Les défaut de la vision sont analysés et classés à partir des caractéristiques mathématiques du front d’onde de l’oeil considéré. Après avoir présenté la méthode actuelle basée sur la décomposition du front d’onde dans la base orthonormale de Zernike ainsi que certaines de ses limitations, on propose ici une nouvelle base de décomposition. Celle-ci repose sur l’utilisation del’espace des fronts d’onde polynomiaux de valuation supérieure ou égale à L + 1 (où L est un entier naturel) et permet de décomposer de manière unique un front d’onde polynomial en la somme d’un front d’onde polynomial de bas degré (inférieur ou égal à L) et un front d’onde polynomial de haute valuation (supérieure ou égal à L + 1). En choisissant L = 2, une nouvelle décomposition est obtenue, appelée D2V3, où le front d’onde polynomial de haut degré ne comporte pas de termes de degré radial inférieur ou égal à deux. Cette approche permet de dissocier parfaitement les aberrations optiques corrigibles ou non par le port de lunettes. Différents cas cliniques présentés dans la dernière section permettent de mettre en évidence l’intérêt de cette nouvelle base de décomposition. / The eye vision defaults are analyzed and classified by studyingthe corresponding eye wavefront. After presenting the orthogonal basis, called the Zernike basis, that is currently used for the medical diagnosis, a new decomposition basis is built. It is based on the use of the space of polynomials of valuation greater or equal to L+1 (for L a natural integer). It allows to uniquely decompose a polynomial wavefront into the sum of a polynomial of low degree (lesser or equal to L) and a polynomial of high valuation (greater or equal to L +1). By choosing L = 2, a new decomposition, called D2V3, is obtained where the polynomial wavefront of high degree does not include terms of radial degree lesser or equal to 2. In particular, it allows to quantify perfectly the aberrations that can be corrected by eyeglasses or not. Various clinical examples clearly show the interest of this new basis compared to a diagnosis based on the Zernike decomposition.

<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>

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.

No description available.

This diploma thesis considers with human vision and human eye. It takes into account both anatomic view and physiology standpoints. There is, among others, description of optical processes occurring in the organ of the sight mentioned in the work. The human eye suffers from optical defects – aberrations – that are able to degrade the retinal image and ultimately visual performance. Substantial part of the text deals with these aberrations. There are also analysed possibilities of their elimination using an inverse aberration. Work also assumes opportunity to optical modeling to calculate distorted images from ocular aberration data. Practical part consist of software application created using Matlab environment ver. 6.5 as well as full documentation. The examples of outputs procured using this application are published. Both software application and detail documentation are included on CD.

O ganho crescen te de desempenho nos computadores modernos tem impulsionado os trabalhos científicos nas áreas de simulação computacional. Muitos autores utilizam em suas pesquisas ferramentas comerciais que limitam seus trabalhos ao esconder os algoritmos internos destas ferramentas e dificultam a adição de dados in-vivo nestes trabalhos. Este trabalho explora esta lacuna deixada por aqueles autores. Elaboramos um arcabouço computacional capaz de reproduzir os fenômenos óticos e fisiológicos do sistema visual. Construímos com superfícies quádricas os modelos esquemáticos do olho humano e propomos um algoritmo de traçado de raio realístico. Então realizamos um estudo nos modelos esquemáticos e a partir deles mais a adição de dados in-vivo obtidos de um topógrafo de córnea extraímos informações óticas destes modelos. Calculamos os coeficientes e Zernike dos modelos para tamanhos diversos de pupila e obtivemos medidas de aberração do olho humano. Os resultados encontrados estão de acordo com os trabalhos relacionados e as simulações com dados in-vivo estão consoantes com as produzidas por um aparelho de frente de onda comerciais. Este trabalho é um esforço em aproveitar as informações adquiridas pelos equipamentos modernos de oftalmologia, além de auxiliar o entendimento de sistemas visuais biológicos acabam também em auxiliar a elaboração de sistemas de visão artificial e os projetistas de sistemas óticos / The increase in performance of the modern computers has driven scientific work in the areas of computer simulation. Many authors use in their research commercial tools that use embedding algorithms, which sources are not provided, and it makes harder and sometimes impossible, the development of novel theories or experiments. This work explores this gap left for those authors. We present a computational framework capable to reproduce the optical and physiological phenomena of the human visual system. We construct schematical models of the human eye from quadrics surfaces and consider an algorithm of realistic ray tracing. Afterward, we performed a study on schematics models and in addition we introduce, in these models, in-vivo data obtained from corneal topography machine and extract optical information. We calculate the Zernike coefficients in the models for different sizes of pupil and measures of aberration of the human eye. The results are in agreement with related work and simulations with in-vivo data are according with the produced by a commercial wave-front device. This work is an effort in using to advantage the information acquired for the modern equipment of ophthalmology, besides assisting the understanding of biological visual systems, it also helps the development of artificial vision systems and the designing of optical systems

O ganho crescen te de desempenho nos computadores modernos tem impulsionado os trabalhos científicos nas áreas de simulação computacional. Muitos autores utilizam em suas pesquisas ferramentas comerciais que limitam seus trabalhos ao esconder os algoritmos internos destas ferramentas e dificultam a adição de dados in-vivo nestes trabalhos. Este trabalho explora esta lacuna deixada por aqueles autores. Elaboramos um arcabouço computacional capaz de reproduzir os fenômenos óticos e fisiológicos do sistema visual. Construímos com superfícies quádricas os modelos esquemáticos do olho humano e propomos um algoritmo de traçado de raio realístico. Então realizamos um estudo nos modelos esquemáticos e a partir deles mais a adição de dados in-vivo obtidos de um topógrafo de córnea extraímos informações óticas destes modelos. Calculamos os coeficientes e Zernike dos modelos para tamanhos diversos de pupila e obtivemos medidas de aberração do olho humano. Os resultados encontrados estão de acordo com os trabalhos relacionados e as simulações com dados in-vivo estão consoantes com as produzidas por um aparelho de frente de onda comerciais. Este trabalho é um esforço em aproveitar as informações adquiridas pelos equipamentos modernos de oftalmologia, além de auxiliar o entendimento de sistemas visuais biológicos acabam também em auxiliar a elaboração de sistemas de visão artificial e os projetistas de sistemas óticos / The increase in performance of the modern computers has driven scientific work in the areas of computer simulation. Many authors use in their research commercial tools that use embedding algorithms, which sources are not provided, and it makes harder and sometimes impossible, the development of novel theories or experiments. This work explores this gap left for those authors. We present a computational framework capable to reproduce the optical and physiological phenomena of the human visual system. We construct schematical models of the human eye from quadrics surfaces and consider an algorithm of realistic ray tracing. Afterward, we performed a study on schematics models and in addition we introduce, in these models, in-vivo data obtained from corneal topography machine and extract optical information. We calculate the Zernike coefficients in the models for different sizes of pupil and measures of aberration of the human eye. The results are in agreement with related work and simulations with in-vivo data are according with the produced by a commercial wave-front device. This work is an effort in using to advantage the information acquired for the modern equipment of ophthalmology, besides assisting the understanding of biological visual systems, it also helps the development of artificial vision systems and the designing of optical systems

Cette thèse cherche à examiner les conditions optimales dans lesquelles les surfaces cornéennes antérieures peuvent être efficacement pré-traitées, classifiées et prédites en utilisant des techniques de modélisation géométriques (MG) et d’apprentissage automatiques (AU). La première étude (Chapitre 2) examine les conditions dans lesquelles la modélisation géométrique peut être utilisée pour réduire la dimensionnalité des données utilisées dans un projet d’apprentissage automatique. Quatre modèles géométriques ont été testés pour leur précision et leur rapidité de traitement : deux modèles polynomiaux (P) – polynômes de Zernike (PZ) et harmoniques sphériques (PHS) – et deux modèles de fonctions rationnelles (R) : fonctions rationnelles de Zernike (RZ) et fonctions rationnelles d’harmoniques sphériques (RSH). Il est connu que les modèles PHS et RZ sont plus précis que les modèles PZ pour un même nombre de coefficients (J), mais on ignore si les modèles PHS performent mieux que les modèles RZ, et si, de manière plus générale, les modèles SH sont plus précis que les modèles R, ou l’inverse. Et prenant en compte leur temps de traitement, est-ce que les modèles les plus précis demeurent les plus avantageux? Considérant des valeurs de J (nombre de coefficients du modèle) relativement basses pour respecter les contraintes de dimensionnalité propres aux taches d’apprentissage automatique, nous avons établi que les modèles HS (PHS et RHS) étaient tous deux plus précis que les modèles Z correspondants (PZ et RR), et que l’avantage de précision conféré par les modèles HS était plus important que celui octroyé par les modèles R. Par ailleurs, les courbes de temps de traitement en fonction de J démontrent qu’alors que les modèles P sont traités en temps quasi-linéaires, les modèles R le sont en temps polynomiaux. Ainsi, le modèle SHR est le plus précis, mais aussi le plus lent (un problème qui peut en partie être remédié en appliquant une procédure de pré-optimisation). Le modèle ZP était de loin le plus rapide, et il demeure une option intéressante pour le développement de projets. SHP constitue le meilleur compromis entre la précision et la rapidité. La classification des cornées selon des paramètres cliniques a une longue tradition, mais la visualisation des effets moyens de ces paramètres sur la forme de la cornée par des cartes topographiques est plus récente. Dans la seconde étude (Chapitre 3), nous avons construit un atlas de cartes d’élévations moyennes pour différentes variables cliniques qui pourrait s’avérer utile pour l’évaluation et l’interprétation des données d’entrée (bases de données) et de sortie (prédictions, clusters, etc.) dans des tâches d’apprentissage automatique, entre autres. Une base de données constituée de plusieurs milliers de surfaces cornéennes antérieures normales enregistrées sous forme de matrices d’élévation de 101 by 101 points a d’abord été traitée par modélisation géométrique pour réduire sa dimensionnalité à un nombre de coefficients optimal dans une optique d’apprentissage automatique. Les surfaces ainsi modélisées ont été regroupées en fonction de variables cliniques de forme, de réfraction et de démographie. Puis, pour chaque groupe de chaque variable clinique, une surface moyenne a été calculée et représentée sous forme de carte d’élévations faisant référence à sa SMA (sphère la mieux ajustée). Après avoir validé la conformité de la base de donnée avec la littérature par des tests statistiques (ANOVA), l’atlas a été vérifié cliniquement en examinant si les transformations de formes cornéennes présentées dans les cartes pour chaque variable étaient conformes à la littérature. C’était le cas. Les applications possibles d’un tel atlas sont discutées. La troisième étude (Chapitre 4) traite de la classification non-supervisée (clustering) de surfaces cornéennes antérieures normales. Le clustering cornéen un domaine récent en ophtalmologie. La plupart des études font appel aux techniques d’extraction des caractéristiques pour réduire la dimensionnalité de la base de données cornéennes. Le but est généralement d’automatiser le processus de diagnostique cornéen, en particulier en ce qui a trait à la distinction entre les cornées normales et les cornées irrégulières (kératocones, Fuch, etc.), et dans certains cas, de distinguer différentes sous-classes de cornées irrégulières. L’étude de clustering proposée ici se concentre plutôt sur les cornées normales afin de mettre en relief leurs regroupements naturels. Elle a recours à la modélisation géométrique pour réduire la dimensionnalité de la base de données, utilisant des polynômes de Zernike, connus pour leur interprétativité transparente (chaque terme polynomial est associé à une caractéristique cornéenne particulière) et leur bonne précision pour les cornées normales. Des méthodes de différents types ont été testées lors de prétests (méthodes de clustering dur (hard) ou souple (soft), linéaires or non-linéaires. Ces méthodes ont été testées sur des surfaces modélisées naturelles (non-normalisées) ou normalisées avec ou sans traitement d’extraction de traits, à l’aide de différents outils d’évaluation (scores de séparabilité et d’homogénéité, représentations par cluster des coefficients de modélisation et des surfaces modélisées, comparaisons statistiques des clusters sur différents paramètres cliniques). Les résultats obtenus par la meilleure méthode identifiée, k-means sans extraction de traits, montrent que les clusters produits à partir de surfaces cornéennes naturelles se distinguent essentiellement en fonction de la courbure de la cornée, alors que ceux produits à partir de surfaces normalisées se distinguent en fonction de l’axe cornéen. La dernière étude présentée dans cette thèse (Chapitre 5) explore différentes techniques d’apprentissage automatique pour prédire la forme de la cornée à partir de données cliniques. La base de données cornéennes a d’abord été traitée par modélisation géométrique (polynômes de Zernike) pour réduire sa dimensionnalité à de courts vecteurs de 12 à 20 coefficients, une fourchette de valeurs potentiellement optimales pour effectuer de bonnes prédictions selon des prétests. Différentes méthodes de régression non-linéaires, tirées de la bibliothèque scikit-learn, ont été testées, incluant gradient boosting, Gaussian process, kernel ridge, random forest, k-nearest neighbors, bagging, et multi-layer perceptron. Les prédicteurs proviennent des variables cliniques disponibles dans la base de données, incluant des variables géométriques (diamètre horizontal de la cornée, profondeur de la chambre cornéenne, côté de l’œil), des variables de réfraction (cylindre, sphère et axe) et des variables démographiques (âge, genre). Un test de régression a été effectué pour chaque modèle de régression, défini comme la sélection d’une des 256 combinaisons possibles de variables cliniques (les prédicteurs), d’une méthode de régression, et d’un vecteur de coefficients de Zernike d’une certaine taille (entre 12 et 20 coefficients, les cibles). Tous les modèles de régression testés ont été évalués à l’aide de score de RMSE établissant la distance entre les surfaces cornéennes prédites (les prédictions) et vraies (les topographies corn¬éennes brutes). Les meilleurs d’entre eux ont été validés sur l’ensemble de données randomisé 20 fois pour déterminer avec plus de précision lequel d’entre eux est le plus performant. Il s’agit de gradient boosting utilisant toutes les variables cliniques comme prédicteurs et 16 coefficients de Zernike comme cibles. Les prédictions de ce modèle ont été évaluées qualitativement à l’aide d’un atlas de cartes d’élévations moyennes élaborées à partir des variables cliniques ayant servi de prédicteurs, qui permet de visualiser les transformations moyennes d’en groupe à l’autre pour chaque variables. Cet atlas a permis d’établir que les cornées prédites moyennes sont remarquablement similaires aux vraies cornées moyennes pour toutes les variables cliniques à l’étude. / This thesis aims to investigate the best conditions in which the anterior corneal surface of normal corneas can be preprocessed, classified and predicted using geometric modeling (GM) and machine learning (ML) techniques. The focus is on the anterior corneal surface, which is the main responsible of the refractive power of the cornea. Dealing with preprocessing, the first study (Chapter 2) examines the conditions in which GM can best be applied to reduce the dimensionality of a dataset of corneal surfaces to be used in ML projects. Four types of geometric models of corneal shape were tested regarding their accuracy and processing time: two polynomial (P) models – Zernike polynomial (ZP) and spherical harmonic polynomial (SHP) models – and two corresponding rational function (R) models – Zernike rational function (ZR) and spherical harmonic rational function (SHR) models. SHP and ZR are both known to be more accurate than ZP as corneal shape models for the same number of coefficients, but which type of model is the most accurate between SHP and ZR? And is an SHR model, which is both an SH model and an R model, even more accurate? Also, does modeling accuracy comes at the cost of the processing time, an important issue for testing large datasets as required in ML projects? Focusing on low J values (number of model coefficients) to address these issues in consideration of dimensionality constraints that apply in ML tasks, it was found, based on a number of evaluation tools, that SH models were both more accurate than their Z counterparts, that R models were both more accurate than their P counterparts and that the SH advantage was more important than the R advantage. Processing time curves as a function of J showed that P models were processed in quasilinear time, R models in polynomial time, and that Z models were fastest than SH models. Therefore, while SHR was the most accurate geometric model, it was the slowest (a problem that can partly be remedied by applying a preoptimization procedure). ZP was the fastest model, and with normal corneas, it remains an interesting option for testing and development, especially for clustering tasks due to its transparent interpretability. The best compromise between accuracy and speed for ML preprocessing is SHP. The classification of corneal shapes with clinical parameters has a long tradition, but the visualization of their effects on the corneal shape with group maps (average elevation maps, standard deviation maps, average difference maps, etc.) is relatively recent. In the second study (Chapter 3), we constructed an atlas of average elevation maps for different clinical variables (including geometric, refraction and demographic variables) that can be instrumental in the evaluation of ML task inputs (datasets) and outputs (predictions, clusters, etc.). A large dataset of normal adult anterior corneal surface topographies recorded in the form of 101×101 elevation matrices was first preprocessed by geometric modeling to reduce the dimensionality of the dataset to a small number of Zernike coefficients found to be optimal for ML tasks. The modeled corneal surfaces of the dataset were then grouped in accordance with the clinical variables available in the dataset transformed into categorical variables. An average elevation map was constructed for each group of corneal surfaces of each clinical variable in their natural (non-normalized) state and in their normalized state by averaging their modeling coefficients to get an average surface and by representing this average surface in reference to the best-fit sphere in a topographic elevation map. To validate the atlas thus constructed in both its natural and normalized modalities, ANOVA tests were conducted for each clinical variable of the dataset to verify their statistical consistency with the literature before verifying whether the corneal shape transformations displayed in the maps were themselves visually consistent. This was the case. The possible uses of such an atlas are discussed. The third study (Chapter 4) is concerned with the use of a dataset of geometrically modeled corneal surfaces in an ML task of clustering. The unsupervised classification of corneal surfaces is recent in ophthalmology. Most of the few existing studies on corneal clustering resort to feature extraction (as opposed to geometric modeling) to achieve the dimensionality reduction of the dataset. The goal is usually to automate the process of corneal diagnosis, for instance by distinguishing irregular corneal surfaces (keratoconus, Fuch, etc.) from normal surfaces and, in some cases, by classifying irregular surfaces into subtypes. Complementary to these corneal clustering studies, the proposed study resorts mainly to geometric modeling to achieve dimensionality reduction and focuses on normal adult corneas in an attempt to identify their natural groupings, possibly in combination with feature extraction methods. Geometric modeling was based on Zernike polynomials, known for their interpretative transparency and sufficiently accurate for normal corneas. Different types of clustering methods were evaluated in pretests to identify the most effective at producing neatly delimitated clusters that are clearly interpretable. Their evaluation was based on clustering scores (to identify the best number of clusters), polar charts and scatter plots (to visualize the modeling coefficients involved in each cluster), average elevation maps and average profile cuts (to visualize the average corneal surface of each cluster), and statistical cluster comparisons on different clinical parameters (to validate the findings in reference to the clinical literature). K-means, applied to geometrically modeled surfaces without feature extraction, produced the best clusters, both for natural and normalized surfaces. While the clusters produced with natural corneal surfaces were based on the corneal curvature, those produced with normalized surfaces were based on the corneal axis. In each case, the best number of clusters was four. The importance of curvature and axis as grouping criteria in corneal data distribution is discussed. The fourth study presented in this thesis (Chapter 5) explores the ML paradigm to verify whether accurate predictions of normal corneal shapes can be made from clinical data, and how. The database of normal adult corneal surfaces was first preprocessed by geometric modeling to reduce its dimensionality into short vectors of 12 to 20 Zernike coefficients, found to be in the range of appropriate numbers to achieve optimal predictions. The nonlinear regression methods examined from the scikit-learn library were gradient boosting, Gaussian process, kernel ridge, random forest, k-nearest neighbors, bagging, and multilayer perceptron. The predictors were based on the clinical variables available in the database, including geometric variables (best-fit sphere radius, white-towhite diameter, anterior chamber depth, corneal side), refraction variables (sphere, cylinder, axis) and demographic variables (age, gender). Each possible combination of regression method, set of clinical variables (used as predictors) and number of Zernike coefficients (used as targets) defined a regression model in a prediction test. All the regression models were evaluated based on their mean RMSE score (establishing the distance between the predicted corneal surfaces and the raw topographic true surfaces). The best model identified was further qualitatively assessed based on an atlas of predicted and true average elevation maps by which the predicted surfaces could be visually compared to the true surfaces on each of the clinical variables used as predictors. It was found that the best regression model was gradient boosting using all available clinical variables as predictors and 16 Zernike coefficients as targets. The most explicative predictor was the best-fit sphere radius, followed by the side and refractive variables. The average elevation maps of the true anterior corneal surfaces and the predicted surfaces based on this model were remarkably similar for each clinical variable.