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

Magnetotransport in 3D Topological Insulator Nanowires

In recent years, the research field of topological insulators (TIs) has grown extremely fast due to its potential to produce revolutionary applications in electronics, spintronics, and quantum computation (to name just a few). Three-dimensional TIs (3DTIs) host massless Dirac-like surface states wrapped around an insulating bulk. The special attributes of these topologically protected states are not only interesting for applications, but also for studying fundamental aspects of physics, such as the Klein paradox. This dissertation deals with the transport properties of 3DTI nanowires in the presence of external electric and magnetic fields, using numerical simulations based on effective surface Dirac Hamiltonians. In the first part, a joint experimental and theoretical effort is presented, which reveals the Dirac-like nature of the surface states on HgTe nanowires. The second part is devoted to nanowires with a varying cross section along their axis. Such curved nanowires grant access to a wealth of intriguing quantum transport phenomena and may serve as building blocks for new types of Dirac electron optic setups

Metrics and visualisation for crime analysis and genomics

In this thesis, a configurable generalisation of some well-known distance measures is introduced. Parameters are given to use this metric in the area of law enforcement, but also molecular biology. With a valid distance measure, it is possible to analyse data by using a dimension reduction technique. One of these techniques is analysed and extended.NWOUBL - phd migration 201

Emergent Design

Explorations in Systems Phenomenology in Relation to Ontology, Hermeneutics and the Meta-dialectics of Design SYNOPSIS A Phenomenological Analysis of Emergent Design is performed based on the foundations of General Schemas Theory. The concept of Sign Engineering is explored in terms of Hermeneutics, Dialectics, and Ontology in order to define Emergent Systems and Metasystems Engineering based on the concept of Meta-dialectics. ABSTRACT Phenomenology, Ontology, Hermeneutics, and Dialectics will dominate our inquiry into the nature of the Emergent Design of the System and its inverse dual, the Meta-system. This is an speculative dissertation that attempts to produce a philosophical, mathematical, and theoretical view of the nature of Systems Engineering Design. Emergent System Design, i.e., the design of yet unheard of and/or hitherto non-existent Systems and Metasystems is the focus. This study is a frontal assault on the hard problem of explaining how Engineering produces new things, rather than a repetition or reordering of concepts that already exist. In this work the philosophies of E. Husserl, A. Gurwitsch, M. Heidegger, J. Derrida, G. Deleuze, A. Badiou, G. Hegel, I. Kant and other Continental Philosophers are brought to bear on different aspects of how new technological systems come into existence through the midwifery of Systems Engineering. Sign Engineering is singled out as the most important aspect of Systems Engineering. We will build on the work of Pieter Wisse and extend his theory of Sign Engineering to define Meta-dialectics in the form of Quadralectics and then Pentalectics. Along the way the various ontological levels of Being are explored in conjunction with the discovery that the Quadralectic is related to the possibility of design primarily at the Third Meta-level of Being, called Hyper Being. Design Process is dependent upon the emergent possibilities that appear in Hyper Being. Hyper Being, termed by Heidegger as Being (Being crossed-out) and termed by Derrida as Differance, also appears as the widest space within the Design Field at the third meta-level of Being and therefore provides the most leverage that is needed to produce emergent effects. Hyper Being is where possibilities appear within our worldview. Possibility is necessary for emergent events to occur. Hyper Being possibilities are extended by Wild Being propensities to allow the embodiment of new things. We discuss how this philosophical background relates to meta-methods such as the Gurevich Abstract State Machine and the Wisse Metapattern methods, as well as real-time architectural design methods as described in the Integral Software Engineering Methodology. One aim of this research is to find the foundation for extending the ISEM methodology to become a general purpose Systems Design Methodology. Our purpose is also to bring these philosophical considerations into the practical realm by examining P. Bourdieu’s ideas on the relationship between theoretical and practical reason and M. de Certeau’s ideas on practice. The relationship between design and implementation is seen in terms of the Set/Mass conceptual opposition. General Schemas Theory is used as a way of critiquing the dependence of Set based mathematics as a basis for Design. The dissertation delineates a new foundation for Systems Engineering as Emergent Engineering based on General Schemas Theory, and provides an advanced theory of Design based on the understanding of the meta-levels of Being, particularly focusing upon the relationship between Hyper Being and Wild Being in the context of Pure and Process Being

From Freud's unconscious to Lacan's subject: identification from Freud to Lacan via Conté.

The thesis starts with the question: ‘Does there exist a subject in Freud?’ and looks for answers first in Freud’s early formulations of the psychical apparatus in the ‘Project (1895), ‘Letter 52’ to Fliess (1896), then Chapter VII of ‘The Interpretation of Dreams’ (1900), that is his first topography. The answer confirms our claim that there exists a subject in Freud, that it is unconscious and that it is largely included in and concealed by the Freudian term of ‘ego’ (Ich). In Chapter 2, our claim is carried forward through the second period of Freud’s work to another aspect of Ich, not as unconscious, but as the narcissistic ego. Freud’s introduction to the theory of narcissism (1914c) highlighted the dimension of ego as a libidinal object and its role in psychosis. The metapsychological papers, ‘Drives and their Vicissitudes’ (1915c), ‘Repression’ (1915d) and ‘The Unconscious’ (1915e) proved on the other hand that Freud had not abandoned his research on the structural, the symbolic dimension of the ego (Ich). In Chapter 3 the thesis focuses on two particular aspects of Freudian metapsychology, the structure of the ideals and identification. The sub-claim here is that identification in Freud is not simply an imaginary process involving regression from love, but also a particular substructure of the ‘ego’. We develop this claim through the study of ‘Group Psychology’ (1921c) and Freud’s second topography in the ‘Ego and the Id’ (1923b). In Chapter 4, we present a post-Freudian, object relations, view of the psychical structure, that is D. Lagache’s : ‘Psychoanalysis and Personality’s Structure’ (1958) and Lacan’s own counter-presentation of the psychical structure as an ‘Optical Schema’ (1958), named after a model he adapted from experimental 19th century physics. In Chapter 5, we present Lacan’s largely unknown theory of identification, as he developed it in Seminar IX Identification(1961-1962), first the identification of the subject to the signifier, then to object a. This supports our final claim that the formalization of object a and the status of the Real were first developed in Seminar IX, which is before Seminars Book X and XI. In Chapter 6, we present two major contributions by C. Conté , ‘The Splitting of the Subject and his Identification’(1970) and ‘Topological Surfaces’ (1993) which lead us to conclude that Topology and the Real are the areas of research most suited to contemporary psychoanalysis which only now begin to show their relevance

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Persistent Homology in Multivariate Data Visualization

Technological advances of recent years have changed the way research is done. When describing complex phenomena, it is now possible to measure and model a myriad of different aspects pertaining to them. This increasing number of variables, however, poses significant challenges for the visual analysis and interpretation of such multivariate data. Yet, the effective visualization of structures in multivariate data is of paramount importance for building models, forming hypotheses, and understanding intrinsic properties of the underlying phenomena. This thesis provides novel visualization techniques that advance the field of multivariate visual data analysis by helping represent and comprehend the structure of high-dimensional data. In contrast to approaches that focus on visualizing multivariate data directly or by means of their geometrical features, the methods developed in this thesis focus on their topological properties. More precisely, these methods provide structural descriptions that are driven by persistent homology, a technique from the emerging field of computational topology. Such descriptions are developed in two separate parts of this thesis. The first part deals with the qualitative visualization of topological features in multivariate data. It presents novel visualization methods that directly depict topological information, thus permitting the comparison of structural features in a qualitative manner. The techniques described in this part serve as low-dimensional representations that make the otherwise high-dimensional topological features accessible. We show how to integrate them into data analysis workflows based on clustering in order to obtain more information about the underlying data. The efficacy of such combined workflows is demonstrated by analysing complex multivariate data sets from cultural heritage and political science, for example, whose structures are hidden to common visualization techniques. The second part of this thesis is concerned with the quantitative visualization of topological features. It describes novel methods that measure different aspects of multivariate data in order to provide quantifiable information about them. Here, the topological characteristics serve as a feature descriptor. Using these descriptors, the visualization techniques in this part focus on augmenting and improving existing data analysis processes. Among others, they deal with the visualization of high-dimensional regression models, the visualization of errors in embeddings of multivariate data, as well as the assessment and visualization of the results of different clustering algorithms. All the methods presented in this thesis are evaluated and analysed on different data sets in order to show their robustness. This thesis demonstrates that the combination of geometrical and topological methods may support, complement, and surpass existing approaches for multivariate visual data analysis

New Foundation in the Sciences: Physics without sweeping infinities under the rug

It is widely known among the Frontiers of physics, that “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. For instance, a quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was to get rid of the infinities in the calculations. The infinities are still there, but now they can be skirted around . . . We have designed a method for sweeping them under the rug. [1] And Paul Dirac himself also wrote with similar tune: “Hence most physicists are very satisfied with the situation. They say: Quantum electrodynamics is a good theory, and we do not have to worry about it any more. I must say that I am very dissatisfied with the situation, because this so-called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small—not neglecting it just because it is infinitely great and you do not want it!”[2] Similarly, dark matter and dark energy were elevated as plausible way to solve the crisis in prevalent Big Bang cosmology. That is why we choose a theme here: New Foundations in the Sciences, in order to emphasize the necessity to introduce a new set of approaches in the Sciences, be it Physics, Cosmology, Consciousness etc

From Freud's unconscious to Lacan's subject : identification from Freud to Lacan via Conté

The thesis starts with the question: 'Does there exist a subject in Freud?' and looks for answers first in Freud's early formulations of the psychical apparatus in the 'Project (1895), 'Letter 52' to Fliess (1896), then Chapter VII of 'The Interpretation of Dreams' (1900), that is his first topography. The answer confirms our claim that there exists a subject in Freud, that it is unconscious and that it is largely included in and concealed by the Freudian term of 'ego' (Ich). In Chapter 2, our claim is carried forward through the second period of Freud's work to another aspect of Ich, not as unconscious, but as the narcissistic ego. Freud's introduction to the theory of narcissism (1914c) highlighted the dimension of ego as a libidinal object and its role in psychosis. The metapsychological papers, 'Drives and their Vicissitudes' (1915c), 'Repression' (1915d) and 'The Unconscious' (1915e) proved on the other hand that Freud had not abandoned his research on the structural, the symbolic dimension of the ego (Ich). In Chapter 3 the thesis focuses on two particular aspects of Freudian metapsychology, the structure of the ideals and identification. The sub-claim here is that identification in Freud is not simply an imaginary process involving regression from love, but also a particular substructure of the 'ego'. We develop this claim through the study of 'Group Psychology' (1921c) and Freud's second topography in the 'Ego and the Id' (1923b). In Chapter 4, we present a post-Freudian, object relations, view of the psychical structure, that is D. Lagache's : 'Psychoanalysis and Personality's Structure' (1958) and Lacan's own counter-presentation of the psychical structure as an 'Optical Schema' (1958), named after a model he adapted from experimental 19th century physics. In Chapter 5, we present Lacan's largely unknown theory of identification, as he developed it in Seminar IX Identification(1961-1962), first the identification of the subject to the signifier, then to object a. This supports our final claim that the formalization of object a and the status of the Real were first developed in Seminar IX, which is before Seminars Book X and XI. In Chapter 6, we present two major contributions by C. Conté , 'The Splitting of the Subject and his Identification'(1970) and 'Topological Surfaces' (1993) which lead us to conclude that Topology and the Real are the areas of research most suited to contemporary psychoanalysis which only now begin to show their relevance.EThOS - Electronic Theses Online ServiceGBUnited Kingdo