Measuring Deformations and Illumination Changes in Images with Applications to Face Recognition

This thesis explores object deformation and lighting change in images, proposing methods that account for both variabilities within a single framework. We construct a deformation- and lighting-insensitive metric that assigns a cost to a pair of images based on their similarity. The primary applications discussed will be in the domain of face recognition, because faces provide a good and important example of highly structured yet deformable objects with readily available datasets. However, our methods can be applied to any domain with deformations and lighting change. In order to model variations in expression, establishing point correspondences between faces is essential, and a primary goal of this thesis is to determine dense correspondences between pairs of face images, assigning a cost to each point pairing based on a novel image metric. We show that an image manifold can be defined to model deformations and illumination changes. Images are considered as points on a high-dimensional manifold given local structure by our new metric, where costs are based on changes in shape and intensity. Curves on this manifold describe transformations such as deformations and lighting changes to connect nearby images, or larger identity changes connecting images far apart. This allows deformations to be introduced gradually over the course of several images, where correspondences are well-defined between every pair of adjacent images along a path. The similarity between two images on the manifold can be defined as the length of the geodesic that connects them. The new local metric is validated in an optical flow-like framework where it is used to determine a dense correspondence vector field between pairs of images. We then demonstrate how to find geodesics between pairs of images on a Riemannian image manifold. The new lighting-insensitive metric is described in the wavelet domain where it is able to handle moderate amounts of deformation, and allows us to derive an algorithm where the analytic geodesics between images can be computed extremely efficiently. To handle larger deformations in addition to changes in illumination, we consider an algorithmic framework where deformations are modeled with diffeomorphisms. We present preliminary implementations of the diffeomorphic framework, and suggest how this work can be extended for further applications

Rekonstruktion und skalierbare Detektion und Verfolgung von 3D Objekten

The task of detecting objects in images is essential for autonomous systems to categorize, comprehend and eventually navigate or manipulate its environment. Since many applications demand not only detection of objects but also the estimation of their exact poses, 3D CAD models can prove helpful since they provide means for feature extraction and hypothesis refinement. This work, therefore, explores two paths: firstly, we will look into methods to create richly-textured and geometrically accurate models of real-life objects. Using these reconstructions as a basis, we will investigate on how to improve in the domain of 3D object detection and pose estimation, focusing especially on scalability, i.e. the problem of dealing with multiple objects simultaneously.Objekterkennung in Bildern ist für ein autonomes System von entscheidender Bedeutung, um seine Umgebung zu kategorisieren, zu erfassen und schließlich zu navigieren oder zu manipulieren. Da viele Anwendungen nicht nur die Erkennung von Objekten, sondern auch die Schätzung ihrer exakten Positionen erfordern, können sich 3D-CAD-Modelle als hilfreich erweisen, da sie Mittel zur Merkmalsextraktion und Verfeinerung von Hypothesen bereitstellen. In dieser Arbeit werden daher zwei Wege untersucht: Erstens werden wir Methoden untersuchen, um strukturreiche und geometrisch genaue Modelle realer Objekte zu erstellen. Auf der Grundlage dieser Konstruktionen werden wir untersuchen, wie sich der Bereich der 3D-Objekterkennung und der Posenschätzung verbessern lässt, wobei insbesondere die Skalierbarkeit im Vordergrund steht, d.h. das Problem der gleichzeitigen Bearbeitung mehrerer Objekte

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments

Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance