2,430 research outputs found
Performance Enhancement of a Computational Persistent Homology Package
In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, voids, etc., from a point cloud by finding out when these features appear and disappear in the filtration sequence. In this project, we focus on improving the performance of Eirene, a fancy computational persistent homology package. Eirene is a 5000-line opensource software implemented by using the dynamic programming language Julia. We use the Julia profiling tools to identify the performance bottlenecks and develop different methods to manage the bottlenecks, including the parallelization of some time-consuming functions on the multicore/manycore hardware. The empirical results show that the performance can be greatly improved
Tuning the Performance of a Computational Persistent Homology Package
In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved
A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI
With respect to spatial overlap, CNN-based segmentation of short axis
cardiovascular magnetic resonance (CMR) images has achieved a level of
performance consistent with inter observer variation. However, conventional
training procedures frequently depend on pixel-wise loss functions, limiting
optimisation with respect to extended or global features. As a result, inferred
segmentations can lack spatial coherence, including spurious connected
components or holes. Such results are implausible, violating the anticipated
topology of image segments, which is frequently known a priori. Addressing this
challenge, published work has employed persistent homology, constructing
topological loss functions for the evaluation of image segments against an
explicit prior. Building a richer description of segmentation topology by
considering all possible labels and label pairs, we extend these losses to the
task of multi-class segmentation. These topological priors allow us to resolve
all topological errors in a subset of 150 examples from the ACDC short axis CMR
training data set, without sacrificing overlap performance.Comment: To be presented at the STACOM workshop at MICCAI 202
Topological learning for the classification of disorder: an application to the design of metasurfaces
Structural disorder can improve the optical properties of metasurfaces,
whether it is emerging from some large-scale fabrication methods, or explicitly
designed and built lithographically. Correlated disorder, induced by a minimum
inter-nanostructure distance or by hyperuniformity properties, is particularly
beneficial in some applications such as light extraction. We introduce
numerical descriptors inspired from topology to provide quantitative measures
of disorder whose universal properties make them suitable for both uncorrelated
and correlated disorder, where statistical descriptors are less accurate. We
prove theoretically and experimentally the accuracy of these topological
descriptors of disorder by using them to design plasmonic metasurfaces of
controlled disorder, that we correlate to the strength of their surface lattice
resonances. These tools can be used for the fast and accurate design of
disordered metasurfaces, or to help tuning large-scale fabrication methods.Comment: 6 figure
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
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