Bullitt E, Liu A, Pizer S M
Division of Neurosurgery, University of North Carolina, Chapel Hill 27599, USA.
Med Phys. 1997 Nov;24(11):1679-87. doi: 10.1118/1.597954.
We have previously described an approach to 3D intracerebral vascular reconstruction that uses an MRA as a reconstruction base. Additional vessels seen only by angiography are added by segmenting 2D curves from projection angiograms and reconstructing these curves into 3D, building upon the MRA. This paper is the second of two that discuss the specific problem of reconstructing a 3D curve from a given pair of 2D curves in the presence of error. The method presented is capable of detecting and handling many errors produced by misregistration, image distortion, or misdefinition of 2D curves. The first paper gives an algorithm. The current paper discusses factors affecting the accuracy of a reconstructed curve, with emphasis upon registration error. We analyze the spatial accuracy of a reconstructed point in terms of the relationships between pixel size, relative viewing angle, 3D point location, and registration error. We provide a theoretical framework that, given the known error properties of a registration algorithm, allows optimization of the viewing geometry so as to produce the highest precision of point reconstruction. A major focus is the effect of registration error upon the reconstruction of a curve. We subdivide registration error into two types, one of which produces smoothly continuous point placement errors and the other of which produces pixel pairing errors. We test our ability to reconstruct a 3D curve in the presence of both. Finally, we summarize approaches to other sources of error. We conclude with a list of recommendations to optimize reconstruction accuracy. When projection points are associated by the rules of epipolar geometry, viewplane point displacements should not exceed 1.5-2 mm along the axis perpendicular to epipolar planes.
我们之前描述了一种三维脑内血管重建方法，该方法以磁共振血管造影（MRA）作为重建基础。仅通过血管造影看到的额外血管，是通过从投影血管造影中分割二维曲线并将这些曲线重建为三维来添加的，这是在MRA的基础上进行的。本文是两篇讨论在存在误差的情况下从给定的一对二维曲线重建三维曲线这一具体问题的论文中的第二篇。所提出的方法能够检测和处理由配准错误、图像失真或二维曲线定义错误产生的许多误差。第一篇论文给出了一种算法。当前论文讨论影响重建曲线精度的因素，重点是配准误差。我们根据像素大小、相对视角、三维点位置和配准误差之间的关系，分析重建点的空间精度。我们提供了一个理论框架，在已知配准算法误差特性的情况下，该框架允许优化视角几何结构，从而实现点重建的最高精度。一个主要重点是配准误差对曲线重建的影响。我们将配准误差细分为两种类型，其中一种会产生平滑连续的点放置误差，另一种会产生像素配对误差。我们测试了在这两种误差同时存在的情况下重建三维曲线的能力。最后，我们总结了针对其他误差来源的方法。我们以一系列优化重建精度的建议作为结论。当投影点按照极线几何规则关联时，沿垂直于极平面的轴，视平面点位移不应超过1.5 - 2毫米。
