Low-rank Based Algorithms for Rectification, Repetition Detection and De-noising in Urban Images

In this thesis, we aim to solve the problem of automatic image rectification and repeated patterns detection on 2D urban images, using novel low-rank based techniques. Repeated patterns (such as windows, tiles, balconies and doors) are prominent and significant features in urban scenes. Detection of the periodic structures is useful in many applications such as photorealistic 3D reconstruction, 2D-to-3D alignment, facade parsing, city modeling, classification, navigation, visualization in 3D map environments, shape completion, cinematography and 3D games. However both of the image rectification and repeated patterns detection problems are challenging due to scene occlusions, varying illumination, pose variation and sensor noise. Therefore, detection of these repeated patterns becomes very important for city scene analysis. Given a 2D image of urban scene, we automatically rectify a facade image and extract facade textures first. Based on the rectified facade texture, we exploit novel algorithms that extract repeated patterns by using Kronecker product based modeling that is based on a solid theoretical foundation. We have tested our algorithms in a large set of images, which includes building facades from Paris, Hong Kong and New York

Geometry-driven feature detection

Matching images taken from different viewpoints is a fundamental step for many computer vision applications including 3D reconstruction, scene recognition, virtual reality, robot localization, etc. The typical approaches detect feature keypoints based on local properties to achieve robustness to viewpoint changes, and establish correspondences between keypoints to recover the 3D geometry or determine the similarity between images. The complexity of perspective distortion challenges the detection of viewpoint invariant features; the lack of 3D geometric information about local features makes their matching inefficient. In this thesis, I explore feature detection based on 3D geometric information for improved projective invariance. The main novel research contributions of this thesis are as follows. First, I give a projective invariant feature detection method that exploits 3D structures recovered from simple stereo matching. By leveraging the rich geometric information of the detected features, I present an efficient 3D matching algorithm to handle large viewpoint changes. Second, I propose a compact high-level feature detector that robustly extracts repetitive structures in urban scenes, which allows efficient wide-baseline matching. I further introduce a novel single-view reconstruction approach to recover the 3D dense geometry of the repetition-based features

Unsupervised detection and localization of structural textures using projection profiles

The main goal of existing approaches for structural texture analysis has been the identification of repeating texture primitives and their placement patterns in images containing a single type of texture. We describe a novel unsupervised method for simultaneous detection and localization of multiple structural texture areas along with estimates of their orientations and scales in real images. First, multi-scale isotropic filters are used to enhance the potential texton locations. Then, regularity of the textons is quantified in terms of the periodicity of projection profiles of filter responses within sliding windows at multiple orientations. Next, a regularity index is computed for each pixel as the maximum regularity score together with its orientation and scale. Finally, thresholding of this regularity index produces accurate localization of structural textures in images containing different kinds of textures as well as non-textured areas. Experiments using three different data sets show the effectiveness of the proposed method in complex scenes. © 2010 Elsevier Ltd. All rights reserved

Geometric Transformation Techniques for Digital Images: A Survey

This survey presents a wide collection of algorithms for the geometric transformation of digital images. Efficient image transformation algorithms are critically important to the remote sensing, medical imaging, computer vision, and computer graphics communities. We review the growth of this field and compare all the described algorithms. Since this subject is interdisciplinary, emphasis is placed on the unification of the terminology, motivation, and contributions of each technique to yield a single coherent framework. This paper attempts to serve a dual role as a survey and a tutorial. It is comprehensive in scope and detailed in style. The primary focus centers on the three components that comprise all geometric transformations: spatial transformations, resampling, and antialiasing. In addition, considerable attention is directed to the dramatic progress made in the development of separable algorithms. The text is supplemented with numerous examples and an extensive bibliography

Crystallographic Topology 2: Overview and Work in Progress

This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties

Local, Semi-Local and Global Models for Texture, Object and Scene Recognition

This dissertation addresses the problems of recognizing textures, objects, and scenes in photographs. We present approaches to these recognition tasks that combine salient local image features with spatial relations and effective discriminative learning techniques. First, we introduce a bag of features image model for recognizing textured surfaces under a wide range of transformations, including viewpoint changes and non-rigid deformations. We present results of a large-scale comparative evaluation indicating that bags of features can be effective not only for texture, but also for object categization, even in the presence of substantial clutter and intra-class variation. We also show how to augment the purely local image representation with statistical co-occurrence relations between pairs of nearby features, and develop a learning and classification framework for the task of classifying individual features in a multi-texture image. Next, we present a more structured alternative to bags of features for object recognition, namely, an image representation based on semi-local parts, or groups of features characterized by stable appearance and geometric layout. Semi-local parts are automatically learned from small sets of unsegmented, cluttered images. Finally, we present a global method for recognizing scene categories that works by partitioning the image into increasingly fine sub-regions and computing histograms of local features found inside each sub-region. The resulting spatial pyramid representation demonstrates significantly improved performance on challenging scene categorization tasks

Engineered repeating prints: computer-aided design approaches to achieving continuity of repeating print across a garment using digital engineered print method

This Master’s research investigated approaches for engineering of repeating prints using digital textile printing technology and universally available computer-aided design software. Current practices for alignment of designs in yardage printed fabrics at garment seams are wasteful and do not allow for mass customisation. This inefficiency can be overcome with engineered digital printing, a method that allows for an integration of prints with garment patterns to generate Ready-to-Print images. Engineered printing offers more cost-effective use of materials, improved visual appearance, potential for mass customisation and more sustainable manufacturing. Still, technical difficulties exist in the integration of prints with garment patterns. As a result, application for apparel is limited to non-repeating prints and one-off fashion show garments. The integration of repeating prints presents even more difficulties. However, the advances in digital printing and computer-aided design technologies call for an examination of possible approaches for achieving improved continuity of a repeating print across a garment. The research used a three-stage mixed method approach. The first qualitative stage examined current practices for design and printing of repeating prints. By undertaking Applied Thematic Analysis, the diversity of meanings assigned to words describing attributes of repeating prints as a result of historical and current usage were identified and the terminology consolidated. A taxonomy of repeating print attributes was established, with three levels observed: a superordinate level for a surface, a basic for a repeat, and a subordinate for a motif. Quantifiable attributes of repeating prints were assigned to each level. The analysis also suggested three potential directions for engineered repeating prints: Modularity Design, Flexible Tiling and Distortion. The second quantitative stage evaluated suggested design directions in four experimental studies: one for each of the directions and a final study combining all three directions to engineer repeating prints for a graded garment. Practical computer-aided design techniques, based on accessible Adobe software tools, were developed for integration of repeating prints with garment patterns. The techniques were then tested in comparison with mainstream printing practices. In each experiment, repeating print attributes were examined for their impact on the adaptability of repeating prints for engineered printing. All three directions were validated as suitable for engineering of repeating prints. Statistical analyses revealed relationships between repeating print attributes and their impact on the adaptability of repeating prints for the engineered printing method. The final stage analysed the combined results of the previous two stages. Existing computer- aided design solutions were found to offer opportunities regarding their ability to be integrated into current digital production for innovative and sustainable engineered printing. While the suggested techniques require knowledge of more advanced dynamic editing tools, the research highlights the benefits for both fashion and textile designers to utilise such tools in order to fully embrace the potential digital printing technology has to offer. The research also highlights the need for dedicated software solutions for integration of repeating prints with garment patterns. The findings on the impact of repeating print attributes on the adaptability for engineered printing can help in the development of dedicated software

Optics of polyhedra: from invisibility cloaks to curved spaces

Transformation optics is a new and highly active field of research, which employs the mathematics of differential geometry to design optical materials and devices with unusual properties.Probably the most exciting device proposed by transformation optics is the invisibility cloak. However, transformation optics can be employed in many other cases, for example when designing a setup mimicking a curved space-time phenomena in a lab. The purpose of this thesis is to establish a new concept of transformation optics: instead of designing complicated materials, we will design our devices using standard optical elements such as lenses or optical wedges. We will stretch the possibilities of geometrical optics by providing a novel description of imaging due to combinations of tilted lenses and the theory of invisibility with ideal thin lenses. This theory will be then applied to design novel transformation optics devices, namely the omnidirectional lens and a number of ideal lens invisibility cloaks. We also present a new approach of building optical systems that simulate light-field propagation in both 2D and 3D curved spaces. Instead of building the actual curved space, the light field is regarded to travel in the respective unfolded net, whose edges are optically identified, using the so-called space-cancelling wedges. By deriving a full analytical solution of the Schrodinger equation, we will also investigate a quantum motion in a number of two dimensional compact surfaces including the Klein bottle, Mobius strip and projective plane. We will show that the wavefunction exhibits perfect revivals on these surfaces and that quantum mechanics on many seemingly unphysical surfaces can be realised as simple diffraction experiments. Our work therefore offers a new concept of optical simulation of curved spaces, and potentially represents a new avenue for research of physics in curved spaces and simulating otherwise inaccessible phenomena in non-Euclidean geometries. We conclude with a summary of potential future projects which lead naturally from the results of this thesis