Topological image modification for object detection and topological image processing of skin lesions

We propose a new method based on Topological Data Analysis (TDA) consisting of Topological Image Modification (TIM) and Topological Image Processing (TIP) for object detection. Through this newly introduced method, we artificially destruct irrelevant objects, and construct new objects with known topological properties in irrelevant regions of an image. This ensures that we are able to identify the important objects in relevant regions of the image. We do this by means of persistent homology, which allows us to simultaneously select appropriate thresholds, as well as the objects corresponding to these thresholds, and separate them from the noisy background of an image. This leads to a new image, processed in a completely unsupervised manner, from which one may more efficiently extract important objects. We demonstrate the usefulness of this proposed method for topological image processing through a case-study of unsupervised segmentation of the ISIC 2018 skin lesion images. Code for this project is available on https://bitbucket.org/ghentdatascience/topimgprocess

Persistent Homology with Improved Locality Information for more Effective Delineation

We present a new, more effective way to use Persistent Homology (PH), a method to compare the topology of two data sets, for training deep networks to delineate road networks in aerial images and neuronal processes in microscopy scans. Its essence is in a novel filtration function, derived from a fusion of two existing techniques: thresholding-based filtration, previously used to train deep networks to segment medical images, and filtration with height functions, used before for comparison of 2D and 3D shapes. We experimentally demonstrate that deep networks trained with our Persistent-Homology-based loss yield reconstructions of road networks and neuronal processes that preserve the connectivity of the originals better than existing topological and non-topological loss functions

Mathematics in Medical Diagnostics - 2022 Proceedings of the 4th International Conference on Trauma Surgery Technology

The 4th event of the Giessen International Conference Series on Trauma Surgery Technology took place on April, the 23rd 2022 in Warsaw, Poland. It aims to bring together practical application research, with a focus on medical imaging, and the TDA experts from Warsaw. This publication contains details of our presentations and discussions

Persistence Bag-of-Words for Topological Data Analysis

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.Comment: Accepted for the Twenty-Eight International Joint Conference on Artificial Intelligence (IJCAI-19). arXiv admin note: substantial text overlap with arXiv:1802.0485

The Discrete Morse Complex of Images: Algorithms, Modeling and Applications

The Morse complex can be used for studying the topology of a function, e.g., an image or terrain height field when understood as bivariate functions. We present an algorithm for the computation of the discrete Morse complex of two-dimensional images using an edge-based data structure. By using this data structure, it is possible to perform local operations efficiently, which is important to construct the complex and make the structure useful for areas like visualization, persistent homology computation, or construction of a topological hierarchy. We present theoretical and applied results to demonstrate benefits and use of our method

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

Scan-based immersed isogeometric analysis

Scan-based simulations contain innate topologically complex three-dimensional geometries, represented by large data sets in formats which are not directly suitable for analysis. Consequently, performing high-fidelity scan-based simulations at practical computational costs is still very challenging. The main objective of this dissertation is to develop an efficient and robust scan-based simulation strategy by acquiring a profound understanding of three prominent challenges in scan-based IGA, viz.: i) balancing the accuracy and computational effort associated with numerical integration; ii) the preservation of topology in the spline-based segmentation procedure; and iii) the control of accuracy using error estimation and adaptivity techniques. In three-dimensional immersed isogeometric simulations, the computational effort associated with integration can be the critical component. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this dissertation we provide a thorough investigation of the accuracy and computational effort of the octree integration technique. We quantify the contribution of the integration error using the theoretical basis provided by Strang’s first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed IGA. To exploit the advantageous properties of IGA in a scan-based setting, it is important to extract a smooth geometry. This can be established by convoluting the voxel data using B-splines, but this can induce problematic topological changes when features with a size similar to that of the voxels are encountered. This dissertation presents a topology-preserving segmentation procedure using truncated hierarchical (TH)B-splines. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which (TH)B-spline refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. A Fourier analysis is presented to explain the effectiveness of the developed procedure. An additional computational challenge in the context of immersed IGA is the construction of optimal approximations using locally refined splines. For scan-based volumetric domains, hierarchical splines are particularly suitable, as they optimally leverage the advantages offered by the availability of a geometrically simple background mesh. Although truncated hierarchical B-splines have been successfully applied in the context of IGA, their application in the immersed setting is largely unexplored. In this dissertation we propose a computational strategy for the application of error estimation-based mesh adaptivity for stabilized immersed IGA. The conducted analyses and developed computational techniques for scan-based immersed IGA are interrelated, and together constitute a significant improvement in the efficiency and robustness of the analysis paradigm. In combination with other state-of-the-art developments regarding immersed FEM/IGA (\emph{e.g.}, iterative solution techniques, parallel computing), the research in this thesis opens the doors to scan-based simulations with more sophisticated physical behavior, geometries of increased complexity, and larger scan-data sizes.Scan-based simulations contain innate topologically complex three-dimensional geometries, represented by large data sets in formats which are not directly suitable for analysis. Consequently, performing high-fidelity scan-based simulations at practical computational costs is still very challenging. The main objective of this dissertation is to develop an efficient and robust scan-based simulation strategy by acquiring a profound understanding of three prominent challenges in scan-based IGA, viz.: i) balancing the accuracy and computational effort associated with numerical integration; ii) the preservation of topology in the spline-based segmentation procedure; and iii) the control of accuracy using error estimation and adaptivity techniques. In three-dimensional immersed isogeometric simulations, the computational effort associated with integration can be the critical component. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this dissertation we provide a thorough investigation of the accuracy and computational effort of the octree integration technique. We quantify the contribution of the integration error using the theoretical basis provided by Strang’s first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed IGA. To exploit the advantageous properties of IGA in a scan-based setting, it is important to extract a smooth geometry. This can be established by convoluting the voxel data using B-splines, but this can induce problematic topological changes when features with a size similar to that of the voxels are encountered. This dissertation presents a topology-preserving segmentation procedure using truncated hierarchical (TH)B-splines. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which (TH)B-spline refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. A Fourier analysis is presented to explain the effectiveness of the developed procedure. An additional computational challenge in the context of immersed IGA is the construction of optimal approximations using locally refined splines. For scan-based volumetric domains, hierarchical splines are particularly suitable, as they optimally leverage the advantages offered by the availability of a geometrically simple background mesh. Although truncated hierarchical B-splines have been successfully applied in the context of IGA, their application in the immersed setting is largely unexplored. In this dissertation we propose a computational strategy for the application of error estimation-based mesh adaptivity for stabilized immersed IGA. The conducted analyses and developed computational techniques for scan-based immersed IGA are interrelated, and together constitute a significant improvement in the efficiency and robustness of the analysis paradigm. In combination with other state-of-the-art developments regarding immersed FEM/IGA (\emph{e.g.}, iterative solution techniques, parallel computing), the research in this thesis opens the doors to scan-based simulations with more sophisticated physical behavior, geometries of increased complexity, and larger scan-data sizes

Topological data analysis of C. elegans locomotion and behavior

We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data. Our methods allow us to distinguish and classify videos from various environmental conditions and we analyze the trade-off between accuracy and interpretability. Furthermore, we present a novel technique for visualizing the outputs of our analysis in terms of the input. Specifically, we use representative cycles of persistent homology to produce synthetic videos of stereotypical behaviors.Comment: 27 pages, 15 figures/table

Specific subdomain localization of ER resident proteins and membrane contact sites resolved by electron microscopy

The endoplasmic reticulum (ER) is a large, single-copy, membrane-bound organelle that comprises an elaborate 3D network of diverse structural subdomains, including highly curved tubules, flat sheets, and parts that form contacts with nearly every other organelle. The dynamic and complex organization of the ER poses a major challenge on understanding how its functioning - maintenance of the structure, distribution of its functions and communication with other organelles - is orchestrated. In this study, we resolved a unique localization profile within the ER network for several resident ER proteins representing a broad range of functions associated with the ER using immuno-electron microscopy and calculation of a relative labeling index (RLI). Our results demonstrated the effect of changing cellular environment on protein localization and highlighted the importance of correct protein expression level when analyzing its localization at subdomain resolution. We present new software tools for anonymization of images for blind analysis and for quantitative assessment of membrane contact sites (MCSs) from thin section transmission electron microscopy micrographs. The analysis of ERmitochondria contacts suggested the presence of at least three different types of MCSs that responded differently to changes in cellular lipid loading status.Peer reviewe