Practical and Optimal LSH for Angular Distance

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.Comment: 22 pages, an extended abstract is to appear in the proceedings of the 29th Annual Conference on Neural Information Processing Systems (NIPS 2015

Model-driven and Data-driven Approaches for some Object Recognition Problems

Recognizing objects from images and videos has been a long standing problem in computer vision. The recent surge in the prevalence of visual cameras has given rise to two main challenges where, (i) it is important to understand different sources of object variations in more unconstrained scenarios, and (ii) rather than describing an object in isolation, efficient learning methods for modeling object-scene `contextual' relations are required to resolve visual ambiguities. This dissertation addresses some aspects of these challenges, and consists of two parts. First part of the work focuses on obtaining object descriptors that are largely preserved across certain sources of variations, by utilizing models for image formation and local image features. Given a single instance of an object, we investigate the following three problems. (i) Representing a 2D projection of a 3D non-planar shape invariant to articulations, when there are no self-occlusions. We propose an articulation invariant distance that is preserved across piece-wise affine transformations of a non-rigid object `parts', under a weak perspective imaging model, and then obtain a shape context-like descriptor to perform recognition; (ii) Understanding the space of `arbitrary' blurred images of an object, by representing an unknown blur kernel of a known maximum size using a complete set of orthonormal basis functions spanning that space, and showing that subspaces resulting from convolving a clean object and its blurred versions with these basis functions are equal under some assumptions. We then view the invariant subspaces as points on a Grassmann manifold, and use statistical tools that account for the underlying non-Euclidean nature of the space of these invariants to perform recognition across blur; (iii) Analyzing the robustness of local feature descriptors to different illumination conditions. We perform an empirical study of these descriptors for the problem of face recognition under lighting change, and show that the direction of image gradient largely preserves object properties across varying lighting conditions. The second part of the dissertation utilizes information conveyed by large quantity of data to learn contextual information shared by an object (or an entity) with its surroundings. (i) We first consider a supervised two-class problem of detecting lane markings from road video sequences, where we learn relevant feature-level contextual information through a machine learning algorithm based on boosting. We then focus on unsupervised object classification scenarios where, (ii) we perform clustering using maximum margin principles, by deriving some basic properties on the affinity of `a pair of points' belonging to the same cluster using the information conveyed by `all' points in the system, and (iii) then consider correspondence-free adaptation of statistical classifiers across domain shifting transformations, by generating meaningful `intermediate domains' that incrementally convey potential information about the domain change

Bayesian MCMC estimation of the rose of directions

summary:The paper concerns estimation of the rose of directions of a stationary fibre process in $R^3$ from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is shown. Properties of the estimation method are studied both theoretically and by simulation

Kaleidoscopic imaging

Kaleidoscopes have a great potential in computational photography as a tool for redistributing light rays. In time-of-flight imaging the concept of the kaleidoscope is also useful when dealing with the reconstruction of the geometry that causes multiple reflections. This work is a step towards opening new possibilities for the use of mirror systems as well as towards making their use more practical. The focus of this work is the analysis of planar kaleidoscope systems to enable their practical applicability in 3D imaging tasks. We analyse important practical properties of mirror systems and develop a theoretical toolbox for dealing with planar kaleidoscopes. Based on this theoretical toolbox we explore the use of planar kaleidoscopes for multi-view imaging and for the acquisition of 3D objects. The knowledge of the mirrors positions is crucial for these multi-view applications. On the other hand, the reconstruction of the geometry of a mirror room from time-of-flight measurements is also an important problem. We therefore employ the developed tools for solving this problem using multiple observations of a single scene point.Kaleidoskope haben in der rechnergestützten Fotografie ein großes Anwendungspotenzial, da sie flexibel zur Umverteilung von Lichtstrahlen genutzt werden können. Diese Arbeit ist ein Schritt auf dem Weg zu neuen Einsatzmöglichkeiten von Spiegelsystemen und zu ihrer praktischen Anwendung. Das Hauptaugenmerk der Arbeit liegt dabei auf der Analyse planarer Spiegelsysteme mit dem Ziel, sie für Aufgaben in der 3D-Bilderzeugung praktisch nutzbar zu machen. Auch für die Time-of-flight-Technologie ist das Konzept des Kaleidoskops, wie in der Arbeit gezeigt wird, bei der Rekonstruktion von Mehrfachreflektionen erzeugender Geometrie von Nutzen. In der Arbeit wird ein theoretischer Ansatz entwickelt der die Analyse planarer Kaleidoskope stark vereinfacht. Mithilfe dieses Ansatzes wird der Einsatz planarer Spiegelsysteme im Multiview Imaging und bei der Erfassung von 3-D-Objekten untersucht. Das Wissen um die Spiegelpositionen innerhalb des Systems ist für diese Anwendungen entscheidend und erfordert die Entwicklung geeigneter Methoden zur Kalibrierung dieser Positionen. Ein ähnliches Problem tritt in Time-of-Flight Anwendungen bei der, oft unerwünschten, Aufnahme von Mehrfachreflektionen auf. Beide Problemstellungen lassen sich auf die Rekonstruktion der Geometrie eines Spiegelraums zurückführen, das mit Hilfe des entwickelten Ansatzes in allgemeinererWeise als bisher gelöst werden kann

Grasp planning in discrete domain.

by Lam Miu-Ling.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 64-67).Abstracts in English and Chinese.Chapter Chapter 1. --- Introduction --- p.1Chapter Chapter 2. --- Mathematical Preliminaries and Problem Definition --- p.6Chapter 2.1 --- Grasp Synthesis in Discrete DomainChapter 2.2 --- AssumptionsChapter 2.3 --- Frictionless Form-Closure GraspChapter 2.4 --- Frictional Form-Closure GraspChapter 2.5 --- Problem DefinitionChapter Chapter 3. --- A Qualitative Test Algorithm and a Local Search Algorithm --- p.18Chapter 3.1 --- A Qualitative Test AlgorithmChapter 3.2 --- A Local Search AlgorithmChapter 3.3 --- Grasp Planning under Kinematic ConstraintsChapter Chapter 4. --- A Divide-and-Conquer Technique --- p.29Chapter 4.1. --- Determining a Separating HyperplaneChapter 4.2. --- Divide-and-Conquer in Frictionless CaseChapter 4.3. --- Divide-and-Conquer in Frictional CaseChapter Chapter 5. --- Implementation and Examples --- p.40Chapter 6.1. --- Examples of Frictionless GraspsChapter 6.2. --- Examples of Frictional GraspsChapter 6.3. --- Examples of Grasps under Kinematic ConstraintsChapter Chapter 6. --- Conclusions --- p.62Bibliography --- p.6