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Stability for Inference with Persistent Homology Rank Functions

computer graphics FORUM 2024年第5期43卷 e15142-e15142页

作者： Wang, Qiquan Garcia-Redondo, Ines Faugere, Pierre Henselman-Petrusek, Gregory Monod, Anthea Imperial Coll London Dept Math London England UCL London Sch Geometry & Number Theory London England ENS Lyon Dept Math Lyon France Pacific Northwest Natl Lab Richland WA USA

Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical settings is challenging due to their complex geometric structure. In this paper, we revisit the persistent homology rank function, which is mathematically equivalent to a barcode and persistence diagram, as a tool for statistics and machine learning. Rank functions, being functions, enable the direct application of the statistical theory of functional data analysis (FDA)-a domain of statistics adapted for data in the form of functions. A key challenge they present over barcodes in practice, however, is their lack of stability-a property that is crucial to validate their use as a faithful representation of the data and therefore a viable summary statistic. In this paper, we fill this gap by deriving two stability results for persistent homology rank functions under a suitable metric for FDA integration. We then study the performance of rank functions in functional inferential statistics and machine learning on real data applications, in both single and multiparameter persistent homology. We find that the use of persistent homology captured by rank functions offers a clear improvement over existing non-persistence-based approaches.

关键词： CCS Concepts center dot Mathematics of computing -> Algebraic topology center dot theory of computation -> Computational geometry center dot General and reference -> Performance

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Parallel Optimization for Robotics: An Undergraduate Introduction to GPU Parallel Programming and Numerical Optimization Research

Parallel Optimization for Robotics: An Undergraduate Introdu...

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IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)

作者： Brian Plancher Barnard College Columbia University New York NY

ISBN: (数字)9798350364606

ISBN: (纸本)9798350364613

While parallel programming, particularly on graphics processing units (GPUs), and numerical optimization hold immense potential to tackle real-world computational challenges across disciplines, their inherent complexity and technical demands often act as daunting barriers to entry. This, unfortunately, limits accessibility and diversity within these crucial areas of computer science. To combat this challenge and ignite excitement among undergraduate learners, we developed an application-driven course, harnessing robotics as a lens to demystify the intricacies of these topics making them tangible and engaging. Our course's prerequisites are limited to the required undergraduate introductory core curriculum, opening doors for a wider range of students. Our course also features a large final-project component to connect theoretical learning to applied practice. In our first offering of the course we attracted 27 students without prior experience in these topics and found that an overwhelming majority of the students felt that they learned both technical and soft skills such that they felt prepared for future study in these fields.

关键词： computer science Distributed processing Parallel programming Educational robots Conferences graphics processing units Complexity theory

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基于物理的可微渲染综述

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中国图象图形学报 2024年第10期29卷 2912-2925页

作者：邢健开徐昆普适计算教育部重点实验室北京100084 北京信息科学与技术国家研究中心北京100084 清华大学计算机系北京100084

可微渲染技术是当前计算机图形学与计算机视觉方向的研究热点,其目标是将计算机图形学中的渲染流水线进行可微化改造以支持计算渲染的输出图像关于输入参数如几何、材质等参数的梯度。结合渲染图像与目标图像之间的损失函数,可微渲染允... 详细信息

可微渲染技术是当前计算机图形学与计算机视觉方向的研究热点,其目标是将计算机图形学中的渲染流水线进行可微化改造以支持计算渲染的输出图像关于输入参数如几何、材质等参数的梯度。结合渲染图像与目标图像之间的损失函数,可微渲染允许在生成式分析的框架中,通过梯度下降的方式从图像中推理出场景参数,是解决三维重建、逆向渲染等领域问题的有效方法,并在虚拟现实、自动驾驶等领域有着广泛的应用前景。基于物理的可微渲染旨在对基于物理的渲染管线进行可微化改造,主要涉及对场景几何和材质的表达,以及光路传输模拟过程的梯度计算方法。本文对近年来基于物理的可微渲染领域的发展情况进行了调研,总结了基于物理的可微渲染研究进展。首先总体介绍正向渲染和可微渲染的计算方法;然后介绍如何针对具体的几何、材质以及相机的表达方式进行梯度计算;讨论如何提高可微渲染的效率和鲁棒性;展示可微渲染如何应用于实际任务中;最后本文展望了可微渲染的发展趋势,期望推动该领域的进一步发展。

关键词：渲染可微渲染逆向渲染光线跟踪三维重建

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Visualization Display System of Gannan Hakka Paper-Cut Works Based on computer graphics Algorithm

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Computational Intelligence and Neuroscience 2022年第0期2022卷 2419689页

作者： Li, Xingping Ganzhou Teachers College Ganzhou341000 China

Today, computer graphics and graphic image processing techniques have been widely used in daily life and industrial production. Due to the development of computers, computer graphics has brought more convenience to our daily life. In order to give full play to the value of computers, this paper takes the Hakka paper-cut art with local characteristics as the starting point, first of all its development history, artistic characteristics, compositional forms, expression techniques, cultural connotations, Hakka paper-cut patterns, and the symbolic meaning of folk customs, and then we design a visualization system for the paper-cut works of Gannan Hakka based on computer graphics. In addition, the system provides a solution for the integration of Gannan Hakka paper-cut art and Jiangxi native product packaging design and provides a reference for the theory and practice of modern native product packaging design. © 2022 Xingping Li.

关键词： Product design

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Data Physicalization

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IEEE computer graphics AND APPLICATIONS 2020年第6期40卷 21-24页

作者： Hogan, Trevor Hinrichs, Uta Huron, Samuel Alexander, Jason Jansen, Yvonne Munster Tech Univ Design Cork Ireland Univ St Andrews St Andrews Fife Scotland Polytech Paris Design Informat Technol Social & Econ Sci Dept Telecom Paris Sch Palaiseau France Univ Bath Dept Comp Sci Human Comp Interact Bath Avon England Sorbonne Univ CNRS ISIR Paris France

The articles in this special section focus on data physicalization. The practice of representing data in physical form has existed for thousands of years, yet it has only become an area of investigation and exploration for scientists, designers, and artists much more recently.3 Advances in areas such as digital fabrication, actuated tangible interfaces, and shape-changing displays have spurred an emerging area of research now called Data Physicalization.1 This Special Issue of IEEE computer graphics and Applications presents four articles spanning a wide breadth of current data physicalization research, from theory to practice.

关键词： Special Issues And Sections Data Visualization computer Science Information Technology Data Analysis

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Application of binary classification of magnetic resonance therapy images to detect the threat of the disease due to COVID-19 3

Application of binary classification of magnetic resonance t...

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3rd IEEE KhPI Week on Advanced Technology, KhPI Week 2022

作者： Zalevska, Olga Vanin, Volodymyr Sydogenko, Julia Finogenov, Oleksii Demydenko, Olga Yablonskyi, Petro Ladogubets, Tetyana Oliinyk, Yurii Miroshnichenko, Ivan National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Department of Automation of Power Processes and Systems Engineering Kyiv Ukraine National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Department of Descriptive Geometry Engineering and Computer Graphics Kyiv Ukraine National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Department of Computer-Aided Science and Data Processing Systems Kyiv Ukraine National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' The Department of Theory Practice and Translation of English Kyiv Ukraine National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Deprtament of Applied Mathematics Kyiv Ukraine

ISBN: (数字)9798350399202

ISBN: (纸本)9798350399202

The paper considers the use of a neural network for the binary classification of magnetic resonance imaging images to establish a possible disease of COVID-19. Processing of input data and their reduction to one format is provided, and neural network software for binary classification is developed and its training based on about 60,000 open patient images. The using of developed software is universal for medical doctors or ordinary Internet users and does not require additional training. © 2022 IEEE.

关键词： Magnetic resonance imaging

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One algorithm for testing annulling of mixed trigonometric polynomial functions on boundary points 30

One algorithm for testing annulling of mixed trigonometric p...

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30th Telecommunications Forum, TELFOR 2022

作者： Malesevic, Branko Banjac, Bojan Sesum-Cavic, Vesna Korolija, Nenad University of Belgrade School of Electrical Engineering Department of Applied mathematics Belgrade Serbia University of Novi Sad Computer graphics chair Faculty of Technical sciences Novi Sad Serbia Digital innovation team Intens d.o.o. Novi Sad Serbia University of Belgrade Faculty of Civil Engineering Department for Geoinformatics Belgrade Serbia University of Belgrade School of Electrical Engineering Department for Computer science and information technology Belgrade Serbia

ISBN: (数字)9781665472739

ISBN: (纸本)9781665472739

This paper considers one problem of automated proving of MTP inequalities f(x) > 0 over [0, π/2] on boundary points. It suggests one algorithm for symbolic checking for f(0) = 0 or f(π/2) = 0 without use of numerical estimations. With stated approach it gives one contribution to theory and practice in this part of the field of automated proving. © 2022 IEEE.

关键词： Rational functions

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RETRACTED: Visualization Display System of Gannan Hakka Paper-Cut Works Based on computer graphics Algorithm (Retracted Article)

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COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022年第1期2022卷

作者： Li, Xingping Ganzhou Teachers Coll Ganzhou 341000 Jiangxi Peoples R China

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Boolean and Fp-Matrix Factorization: From theory to practice

Boolean and Fp-Matrix Factorization: From Theory to Practice

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) / IEEE World Congress on Computational Intelligence (IEEE WCCI) / International Joint Conference on Neural Networks (IJCNN) / IEEE Congress on Evolutionary Computation (IEEE CEC)

作者： Fomin, Fedor Panolan, Fahad Patil, Anurag Tanveer, Adil Univ Bergen Dept Informat Bergen Norway IIT Hyderabad Dept CSE Sangareddy India EdgeVerve Syst Ltd Bengaluru India Amazon Chennai Tamil Nadu India

ISBN: (纸本)9781728186719

Boolean Matrix Factorization (BMF) aims to find an approximation of a given binary matrix as the Boolean product of two low-rank binary matrices. Binary data is ubiquitous in many fields, and representing data by binary matrices is common in medicine, natural language processing, bioinformatics, computer graphics, among many others. Factorizing a matrix into low-rank matrices is used to gain more information about the data, like discovering relationships between the features and samples, roles and users, topics and articles, etc. In many applications, the binary nature of the factor matrices could enormously increase the interpretability of the data. Unfortunately, BMF is computationally hard and heuristic algorithms are used to compute Boolean factorizations. Very recently, the theoretical breakthrough was obtained independently by two research groups. Ban et al. (SODA 2019) and Fomin et al. (Trans. Algorithms 2020) show that BMF admits an efficient polynomial-time approximation scheme (EPTAS). However, despite the theoretical importance, the high double-exponential dependence of the running times from the rank makes these algorithms unimplementable in practice. The primary research question motivating our work is whether the theoretical advances on BMF could lead to practical algorithms. The main conceptional contribution of our work is the following. While EPTAS for BMF is a purely theoretical advance, the general approach behind these algorithms could serve as the basis in designing better heuristics. We also use this strategy to develop new algorithms for related F-p-Matrix Factorization. Here, given a matrix A over a finite field GF(p) where p is a prime, and an integer r, our objective is to find a matrix B over the same field with GF(p)-rank at most r minimizing some norm of A - B. Our empirical research on synthetic and real-world data demonstrates the advantage of the new algorithms over previous works on BMF and F-p-Matrix Factorization.

关键词： Binary matrix factorization Categorical data Data mining

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A Survey on Bounding Volume Hierarchies for Ray Tracing

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computer graphics FORUM 2021年第2期40卷 683-712页

作者： Meister, Daniel Ogaki, Shinji Benthin, Carsten Doyle, Michael J. Guthe, Michael Bittner, Jiri Univ Tokyo Tokyo Japan ZOZO Res Chiba Japan Intel Corp Santa Clara CA 95051 USA Univ Bayreuth Bayreuth Germany Czech Tech Univ Prague Czech Republic

Ray tracing is an inherent part of photorealistic image synthesis algorithms. The problem of ray tracing is to find the nearest intersection with a given ray and scene. Although this geometric operation is relatively simple, in practice, we have to evaluate billions of such operations as the scene consists of millions of primitives, and the image synthesis algorithms require a high number of samples to provide a plausible result. Thus, scene primitives are commonly arranged in spatial data structures to accelerate the search. In the last two decades, the bounding volume hierarchy (BVH) has become the de facto standard acceleration data structure for ray tracing-based rendering algorithms in offline and recently also in real-time applications. In this report, we review the basic principles of bounding volume hierarchies as well as advanced state of the art methods with a focus on the construction and traversal. Furthermore, we discuss industrial frameworks, specialized hardware architectures, other applications of bounding volume hierarchies, best practices, and related open problems.

关键词： CCS Concepts center dot Computing methodologies -> Ray tracing Visibility Massively parallel algorithms center dot theory of computation -> Computational geometry Massively parallel algorithms Sorting and searching

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