é proposta, baseada em conjuntos de transformações afins (affine transformations - ATs), normalmente conhecidos como sistemas de funções iteradas (iterated function system - IFS). Pesquisas anteriores mostraram que uma imagem poderia ser aproximada pela aplicação de um grupo de ATs em conjuntos de sub-regiões da imagem, de forma iterativa. Através deste processo, a imagem original seria subdividida em regiões e sobre a coordenada de cada ponto habilitado de cada região seria aplicada uma transformação afim. O resultado representaria um novo conjunto de pontos similares a outras regiões da imagem. A execução de forma iterada deste processo de identificação das ATs para o maior conjunto de regiões similares de uma determinada imagem permitiria uma redução no armazenamento, já que as regiões similares poderiam ser armazenadas como os coeficientes das transformações afins. Apesar desta vantagem em termos de compressão, a técnica é computacionalmente intensiva, pela busca exaustiva de sub-regiões e das ATs geradoras, de forma a proporcionar o melhor preenchimento em outras regiões da imagem. Esta pesquisa propõe uma nova forma de compressão baseada em ATs, utilizando a sequência de pontos gerada pela iteração das ATs. Entendendo uma AT como um sistema dinâmico em tempo discreto, cada novo ponto identificado é consequência direta da iteração da AT sobre o ponto anterior, permitindo a captura de similaridades nesta sequência de pontos. Através do salvamento dos coeficientes das ATs e das coordenadas iniciais, é possível a reconstrução da imagem pela iteração da AT a partir do ponto inicial. Isto pode resultar em menor esforço computacional, pois apenas comparações simples de pontos são necessárias, ao invés de comparações entre os pontos de regiões da imagem. Foram feitos experimentos em um conjunto de 10 classes de imagens, representando um espectro de diferentes características gerais e resoluções. O algoritmo proposto rivaliza em termos de armazenamento quando comparado ao formato JPEG, principalmente para imagens de pequeno tamanho e com número de cores reduzidas, como as utilizadas com frequência na Internet. Apesar de ser mais rápido para a compressão do que outros métodos baseados em IFS, ele é mais lento do que métodos clássicos como o JPEG.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.