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Applications of anti-geometric diffusion to computer vision: Thresholding, segmentation, and distance functions.

机译：反几何扩散在计算机视觉中的应用：阈值，分割和距离函数。

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摘要

Society is increasingly relying on computers to extract meaning and information from digital images. Partial differential equations are a popular and well-studied tool for computer vision applications, but the anti-geometric heat flow has been overlooked. The goal of this thesis is to demonstrate several applications for which the anti-geometric flow is appropriate and more generally to expand the appreciation and deepen the understanding within the fields of image processing and computer vision of this flow that has received so little attention in comparison to its geometric cousins.; One contribution of this thesis is the development of a general anti-geometric diffusion-based segmentation framework. We select the anti-geometric diffusion so that the local diffusion direction smears edges in the image, al lowing us to rapidly detect and discriminate between entire image regions that lie nearby, but on opposite sides, of a prominent edge. The detection of such regions occurs during the diffusion process rather than afterward, exploiting the multi-scale properties of the flow. We initially outline a procedure for adaptive thresholding, but ultimately combine this splitting model with an energy-based merging procedure to provide a general framework for image segmentation. We discuss a fast implementation of one such framework and demonstrate its effectiveness in segmenting medical, military, and scene imagery. We then propose generalizations of the framework to include higher-order image models and more general merging criteria, such as shape.; We also present another motivating application, registration for image guided cranial surgery. We outline two optimization-based approaches that rely on the computation of a Euclidean distance function and its derivatives in order to demonstrate that higher-order optimization methods rely on the accuracy of higher-order derivatives of the underlying distance function, and that inaccurate derivatives can lead to divergence of the optimization method. We address the issue of ill-behaved properties of these derivatives by proposing a partial differential equation that includes the anti-geometric flow to improve these properties. We also show some substantial limitations that greatly affect the suitability of the this flow for this application.
机译：社会越来越依赖计算机从数字图像中提取含义和信息。偏微分方程是计算机视觉应用中流行的且经过深入研究的工具，但是反几何热流却被忽略了。本文的目的是演示适合反几何流程的几种应用，并且更广泛地在图像处理和计算机视觉领域扩大对这种流程的认识并加深对这种流程的关注，而相比之下，这种应用很少受到关注到它的几何表亲。本文的一个贡献是开发了一种基于反几何扩散的通用分割框架。我们选择反几何扩散，以使局部扩散方向在图像中涂抹边缘，从而使我们能够快速检测并区分出位于显着边缘附近但相对两侧的整个图像区域。利用流的多尺度特性，对这些区域的检测发生在扩散过程中，而不是之后。我们最初概述了自适应阈值的过程，但最终将此拆分模型与基于能量的合并过程结合起来，以提供用于图像分割的通用框架。我们讨论了这样一个框架的快速实现，并展示了其在分割医学，军事和场景图像方面的有效性。然后，我们提出对该框架的概括，以包括更高阶的图像模型和更通用的合并标准，例如形状。我们还提出了另一个激励性的应用程序，即影​​像引导颅骨手术的注册。我们概述了两种基于优化的方法，这些方法依赖于欧几里得距离函数及其导数的计算，以证明高阶优化方法依赖于基础距离函数的高阶导数的准确性，并且不精确的导数可以导致优化方法的分歧。我们通过提出一个偏微分方程来解决这些导数的不良特性问题，该方程包括反几何流动以改善这些特性。我们还显示了一些实质性的限制，这些限制极大地影响了此流程对该应用程序的适用性。

著录项

  • 作者

    Manay, Siddharth.;

  • 作者单位

    Georgia Institute of Technology.;

  • 授予单位 Georgia Institute of Technology.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 98 p.
  • 总页数 98
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

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