Advanced retinal imaging: Feature extraction, 2-D registration, and 3-D reconstruction

In this dissertation, we have studied feature extraction and multiple view geometry in the context of retinal imaging. Specifically, this research involves three components, i.e., feature extraction, 2-D registration, and 3-D reconstruction. First, the problem of feature extraction is investigated. Features are significantly important in motion estimation techniques because they are the input to the algorithms. We have proposed a feature extraction algorithm for retinal images. Bifurcations/crossovers are used as features. A modified local entropy thresholding algorithm based on a new definition of co-occurrence matrix is proposed. Then, we consider 2-D retinal image registration which is the problem of the transformation of 2-D/2-D. Both linear and nonlinear models are incorporated to account for motions and distortions. A hybrid registration method has been introduced in order to take advantages of both feature-based and area-based methods have offered along with relevant decision-making criteria. Area-based binary mutual information is proposed or translation estimation. A feature-based hierarchical registration technique, which involves the affine and quadratic transformations, is developed. After that, a 3-D retinal surface reconstruction issue has been addressed. To generate a 3-D scene from 2-D images, a camera projection or transformations of 3-D/2-D techniques have been investigated. We choose an affine camera to characterize for 3-D retinal reconstruction. We introduce a constrained optimization procedure which incorporates a geometrically penalty function and lens distortion into the cost function. The procedure optimizes all of the parameters, camera's parameters, 3-D points, the physical shape of human retina, and lens distortion, simultaneously. Then, a point-based spherical fitting method is introduced. The proposed retinal imaging techniques will pave the path to a comprehensive visual 3-D retinal model for many medical applications

Study of Computational Image Matching Techniques: Improving Our View of Biomedical Image Data

Image matching techniques are proven to be necessary in various fields of science and engineering, with many new methods and applications introduced over the years. In this PhD thesis, several computational image matching methods are introduced and investigated for improving the analysis of various biomedical image data. These improvements include the use of matching techniques for enhancing visualization of cross-sectional imaging modalities such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), denoising of retinal Optical Coherence Tomography (OCT), and high quality 3D reconstruction of surfaces from Scanning Electron Microscope (SEM) images. This work greatly improves the process of data interpretation of image data with far reaching consequences for basic sciences research. The thesis starts with a general notion of the problem of image matching followed by an overview of the topics covered in the thesis. This is followed by introduction and investigation of several applications of image matching/registration in biomdecial image processing: a) registration-based slice interpolation, b) fast mesh-based deformable image registration and c) use of simultaneous rigid registration and Robust Principal Component Analysis (RPCA) for speckle noise reduction of retinal OCT images. Moving towards a different notion of image matching/correspondence, the problem of view synthesis and 3D reconstruction, with a focus on 3D reconstruction of microscopic samples from 2D images captured by SEM, is considered next. Starting from sparse feature-based matching techniques, an extensive analysis is provided for using several well-known feature detector/descriptor techniques, namely ORB, BRIEF, SURF and SIFT, for the problem of multi-view 3D reconstruction. This chapter contains qualitative and quantitative comparisons in order to reveal the shortcomings of the sparse feature-based techniques. This is followed by introduction of a novel framework using sparse-dense matching/correspondence for high quality 3D reconstruction of SEM images. As will be shown, the proposed framework results in better reconstructions when compared with state-of-the-art sparse-feature based techniques. Even though the proposed framework produces satisfactory results, there is room for improvements. These improvements become more necessary when dealing with higher complexity microscopic samples imaged by SEM as well as in cases with large displacements between corresponding points in micrographs. Therefore, based on the proposed framework, a new approach is proposed for high quality 3D reconstruction of microscopic samples. While in case of having simpler microscopic samples the performance of the two proposed techniques are comparable, the new technique results in more truthful reconstruction of highly complex samples. The thesis is concluded with an overview of the thesis and also pointers regarding future directions of the research using both multi-view and photometric techniques for 3D reconstruction of SEM images

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed

Iterative Solvers for Physics-based Simulations and Displays

La génération d’images et de simulations réalistes requiert des modèles complexes pour capturer tous les détails d’un phénomène physique. Les équations mathématiques qui composent ces modèles sont compliquées et ne peuvent pas être résolues analytiquement. Des procédures numériques doivent donc être employées pour obtenir des solutions approximatives à ces modèles. Ces procédures sont souvent des algorithmes itératifs, qui calculent une suite convergente vers la solution désirée à partir d’un essai initial. Ces méthodes sont une façon pratique et efficace de calculer des solutions à des systèmes complexes, et sont au coeur de la plupart des méthodes de simulation modernes. Dans cette thèse par article, nous présentons trois projets où les algorithmes itératifs jouent un rôle majeur dans une méthode de simulation ou de rendu. Premièrement, nous présentons une méthode pour améliorer la qualité visuelle de simulations fluides. En créant une surface de haute résolution autour d’une simulation existante, stabilisée par une méthode itérative, nous ajoutons des détails additionels à la simulation. Deuxièmement, nous décrivons une méthode de simulation fluide basée sur la réduction de modèle. En construisant une nouvelle base de champ de vecteurs pour représenter la vélocité d’un fluide, nous obtenons une méthode spécifiquement adaptée pour améliorer les composantes itératives de la simulation. Finalement, nous présentons un algorithme pour générer des images de haute qualité sur des écrans multicouches dans un contexte de réalité virtuelle. Présenter des images sur plusieurs couches demande des calculs additionels à coût élevé, mais nous formulons le problème de décomposition des images afin de le résoudre efficacement avec une méthode itérative simple.Realistic computer-generated images and simulations require complex models to properly capture the many subtle behaviors of each physical phenomenon. The mathematical equations underlying these models are complicated, and cannot be solved analytically. Numerical procedures must thus be used to obtain approximate solutions. These procedures are often iterative algorithms, where an initial guess is progressively improved to converge to a desired solution. Iterative methods are a convenient and efficient way to compute solutions to complex systems, and are at the core of most modern simulation methods. In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm

Multimodal Three Dimensional Scene Reconstruction, The Gaussian Fields Framework

The focus of this research is on building 3D representations of real world scenes and objects using different imaging sensors. Primarily range acquisition devices (such as laser scanners and stereo systems) that allow the recovery of 3D geometry, and multi-spectral image sequences including visual and thermal IR images that provide additional scene characteristics. The crucial technical challenge that we addressed is the automatic point-sets registration task. In this context our main contribution is the development of an optimization-based method at the core of which lies a unified criterion that solves simultaneously for the dense point correspondence and transformation recovery problems. The new criterion has a straightforward expression in terms of the datasets and the alignment parameters and was used primarily for 3D rigid registration of point-sets. However it proved also useful for feature-based multimodal image alignment. We derived our method from simple Boolean matching principles by approximation and relaxation. One of the main advantages of the proposed approach, as compared to the widely used class of Iterative Closest Point (ICP) algorithms, is convexity in the neighborhood of the registration parameters and continuous differentiability, allowing for the use of standard gradient-based optimization techniques. Physically the criterion is interpreted in terms of a Gaussian Force Field exerted by one point-set on the other. Such formulation proved useful for controlling and increasing the region of convergence, and hence allowing for more autonomy in correspondence tasks. Furthermore, the criterion can be computed with linear complexity using recently developed Fast Gauss Transform numerical techniques. In addition, we also introduced a new local feature descriptor that was derived from visual saliency principles and which enhanced significantly the performance of the registration algorithm. The resulting technique was subjected to a thorough experimental analysis that highlighted its strength and showed its limitations. Our current applications are in the field of 3D modeling for inspection, surveillance, and biometrics. However, since this matching framework can be applied to any type of data, that can be represented as N-dimensional point-sets, the scope of the method is shown to reach many more pattern analysis applications

Generalizable automated pixel-level structural segmentation of medical and biological data

Over the years, the rapid expansion in imaging techniques and equipments has driven the demand for more automation in handling large medical and biological data sets. A wealth of approaches have been suggested as optimal solutions for their respective imaging types. These solutions span various image resolutions, modalities and contrast (staining) mechanisms. Few approaches generalise well across multiple image types, contrasts or resolution. This thesis proposes an automated pixel-level framework that addresses 2D, 2D+t and 3D structural segmentation in a more generalizable manner, yet has enough adaptability to address a number of specific image modalities, spanning retinal funduscopy, sequential fluorescein angiography and two-photon microscopy. The pixel-level segmentation scheme involves: i ) constructing a phase-invariant orientation field of the local spatial neighbourhood; ii ) combining local feature maps with intensity-based measures in a structural patch context; iii ) using a complex supervised learning process to interpret the combination of all the elements in the patch in order to reach a classification decision. This has the advantage of transferability from retinal blood vessels in 2D to neural structures in 3D. To process the temporal components in non-standard 2D+t retinal angiography sequences, we first introduce a co-registration procedure: at the pairwise level, we combine projective RANSAC with a quadratic homography transformation to map the coordinate systems between any two frames. At the joint level, we construct a hierarchical approach in order for each individual frame to be registered to the global reference intra- and inter- sequence(s). We then take a non-training approach that searches in both the spatial neighbourhood of each pixel and the filter output across varying scales to locate and link microvascular centrelines to (sub-) pixel accuracy. In essence, this \link while extract" piece-wise segmentation approach combines the local phase-invariant orientation field information with additional local phase estimates to obtain a soft classification of the centreline (sub-) pixel locations. Unlike retinal segmentation problems where vasculature is the main focus, 3D neural segmentation requires additional exibility, allowing a variety of structures of anatomical importance yet with different geometric properties to be differentiated both from the background and against other structures. Notably, cellular structures, such as Purkinje cells, neural dendrites and interneurons, all display certain elongation along their medial axes, yet each class has a characteristic shape captured by an orientation field that distinguishes it from other structures. To take this into consideration, we introduce a 5D orientation mapping to capture these orientation properties. This mapping is incorporated into the local feature map description prior to a learning machine. Extensive performance evaluations and validation of each of the techniques presented in this thesis is carried out. For retinal fundus images, we compute Receiver Operating Characteristic (ROC) curves on existing public databases (DRIVE & STARE) to assess and compare our algorithms with other benchmark methods. For 2D+t retinal angiography sequences, we compute the error metrics ("Centreline Error") of our scheme with other benchmark methods. For microscopic cortical data stacks, we present segmentation results on both surrogate data with known ground-truth and experimental rat cerebellar cortex two-photon microscopic tissue stacks.Open Acces

Higher-Order Regularization in Computer Vision

At the core of many computer vision models lies the minimization of an objective function consisting of a sum of functions with few arguments. The order of the objective function is defined as the highest number of arguments of any summand. To reduce ambiguity and noise in the solution, regularization terms are included into the objective function, enforcing different properties of the solution. The most commonly used regularization is penalization of boundary length, which requires a second-order objective function. Most of this thesis is devoted to introducing higher-order regularization terms and presenting efficient minimization schemes. One of the topics of the thesis covers a reformulation of a large class of discrete functions into an equivalent form. The reformulation is shown, both in theory and practical experiments, to be advantageous for higher-order regularization models based on curvature and second-order derivatives. Another topic is the parametric max-flow problem. An analysis is given, showing its inherent limitations for large-scale problems which are common in computer vision. The thesis also introduces a segmentation approach for finding thin and elongated structures in 3D volumes. Using a line-graph formulation, it is shown how to efficiently regularize with respect to higher-order differential geometric properties such as curvature and torsion. Furthermore, an efficient optimization approach for a multi-region model is presented which, in addition to standard regularization, is able to enforce geometric constraints such as inclusion or exclusion of different regions. The final part of the thesis deals with dense stereo estimation. A new regularization model is introduced, penalizing the second-order derivatives of a depth or disparity map. Compared to previous second-order approaches to dense stereo estimation, the new regularization model is shown to be more easily optimized