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On several geometric optimization problems in biomedical computation.

机译：关于生物医学计算中的几个几何优化问题。

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摘要

Biomedical computation is an emerging field that includes the use of algorithmic approaches and optimization methods to solve challenging biomedical problems. The problems studied in this field originate from traditional medical image analysis, cancer therapy, computer aided surgery, and a variety of other areas. In this dissertation, we study several such problems motivated from important biomedical imaging applications.; The first problem we study is the Biplane Imaging Geometry Determination problem, motivated from the need for an accurate 3D coronary vasculature reconstruction from only two views in cardio-vascular interventional situations. Here, we seek to determine the orientation parameters (triplet of Euler angles and translation vector) from known corresponding points in two views. We propose a polynomial time geometric algorithm that determines the 'pose' by transforming the geometry optimization problem into a cell search problem in R6 parameter space of the geometry variables. Our algorithm then employs this construction to explain the equivalence (in terms of reconstruction errors) among existing algorithms for this problem. We show that input configuration shapes have a strong effect on what we call the solution space of feasible geometries, this can be queried to determine preferable input configurations and predict the accuracy attainable for given inputs.; The second problem we study is the Brachytherapy Seed Localization problem. Here, one seeks to localize the 3D positions of implanted seeds from multiple views in prostate brachytherapy, a common treatment for prostate cancer. An automatic reconstruction of the 3D seed configuration is not possible because correspondences between the 2 D seeds are not known and the orientation geometry could be inaccurate. We propose an optimization algorithm by formulating a minimization Integer Program with special constraints that capture the geometric information available from the imaging setup. We solve the equivalent linear program and 'round' the fractional solution vector to yield correspondences. We also present extensive evaluations on clinical datasets.; The third problem we study is the Ensemble Clustering problem. The input is in the form of multiple classifications or clustering solutions ( e.g., outputs from multiple computer assisted diagnosis procedures or image segmentations) and one seeks to "aggregate" the solutions into one solution that maximizes the agreement in the input ensemble. For this problem, we obtain several improvements over the best existing algorithms. More specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. We propose a polynomial time algorithm for solving the relaxed version of the SDP and discuss experimental evaluations.; The fourth problem we study is the limited view Computed Tomography reconstruction. The problem has several important clinical applications spanning coronary angiographic imaging and breast tomosynthesis. We first show that the limited view reconstruction problem can be formulated as a "constrained" version of the metric labeling problem. This lays the groundwork for a linear programming framework that brings together metric labeling classification and algebraic tomographic reconstruction (ART) in a unified model: where voxels must be reassigned subject to maximally maintaining consistency with the input reconstruction and the ART objective simultaneously. The approach can reliably reconstruct volumes with several multiple contrast objects, we present experiments on cone bean computed tomography.
机译：生物医学计算是一个新兴领域，其中包括使用算法方法和优化方法来解决具有挑战性的生物医学问题。在该领域中研究的问题源于传统医学图像分析，癌症治疗，计算机辅助手术以及许多其他领域。本文研究了一些重要的生物医学成像应用引起的此类问题。我们研究的第一个问题是双平面成像几何确定问题，这是出于仅在心血管介入情况下仅从两种角度进行精确的3D冠状动脉血管重建的需要。在这里，我们试图从两个视图中的已知对应点确定方向参数（欧拉角的三重形和平移矢量）。我们提出了一种多项式时间几何算法，该算法通过将几何优化问题转换为几何变量的R6参数空间中的像元搜索问题来确定“姿势”。然后，我们的算法采用此构造来解释该问题的现有算法之间的等效性（就重构误差而言）。我们证明了输入配置形状对我们所说的可行几何的求解空间有很大的影响，可以查询确定最佳输入配置并预测给定输入可获得的精度。我们研究的第二个问题是近距离放射疗法种子定位问题。在这里，人们试图从前列腺近距离放射治疗（前列腺癌的一种常见治疗方法）的多角度定位植入种子的3D位置。 3D种子配置的自动重建是不可能的，因为2D种子之间的对应关系未知，并且方向几何形状可能不准确。我们通过制定具有特殊约束条件的最小化整数程序来提出一种优化算法，以捕获可从成像设置中获取的几何信息。我们求解等效线性程序，并将分数解矢量“舍入”以产生对应关系。我们还对临床数据集进行了广泛的评估。我们研究的第三个问题是集成聚类问题。输入采用多种分类或聚类解决方案的形式（例如，来自多个计算机辅助诊断程序或图像分割的输出），并且人们试图将这些解决方案“聚合”成一个使输入集合中的一致性最大化的解决方案。对于此问题，我们对现有最佳算法进行了一些改进。更具体地说，我们表明，在这种情况下，使用2D字符串编码而不是投票策略可以更好地捕获协议的概念。首先通过构造非线性目标函数进行优化，然后使用新颖的凸化技术将其转换为0-1半定程序（SDP）。我们提出了多项式时间算法来求解SDP的宽松版本，并讨论了实验评估。我们研究的第四个问题是计算机断层扫描重建的局限性。该问题在冠状动脉血管造影成像和乳房断层合成中有几个重要的临床应用。我们首先表明，有限视图重建问题可以表述为度量标签问题的“约束”版本。这为线性规划框架奠定了基础，该线性规划框架将度量标准标签分类和代数层析重建（ART）统一在一个统一模型中：必须重新分配体素，以最大程度地保持与输入重建和ART目标的一致性。该方法可以可靠地重建具有多个对比对象的体积，我们在锥豆计算机体层摄影术上进行了实验。

著录项

  • 作者

    Singh, Vikas.;

  • 作者单位

    State University of New York at Buffalo.$bComputer Science and Engineering.;

  • 授予单位 State University of New York at Buffalo.$bComputer Science and Engineering.;
  • 学科 Engineering Biomedical.; Health Sciences Radiology.; Computer Science.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 177 p.
  • 总页数 177
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 生物医学工程;预防医学、卫生学;自动化技术、计算机技术;
  • 关键词

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