Mathematical Sciences: RUI: Geometric Tomography

首席研究员将研究几何问题 断层扫描和开发方法，以重建的几何形状 凸体的投影。他将探索新的 方向的算法方面的重建凸 体和多面体从X射线，他们的互动测定 以及交叉体的分类。两 本科生将在该项目的部分工作下， 主要研究者的指导。 该奖项将支持一般领域的研究， 积分几何通常可以分析集合的几何 并通过将集合分解为切片来描述。的 切片的几何形状通常相当简单， 形容分析的主要困难通常是 重建的基本几何特征的整个 从切片的几何形状设置。一个众所周知的应用 这个数学领域就是CAT扫描。

The principal investigator will study problems in geometric tomography and develop methods to reconstruct the geometry of convex bodies from projections. In particular he will explore new directions in the algorithmic aspects of reconstructing convex bodies and polytopes from X-rays, their interactive determination from X-rays, and the classification of intersection bodies. Two undergraduate students will work on parts of the project under the direction of the principal investigator. This award will support research in the general area of integral geometry. The geometry of a set may often be analyzed and described by a decomposition of the set into slices. The geometry of the slices is often fairly simple and easy to describe. The main difficulty in the analysis is usually the reconstruction of the underlying geometric features of the entire set from the geometry of the slices. One well know application of this area of mathematics is the CAT scan.