Persistent Homology Tools for Image Analysis

Topological Data Analysis (TDA) is a new field of mathematics emerged rapidly since the first decade of the century from various works of algebraic topology and geometry. The goal of TDA and its main tool of persistent homology (PH) is to provide topological insight into complex and high dimensional datasets. We take this premise onboard to get more topological insight from digital image analysis and quantify tiny low-level distortion that are undetectable except possibly by highly trained persons. Such image distortion could be caused intentionally (e.g. by morphing and steganography) or naturally in abnormal human tissue/organ scan images as a result of onset of cancer or other diseases. The main objective of this thesis is to design new image analysis tools based on persistent homological invariants representing simplicial complexes on sets of pixel landmarks over a sequence of distance resolutions. We first start by proposing innovative automatic techniques to select image pixel landmarks to build a variety of simplicial topologies from a single image. Effectiveness of each image landmark selection demonstrated by testing on different image tampering problems such as morphed face detection, steganalysis and breast tumour detection. Vietoris-Rips simplicial complexes constructed based on the image landmarks at an increasing distance threshold and topological (homological) features computed at each threshold and summarized in a form known as persistent barcodes. We vectorise the space of persistent barcodes using a technique known as persistent binning where we demonstrated the strength of it for various image analysis purposes. Different machine learning approaches are adopted to develop automatic detection of tiny texture distortion in many image analysis applications. Homological invariants used in this thesis are the 0 and 1 dimensional Betti numbers. We developed an innovative approach to design persistent homology (PH) based algorithms for automatic detection of the above described types of image distortion. In particular, we developed the first PH-detector of morphing attacks on passport face biometric images. We shall demonstrate significant accuracy of 2 such morph detection algorithms with 4 types of automatically extracted image landmarks: Local Binary patterns (LBP), 8-neighbour super-pixels (8NSP), Radial-LBP (R-LBP) and centre-symmetric LBP (CS-LBP). Using any of these techniques yields several persistent barcodes that summarise persistent topological features that help gaining insights into complex hidden structures not amenable by other image analysis methods. We shall also demonstrate significant success of a similarly developed PH-based universal steganalysis tool capable for the detection of secret messages hidden inside digital images. We also argue through a pilot study that building PH records from digital images can differentiate breast malignant tumours from benign tumours using digital mammographic images. The research presented in this thesis creates new opportunities to build real applications based on TDA and demonstrate many research challenges in a variety of image processing/analysis tasks. For example, we describe a TDA-based exemplar image inpainting technique (TEBI), superior to existing exemplar algorithm, for the reconstruction of missing image regions

How Not to Be Seen -- Inpainting Dynamic Objects in Crowded Scenes

Removing dynamic objects from videos is an extremely challenging problem that even visual effects professionals often solve with time-consuming manual frame-by-frame editing. We propose a new approach to video completion that can deal with complex scenes containing dynamic background and non-periodical moving objects. We build upon the idea that the spatio-temporal hole left by a removed object can be filled with data available on other regions of the video where the occluded objects were visible. Video completion is performed by solving a large combinatorial problem that searches for an optimal pattern of pixel offsets from occluded to unoccluded regions. Our contribution includes an energy functional that generalizes well over different scenes with stable parameters, and that has the desirable convergence properties for a graph-cut-based optimization. We provide an interface to guide the completion process that both reduces computation time and allows for efficient correction of small errors in the result. We demonstrate that our approach can effectively complete complex, high-resolution occlusions that are greater in difficulty than what existing methods have shown

Understanding and advancing PDE-based image compression

This thesis is dedicated to image compression with partial differential equations (PDEs). PDE-based codecs store only a small amount of image points and propagate their information into the unknown image areas during the decompression step. For certain classes of images, PDE-based compression can already outperform the current quasi-standard, JPEG2000. However, the reasons for this success are not yet fully understood, and PDE-based compression is still in a proof-of-concept stage. With a probabilistic justification for anisotropic diffusion, we contribute to a deeper insight into design principles for PDE-based codecs. Moreover, by analysing the interaction between efficient storage methods and image reconstruction with diffusion, we can rank PDEs according to their practical value in compression. Based on these observations, we advance PDE-based compression towards practical viability: First, we present a new hybrid codec that combines PDE- and patch-based interpolation to deal with highly textured images. Furthermore, a new video player demonstrates the real-time capacities of PDE-based image interpolation and a new region of interest coding algorithm represents important image areas with high accuracy. Finally, we propose a new framework for diffusion-based image colourisation that we use to build an efficient codec for colour images. Experiments on real world image databases show that our new method is qualitatively competitive to current state-of-the-art codecs.Diese Dissertation ist der Bildkompression mit partiellen Differentialgleichungen (PDEs, partial differential equations) gewidmet. PDE-Codecs speichern nur einen geringen Anteil aller Bildpunkte und transportieren deren Information in fehlende Bildregionen. In einigen Fällen kann PDE-basierte Kompression den aktuellen Quasi-Standard, JPEG2000, bereits schlagen. Allerdings sind die Gründe für diesen Erfolg noch nicht vollständig erforscht, und PDE-basierte Kompression befindet sich derzeit noch im Anfangsstadium. Wir tragen durch eine probabilistische Rechtfertigung anisotroper Diffusion zu einem tieferen Verständnis PDE-basierten Codec-Designs bei. Eine Analyse der Interaktion zwischen effizienten Speicherverfahren und Bildrekonstruktion erlaubt es uns, PDEs nach ihrem Nutzen für die Kompression zu beurteilen. Anhand dieser Einsichten entwickeln wir PDE-basierte Kompression hinsichtlich ihrer praktischen Nutzbarkeit weiter: Wir stellen einen Hybrid-Codec für hochtexturierte Bilder vor, der umgebungsbasierte Interpolation mit PDEs kombiniert. Ein neuer Video-Dekodierer demonstriert die Echtzeitfähigkeit PDE-basierter Interpolation und eine Region-of-Interest-Methode erlaubt es, wichtige Bildbereiche mit hoher Genauigkeit zu speichern. Schlussendlich stellen wir ein neues diffusionsbasiertes Kolorierungsverfahren vor, welches uns effiziente Kompression von Farbbildern ermöglicht. Experimente auf Realwelt-Bilddatenbanken zeigen die Konkurrenzfähigkeit dieses Verfahrens auf

Understanding and advancing PDE-based image compression

This thesis is dedicated to image compression with partial differential equations (PDEs). PDE-based codecs store only a small amount of image points and propagate their information into the unknown image areas during the decompression step. For certain classes of images, PDE-based compression can already outperform the current quasi-standard, JPEG2000. However, the reasons for this success are not yet fully understood, and PDE-based compression is still in a proof-of-concept stage. With a probabilistic justification for anisotropic diffusion, we contribute to a deeper insight into design principles for PDE-based codecs. Moreover, by analysing the interaction between efficient storage methods and image reconstruction with diffusion, we can rank PDEs according to their practical value in compression. Based on these observations, we advance PDE-based compression towards practical viability: First, we present a new hybrid codec that combines PDE- and patch-based interpolation to deal with highly textured images. Furthermore, a new video player demonstrates the real-time capacities of PDE-based image interpolation and a new region of interest coding algorithm represents important image areas with high accuracy. Finally, we propose a new framework for diffusion-based image colourisation that we use to build an efficient codec for colour images. Experiments on real world image databases show that our new method is qualitatively competitive to current state-of-the-art codecs.Diese Dissertation ist der Bildkompression mit partiellen Differentialgleichungen (PDEs, partial differential equations) gewidmet. PDE-Codecs speichern nur einen geringen Anteil aller Bildpunkte und transportieren deren Information in fehlende Bildregionen. In einigen Fällen kann PDE-basierte Kompression den aktuellen Quasi-Standard, JPEG2000, bereits schlagen. Allerdings sind die Gründe für diesen Erfolg noch nicht vollständig erforscht, und PDE-basierte Kompression befindet sich derzeit noch im Anfangsstadium. Wir tragen durch eine probabilistische Rechtfertigung anisotroper Diffusion zu einem tieferen Verständnis PDE-basierten Codec-Designs bei. Eine Analyse der Interaktion zwischen effizienten Speicherverfahren und Bildrekonstruktion erlaubt es uns, PDEs nach ihrem Nutzen für die Kompression zu beurteilen. Anhand dieser Einsichten entwickeln wir PDE-basierte Kompression hinsichtlich ihrer praktischen Nutzbarkeit weiter: Wir stellen einen Hybrid-Codec für hochtexturierte Bilder vor, der umgebungsbasierte Interpolation mit PDEs kombiniert. Ein neuer Video-Dekodierer demonstriert die Echtzeitfähigkeit PDE-basierter Interpolation und eine Region-of-Interest-Methode erlaubt es, wichtige Bildbereiche mit hoher Genauigkeit zu speichern. Schlussendlich stellen wir ein neues diffusionsbasiertes Kolorierungsverfahren vor, welches uns effiziente Kompression von Farbbildern ermöglicht. Experimente auf Realwelt-Bilddatenbanken zeigen die Konkurrenzfähigkeit dieses Verfahrens auf

Structure-aware image denoising, super-resolution, and enhancement methods

Denoising, super-resolution and structure enhancement are classical image processing applications. The motive behind their existence is to aid our visual analysis of raw digital images. Despite tremendous progress in these fields, certain difficult problems are still open to research. For example, denoising and super-resolution techniques which possess all the following properties, are very scarce: They must preserve critical structures like corners, should be robust to the type of noise distribution, avoid undesirable artefacts, and also be fast. The area of structure enhancement also has an unresolved issue: Very little efforts have been put into designing models that can tackle anisotropic deformations in the image acquisition process. In this thesis, we design novel methods in the form of partial differential equations, patch-based approaches and variational models to overcome the aforementioned obstacles. In most cases, our methods outperform the existing approaches in both quality and speed, despite being applicable to a broader range of practical situations.Entrauschen, Superresolution und Strukturverbesserung sind klassische Anwendungen der Bildverarbeitung. Ihre Existenz bedingt sich in dem Bestreben, die visuelle Begutachtung digitaler Bildrohdaten zu unterstützen. Trotz erheblicher Fortschritte in diesen Feldern bedürfen bestimmte schwierige Probleme noch weiterer Forschung. So sind beispielsweise Entrauschungsund Superresolutionsverfahren, welche alle der folgenden Eingenschaften besitzen, sehr selten: die Erhaltung wichtiger Strukturen wie Ecken, Robustheit bezüglich der Rauschverteilung, Vermeidung unerwünschter Artefakte und niedrige Laufzeit. Auch im Gebiet der Strukturverbesserung liegt ein ungelöstes Problem vor: Bisher wurde nur sehr wenig Forschungsaufwand in die Entwicklung von Modellen investieret, welche anisotrope Deformationen in bildgebenden Verfahren bewältigen können. In dieser Arbeit entwerfen wir neue Methoden in Form von partiellen Differentialgleichungen, patch-basierten Ansätzen und Variationsmodellen um die oben erwähnten Hindernisse zu überwinden. In den meisten Fällen übertreffen unsere Methoden nicht nur qualitativ die bisher verwendeten Ansätze, sondern lösen die gestellten Aufgaben auch schneller. Zudem decken wir mit unseren Modellen einen breiteren Bereich praktischer Fragestellungen ab

Beyond the pixels: learning and utilising video compression features for localisation of digital tampering.

Video compression is pervasive in digital society. With rising usage of deep convolutional neural networks (CNNs) in the fields of computer vision, video analysis and video tampering detection, it is important to investigate how patterns invisible to human eyes may be influencing modern computer vision techniques and how they can be used advantageously. This work thoroughly explores how video compression influences accuracy of CNNs and shows how optimal performance is achieved when compression levels in the training set closely match those of the test set. A novel method is then developed, using CNNs, to derive compression features directly from the pixels of video frames. It is then shown that these features can be readily used to detect inauthentic video content with good accuracy across multiple different video tampering techniques. Moreover, the ability to explain these features allows predictions to be made about their effectiveness against future tampering methods. The problem is motivated with a novel investigation into recent video manipulation methods, which shows that there is a consistent drive to produce convincing, photorealistic, manipulated or synthetic video. Humans, blind to the presence of video tampering, are also blind to the type of tampering. New detection techniques are required and, in order to compensate for human limitations, they should be broadly applicable to multiple tampering types. This thesis details the steps necessary to develop and evaluate such techniques

Exemplar-based Video Colorization with Long-term Spatiotemporal Dependency

Exemplar-based video colorization is an essential technique for applications like old movie restoration. Although recent methods perform well in still scenes or scenes with regular movement, they always lack robustness in moving scenes due to their weak ability in modeling long-term dependency both spatially and temporally, leading to color fading, color discontinuity or other artifacts. To solve this problem, we propose an exemplar-based video colorization framework with long-term spatiotemporal dependency. To enhance the long-term spatial dependency, a parallelized CNN-Transformer block and a double head non-local operation are designed. The proposed CNN-Transformer block can better incorporate long-term spatial dependency with local texture and structural features, and the double head non-local operation further leverages the performance of augmented feature. While for long-term temporal dependency enhancement, we further introduce the novel linkage subnet. The linkage subnet propagate motion information across adjacent frame blocks and help to maintain temporal continuity. Experiments demonstrate that our model outperforms recent state-of-the-art methods both quantitatively and qualitatively. Also, our model can generate more colorful, realistic and stabilized results, especially for scenes where objects change greatly and irregularly

Synthèse de textures par l’exemple pour les applications interactives

Millions of individuals explore virtual worlds every day, for entertainment, training, or to plan business trips and vacations. Video games such as Eve Online, World of Warcraft, and many others popularized their existence. Sand boxes such as Minecraft and Second Life illustrated how they can serve as a media, letting people create, share and even sell their virtual productions. Navigation and exploration software such as Google Earth and Virtual Earth let us explore a virtual version of the real world, and let us enrich it with information shared between the millions of users using these services every day.Virtual environments are massive, dynamic 3D scenes, that are explored and manipulated interactively bythousands of users simultaneously. Many challenges have to be solved to achieve these goals. Among those lies the key question of content management. How can we create enough detailed graphical content so as to represent an immersive, convincing and coherent world? Even if we can produce this data, how can we then store the terra–bytes it represents, and transfer it for display to each individual users? Rich virtual environments require a massive amount of varied graphical content, so as to represent an immersive, convincing and coherent world. Creating this content is extremely time consuming for computer artists and requires a specific set of technical skills. Capturing the data from the real world can simplify this task but then requires a large quantity of storage, expensive hardware and long capture campaigns. While this is acceptable for important landmarks (e.g. the statue of Liberty in New York, the Eiffel tower in Paris) this is wasteful on generic or anonymous landscapes. In addition, in many cases capture is not an option, either because an imaginary scenery is required or because the scene to be represented no longer exists. Therefore, researchers have proposed methods to generate new content programmatically, using captured data as an example. Typically, building blocks are extracted from the example content and re–assembled to form new assets. Such approaches have been at the center of my research for the past ten years. However, algorithms for generating data programmatically only partially address the content management challenge: the algorithm generates content as a (slow) pre–process and its output has to be stored for later use. On the contrary, I have focused on proposing models and algorithms which can produce graphical content while minimizing storage. The content is either generated when it is needed for the current viewpoint, or is produced under a very compact form that can be later used for rendering. Thanks to such approaches developers gain time during content creation, but this also simplifies the distribution of the content by reducing the required data bandwidth.In addition to the core problem of content synthesis, my approaches required the development of new data-structures able to store sparse data generated during display, while enabling an efficient access. These data-structures are specialized for the massive parallelism of graphics processors. I contributed early in this domain and kept a constant focus on this area. The originality of my approach has thus been to consider simultaneously the problems of generating, storing and displaying the graphical content. As we shall see, each of these area involve different theoretical and technical backgrounds, that nicely complement each other in providing elegant solutions to content generation, management and display

Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics

This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p

DEEP LEARNING FOR IMAGE RESTORATION AND ROBOTIC VISION

Traditional model-based approach requires the formulation of mathematical model, and the model often has limited performance. The quality of an image may degrade due to a variety of reasons: It could be the context of scene is affected by weather conditions such as haze, rain, and snow; It\u27s also possible that there is some noise generated during image processing/transmission (e.g., artifacts generated during compression.). The goal of image restoration is to restore the image back to desirable quality both subjectively and objectively. Agricultural robotics is gaining interest these days since most agricultural works are lengthy and repetitive. Computer vision is crucial to robots especially the autonomous ones. However, it is challenging to have a precise mathematical model to describe the aforementioned problems. Compared with traditional approach, learning-based approach has an edge since it does not require any model to describe the problem. Moreover, learning-based approach now has the best-in-class performance on most of the vision problems such as image dehazing, super-resolution, and image recognition. In this dissertation, we address the problem of image restoration and robotic vision with deep learning. These two problems are highly related with each other from a unique network architecture perspective: It is essential to select appropriate networks when dealing with different problems. Specifically, we solve the problems of single image dehazing, High Efficiency Video Coding (HEVC) loop filtering and super-resolution, and computer vision for an autonomous robot. Our technical contributions are threefold: First, we propose to reformulate haze as a signal-dependent noise which allows us to uncover it by learning a structural residual. Based on our novel reformulation, we solve dehazing with recursive deep residual network and generative adversarial network which emphasizes on objective and perceptual quality, respectively. Second, we replace traditional filters in HEVC with a Convolutional Neural Network (CNN) filter. We show that our CNN filter could achieve 7% BD-rate saving when compared with traditional filters such as bilateral and deblocking filter. We also propose to incorporate a multi-scale CNN super-resolution module into HEVC. Such post-processing module could improve visual quality under extremely low bandwidth. Third, a transfer learning technique is implemented to support vision and autonomous decision making of a precision pollination robot. Good experimental results are reported with real-world data