Surfaces, Objects, and Their Borders in Multidimensional Images: Theory and Algorithms

本研究的目的是（一）制定一个统一的 n维物体及其边界的几何理论 离散空间，以及（ii）开发用于检测的算法 n维图像中的对象和边界。 的途径 理论发展使用n空间的正交镶嵌 变成超立方体，导致离散的结果 连续拓扑的一些基本结果的对应。 因此，对象和边界可以表示为图形， 它们的检测转换为图遍历。 该算法 开发集中于设计有效的遍历算法， 当图像是局部可分割的时和当它们可以 不是。 在前一种情况下， 一棵树，很容易就能爬起来。 在后一种情况下，没有 独特的解决方案，因此该方法是开发最佳的 (e.g.,使用动态规划）和次优遍历 战略布局 长期以来，PI一直致力于 医学图像和断层扫描分析。 的发展 可视化和分析的常用理论和算法 图像将在许多学科中使用多维 图像数据。

The objectives of this research are (i) to develop a unified geometric theory of objects and their boundaries in n-dimensional discrete spaces, and (ii) to develop algorithms for detecting objects and boundaries in n-dimensional images. The approach to theory development uses an orthogonal tesselation of the n-space into hypercubes, leading to results which are discrete counterparts of some essential results of continuous topology. Thus, objects and boundaries can be represented as graphs, and their detection translates to graph traversal. The algorithm development focuses on devising efficient traversal algorithms, both when the images are locally segmentable and when they may not be. In the former case there is always a unique spanning tree which is easy to traverse. In the latter case, there is no unique solutino and hence the approach is to develop optimal (e.g., using dynamic programming) and suboptimal traversal strategies. The PIs have a long history of contributions to the analysis of medical images and tomography. The development of common theory and algorithms for visualization and analysis of images will be of use in many disciplines using multidimensional image data.