用于图像数据拓扑分析的持续同调的GPU加速计算
GPU-Accelerated Computation of Persistent Homology for Topological Analysis of Image Data
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中文总结 AI 辅助
本文提出GPU加速的TopoGPU流管道，结合分层感知离散Morse匹配等技术，实现持续同调计算的大幅提速，优于Cubical Ripser，集成入深度网络可降低训练成本，为开源项目
中文摘要 AI 辅助
近年来，持续同调在深度学习中得到了快速应用，但其计算仍是网络训练中的主要瓶颈。本文提出TopoGPU，一种GPU流管道，用于计算由2D和3D图像诱导的立方复形的持续图。TopoGPU逐块流式输入图像，在GPU块网格上使用大规模并行GPU内核处理每个块；生成的边界关系在主机内存中累积，由CPU执行边界矩阵约简。TopoGPU引入了分层感知离散Morse匹配，该匹配可在流式处理下保证持续同调的正确性，同时结合并行拓扑排序算法和并行V路径奇偶校验算法，用于在GPU上推导Morse边界。在所有评估的基准测试中，TopoGPU均优于当前持续同调计算的最优方法Cubical Ripser，实现了平均端到端加速53.24倍，最大加速达198.01倍。我们进一步将TopoGPU集成到拓扑保持的深度网络中，证明其可大幅降低网络训练期间持续同调计算的成本。TopoGPU为开源项目，提供预编译二进制文件、Google Colab笔记本和Docker镜像，可在项目GitHub页面获取：this https URL
英文摘要
In recent years, persistent homology has seen rapid adoption in deep learning, yet its computation remains a major bottleneck in network training. This paper introduces TopoGPU, a GPU streaming pipeline that computes persistence diagrams of cubical complexes induced by 2D and 3D images. TopoGPU streams the input image chunk by chunk, processing each chunk with massively parallel GPU kernels on a grid of GPU blocks; the resulting boundary relations are accumulated in host memory, where the CPU performs the boundary matrix reduction. TopoGPU introduces a stratification-aware discrete Morse matching that provably preserves persistent homology under streaming, together with a parallel topological sorting algorithm and a parallel V-path parity algorithm for deriving Morse boundaries on the GPU. TopoGPU outperforms Cubical Ripser, a state-of-the-art method for persistent homology computation, on every benchmark evaluated, achieving an average end-to-end speedup of 53.24x and a maximum of 198.01x. We further integrate TopoGPU into a topology-preserving deep network, demonstrating that it substantially reduces the cost of persistent homology computation during network training. TopoGPU is open source, with pre-built binaries, Google Colab notebooks, and Docker images available at the project's GitHub page: https://github.com/seravee08/GPU-Computation-of-Persistent-Homology-for-Image-Data.
发表机构
- Stony Brook University（石溪大学）
- University of Florida（佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。
