國立虎尾科技大學 |

Topology-Driven Learning for Images: Applications and Acceleration /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Topology-Driven Learning for Images: Applications and Acceleration // Fan Wang.
Author:	Wang, Fan,
Description:	1 electronic resource (141 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-05, Section: A.
Contained By:	Dissertations Abstracts International86-05A.
Subject:	Computer science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31481887
ISBN:	9798342728478

Topology-Driven Learning for Images: Applications and Acceleration /
Wang, Fan,

Topology-Driven Learning for Images: Applications and Acceleration /Fan Wang. - 1 electronic resource (141 pages)

Source: Dissertations Abstracts International, Volume: 86-05, Section: A.

The integration of topological methods into deep learning, particularly through persistent homology, has seen significant growth recently. Persistent homology, a key concept in Topological Data Analysis (TDA), offers insight into the topological characteristics of data by tracing their evolution across scales. This thesis explores the application of persistent homology to deep learning challenges, specifically focusing on ensuring the topological integrity of generated images. We enhance the robustness of a generative adversarial network by introducing a penalty based on the disparity in topological properties between the generated images and the training distribution. This approach ensures that the generated images resemble the training data not only visually but also in their topological characteristics.As the second application, We extract persistent homology from breast DEC-MRI volumes as an approximation of fibroglandular tissues and use it to explicitly direct the attention of a 3D network to a smaller set of voxels with high biological relevance. This targeted approach allows the network to focus on areas that are most indicative of underlying pathologies.Despite the practical benefits, challenges remain in melding persistent homology with deep learning due to computational demands. Addressing this, the research focuses on massively parallel GPU algorithms to expedite persistent homology calculations, aiming to bridge this gap in deep learning frameworks. The shift from CPU to GPU computing is driven by the diminishing returns of Moore's Law, prompting a transition to accelerated computing with GPUs leading the performance enhancement.This research delves into persistent homology computation for image data-essential in fields ranging from medical imaging to physical simulations, and crucial in deep learning as convolutional network outputs. This thesis introduces a streaming GPU algorithm for computing persistent homology in 2D and 3D digital images, addressing a notable bottleneck in deep learning training times. By constructing a cubical complex and utilizing discrete Morse theory for gradient vector field development, the proposed algorithm applies innovative massively parallel algorithms for topological sorting and path parity to formulate Morse boundaries. It assembles partial boundary relations from discrete data segments into a unified global boundary matrix for reduction, employing specialized measures to manage Morse matchings at chunk and GPU borders. This ensures the fidelity of persistent homology within a streaming context. The resulting algorithm exhibits exceptional speed improvements in preprocessing and persistent homology computations, surpassing existing state-of-the-art methods.This work aims to contribute substantially improved algorithms to the TDA community, significantly reducing computation times and fostering further applications of topological loss in deep learning, thereby removing computational barriers and advancing the field.

English

ISBN: 9798342728478Subjects--Topical Terms:

573171
Computer science.
Subjects--Index Terms:

Generative adversarial network

Topology-Driven Learning for Images: Applications and Acceleration /
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520 $a The integration of topological methods into deep learning, particularly through persistent homology, has seen significant growth recently. Persistent homology, a key concept in Topological Data Analysis (TDA), offers insight into the topological characteristics of data by tracing their evolution across scales. This thesis explores the application of persistent homology to deep learning challenges, specifically focusing on ensuring the topological integrity of generated images. We enhance the robustness of a generative adversarial network by introducing a penalty based on the disparity in topological properties between the generated images and the training distribution. This approach ensures that the generated images resemble the training data not only visually but also in their topological characteristics.As the second application, We extract persistent homology from breast DEC-MRI volumes as an approximation of fibroglandular tissues and use it to explicitly direct the attention of a 3D network to a smaller set of voxels with high biological relevance. This targeted approach allows the network to focus on areas that are most indicative of underlying pathologies.Despite the practical benefits, challenges remain in melding persistent homology with deep learning due to computational demands. Addressing this, the research focuses on massively parallel GPU algorithms to expedite persistent homology calculations, aiming to bridge this gap in deep learning frameworks. The shift from CPU to GPU computing is driven by the diminishing returns of Moore's Law, prompting a transition to accelerated computing with GPUs leading the performance enhancement.This research delves into persistent homology computation for image data-essential in fields ranging from medical imaging to physical simulations, and crucial in deep learning as convolutional network outputs. This thesis introduces a streaming GPU algorithm for computing persistent homology in 2D and 3D digital images, addressing a notable bottleneck in deep learning training times. By constructing a cubical complex and utilizing discrete Morse theory for gradient vector field development, the proposed algorithm applies innovative massively parallel algorithms for topological sorting and path parity to formulate Morse boundaries. It assembles partial boundary relations from discrete data segments into a unified global boundary matrix for reduction, employing specialized measures to manage Morse matchings at chunk and GPU borders. This ensures the fidelity of persistent homology within a streaming context. The resulting algorithm exhibits exceptional speed improvements in preprocessing and persistent homology computations, surpassing existing state-of-the-art methods.This work aims to contribute substantially improved algorithms to the TDA community, significantly reducing computation times and fostering further applications of topological loss in deep learning, thereby removing computational barriers and advancing the field.
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