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

Low prevalence of asthma among textile workers in Karachi, Pakistan

Objective: To determine the prevalence of asthma in textile workers through post-bronchodilator spirometry and to compare the differences in prevalence based on different criteria used to assess asthma.Methods: The cross-sectional study was conducted between July and December 2013 in Karachi, Pakistan, and comprised workers from15 textile mills in the city and its outskirts. Asthma and associated respiratory symptoms were assessed using the American Thoracic Society Division of Lung Diseases Questionnaire, and post-bronchodilator spirometry. SPSS 19 was used for statistical analysis.Results: Among the 372 workers in the study, asthma was found in 19(5%) as diagnosed on post-bronchodilator spirometry. The prevalence of self-reported and physician-diagnosed asthma was 15(4%) and 8(2%) respectively. Work in the spinning section, age ≥38 years, duration of work ≥10 years in textile industry, history of smoking, and ≥10 pack years of smoking were found to be important predictors of asthma.Conclusions: Textile industry workers had low prevalence of asthma, assessed through post-bronchodilator spirometry, compared to estimates for the general population. This could possibly be due to some protective effect of endotoxin exposure although further evaluation with better exposure assessment is warranted

γ-PS-functions in topological spaces

This paper introduces some new classes of functions called γ-PScontinuous, β-PS-open and β-PS-closed using γ-PS-open set and γ-PSclosed set.In addition, some properties and characterizations of these functions are given.The result shows that γ-PS-continuous function and γ-continuous function are independent

Nearly Injective Semimodules

 في الفترة الماضية تم دراسة مفهوم الاغمار في فئة شبه المقاسات على شبه الحلقة من قبل عدد من الباحثين. من ناحية اخرى, فقد تم تعميم مفهوم الاغمار في فئة المقاسات على الحلقة في عدة اتجاهات مختلفة . على الخصوص المقاسات الاغمارية بالنسبة الى الجذر الابتدائي هي بعض من تلك التعميمات.        بالتناظر مع نظرية المقاسات, استحدثنا ودرسنا في هذا البحث مفهوم شبه المقاس الاغماري نسبة الى جذر جاكوبسن حيث اسميناه شبه المقاس الاغماري تقريبا.An injectivity in the category of semimodules over semiring was studied by many authors recently. On the other hand, the concept of injectivity, in the category of modules over ring, was generalized in many different directions. In particular, injective modules relative to preradical were some of those generalizations.        As an analogue to module theory, in this paper, we introduce  and investigate the notion of "injective semimodule relative to Jacobson radical (namely nearly injective semimodule)"

Plastic surgery lockdown learning during coronavirus disease 2019: are adaptations in education here to stay?

The novel coronavirus disease 2019 has had a major impact on human life and livelihood. The unprecedented challenges have expanded beyond just social and work life, and have grown to impact resident education. In this article, we review the structure of plastic surgery education before the pandemic, the different online learning opportunities for self-directed learning. A summary of the range of platforms and approaches of online remote access delivery of conferences and education that emerged or expanded as a result of the crisis has been reported. This article highlighted the rapid initiatives and efforts of programs and national and international societies to support continuing medical education in conjunction with the guidelines to “shelter at home” and maintain social distancing, and possible future for expanding the reach of online academic initiatives, in addition to the role of developing virtual technologies. The coronavirus disease 2019 crisis has created an opportunity to analyze and advance online learning options to overcome the associated challenges and continue as a reliable platform even following the resolution of the social distancing requirements

γ-PS-generalized closed sets and γ-PS-T 1/2 spaces

This paper defines new class of sets called γ-PS-generalized closed using γ-PS-open set and τγ-PS-closure of a set in a topological space.By using this new set, we introduce a new space called γ-PS-T 1/2 and define three functions namely γ-PS-g-continuous, γ-PS-g-closed and γ-PS-g-open.Some theoretical results and properties for this space and these functions are obtained. Several examples are given to illustrate some of the results

On Preradical of Semimodules

In this paper we study the notion of preradical on some subcategories of the category of semimodules and homomorphisms of semimodules.Since some of the known preradicals on modules fail to satisfy the conditions of preradicals, if the category of modules was extended to semimodules, it is necessary to investigate some subcategories of semimodules, like the category of subtractive semimodules with homomorphisms and the category of subtractive semimodules with ҽҟ-regular homomorphisms

π-Projective Semimodule Over Semiring

سابقا تم دراسة  مفهوم المقاس الاسقاطي من النوع π على  الحلقة من قبل عدة مؤلفين. في هذا البحث هذا المفهوم سيقدم ويعمم لشبه المقاس على شبه الحلقة. ليكنT شبه مقاس يساري وحدوي, فنقول انه اسقاطي من النوع π اذا كان لكل شبه مقاسين جزئيين منه بشرط ان شبه المقاس يساوي مجموع هذين الشبه المقاسين الجزئيين,  فيوجد تشاكلين بحيث ان التشاكل الاول مجموعة جزئية من احد شبه المقاسين الجزئيين,  والتشاكل الثاني مجموعة جزئية من الاخر و مجموع التشاكلين يساوي الدالة الاحادية بالنسبة لشبه المقاس المعطى.   Previously the concept of π-projective modules over ring was studied by some authors. The aim of this research is to give a comprehensive study of π-projective semimodule and access to some new properties and characterizations for this class of semimodules.           Let S be a commutative semiring with identity 1≠0 and T a unital left semimodule, then we say that T is π-projective  if for every two subsemimodules M and L of T with T=M+L, there exist f and g ϵEnd(T), such that f +g=1T,  f(T) M and g(T) L