A Computational Framework for the Structural Change Analysis of 3D Volumes of Microscopic Specimens

Glaucoma, commonly observed with an elevation in the intraocular pressure level (IOP), is one of the leading causes of blindness. The lamina cribrosa is a mesh-like structure that provides axonal support for the optic nerves leaving the eye. The changes in the laminar structure under IOP elevations may result in the deaths of retinal ganglion cells, leading to vision degradation and loss. We have developed a comprehensive computational framework that can assist the study of structural changes in microscopic structures such as lamina cribrosa. The optical sectioning property of a confocal microscope facilitates imaging thick microscopic specimen at various depths without physical sectioning. The confocal microscope images are referred to as optical sections. The computational framework developed includes: 1) a multi-threaded system architecture for tracking a volume-of-interest within a microscopic specimen in a parallel computation environment using a reliable-multicast for collective-communication operations 2) a Karhunen-Loève (KL) expansion based adaptive noise prefilter for the restoration of the optical sections using an inverse restoration method 3) a morphological operator based ringing metric to quantify the ringing artifacts introduced during iterative restoration of optical sections 4) a l2 norm based error metric to evaluate the performance of optical flow algorithms without a priori knowledge of the true motion field and 5) a Compute-and-Propagate (CNP) framework for iterative optical flow algorithms. The realtime tracking architecture can convert a 2D-confocal microscope into a 4D-confocal microscope with tracking. The adaptive KL filter is suitable for realtime restoration of optical sections. The CNP framework significantly improves the speed and convergence of the iterative optical flow algorithms. Also, the CNP framework can reduce the errors in the motion field estimates due to the aperture problem. The performance of the proposed framework is demonstrated on real-life image sequences and on z-Stack datasets of random cotton fibers and lamina cribrosa of a cow retina with an experimentally induced glaucoma. The proposed framework can be used for routine laboratory and clinical investigation of microstructures such as cells and tissues, for the evaluation of complex structures such as cornea and has potential use as a surgical guidance tool

Résolution du problème de transfert de chaleur par une approche TAC : application au traitement et à l'analyse des images

Nous proposons une alternative aux équations aux dérivées partielles (EDP) en vue de solutionner certains problèmes en traitement d'images qui sont basés sur un modèle de transfert de chaleur. Traditionnellement , la démarche pour solutionner de tels problèmes basés sur un modèle de champs physiques est de discrétiser et de solutionner une EDP par un procédé purement mathématique. Au lieu de l'EDP, nous proposons d'utiliser une approche qui consiste à décomposer en lois de base, le principe global de conservation de chaleur. Nous montrons que certaines de ces lois admettent une version globale et exacte puisqu'elles proviennent de principes conservateurs. Nous montrons également que les hypothèses sur les autres lois de base peuvent être faites de façon avisée, en tenant compte de certaines connaissances sur le problème et le domaine. Nous utilisons un modèle d'images basé sur la topologie algébrique calculatoire qui nous permet d'encoder simplement les lois de conservation en liant une valeur globale sur un domaine avec des valeurs sur les frontières de ce domaine. Le schéma numérique est dérivé directement du problème modélisé. Ce procédé fournit une explication physique de chaque étape de la résolution. Nous appliquons ce schéma à plusieurs problèmes de traitement d'images qui sont tous régis par le transfert de chaleur : la reconstruction d'images à partir du Laplacien, le calcul du flot optique, le débruitage par diffusion des niveaux de gris et des couleurs ainsi que la retouche d'images ( «inpainting» ).Abstract: This thesis proposes an alternative to partial differential equations (PDEs) for the solution of some problems in computer vision based on the heat transfer equation. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a purely mathematical process. Instead of using the PDE, we propose to use the global heat equation and to decompose it into basic laws. We show that some of these laws admit an exact global version since they arise from balance principles. We also show that the assumptions made on the other basic laws can be made wisely, taking into account knowledge about the problem and the domain. We use a computational algebraic topology-based image model which allows us to encode a physical conservative law by linking a global value on a domain with values on its boundary. The numerical scheme is derived in a straightforward way from the problem modeled. It thus provides a physical explanation of each solving step in the solution. We apply the scheme to various applications: image reconstruction from the Laplacian, optical flow computation, denoising by graylevel and multispectral diffusion and inpainting which are all modeled with the heat transfer equation