Three‐dimensional reconstruction of curves from pairs of projection views in the presence of error. I. Algorithms

Abstract

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. Intracerebral vascular reconstruction is difficult for at least two reasons. First, 2D curves must be associated on projection images even when the human eye cannot do so. Second, 3D curves must be reconstructed in the presence of errors such as misregistration, image distortion, and misdefinition of 2D curves. This paper is the first of two that address the specific issue of reconstruction of a 3D curve from a given pair of 2D curves in the presence of error. The method explicitly separates what can and cannot be determined from a pair of projection views. It is also capable of recognizing interruptions produced by viewplane errors, of continuing reconstruction beyond such interruptions, and of localizing and estimating the magnitude of the interruptions. These measurements can also be used to estimate the lengths of regional disparities between a pair of 2D curves, leading to a quantitative estimate of the capacity of a pair of 2D curves to combine to create a 3D object (match value). Match values can be used, in turn, as part of the strategy for automatically associating pairs of 2D curves. This paper provides methods for reconstructing a given pair of 2D curves into 3D in the presence of error and for calculating match values. Error analysis is given in the companion report.

Generating of 3D data during neurovascular interventions by using multi-projection imaging

“…The gantry information is used as an initial estimate of the imaging geometry, which is the rigid transformation (i.e., the rotation and translation) relating the coordinate systems of the two imaging systems. Using the determined imaging geometry, the corresponding points along the vessel centerlines in the two images are determined using epipolar constraints [8][9][10]. These pairs of corresponding 2D points are then triangulated using the imaging geometry to yield the 3D centerline points in the coordinate system of the bcommonQ view.…”

3D/2D registration via skeletal near projective invariance in tubular objects

“…For example, vessels "A" and "C". 3D/2D registration algorithms have applications in surgical instrument guidance (e.g., [7], [8], and [9]) and in anatomical model synthesis (e.g., [10]). An accurate, robust registration algorithm significantly improves the accuracy of reconstruction and surgical guidance.…”

Reconstruction of 3D tubular structures from cone-beam projections

“…The methods that do not require 3D cone-beam reconstruction usually first perform 2D segmentation in each projection to extract 2D centerlines, then perform tree matching over the trees from different projections to reconstruct 3D tubular structures. For example, in [2], Bullitt et al addressed the specific problem of reconstruction of 3D curves from a pair of 2D curves in the presence of error. In [1], Blondel et al performed multiocular matching to build correspondences between the centerlines of different projections.…”

“…For example, the extraction of 3D coronary arteries in the analysis of X-ray coronary angiographies [1], and the intracerebral vascular reconstruction in neurosurgeon practice [2], are both concerned with reconstructing 3D blood vessels from conebeam projections. Using a digital flat panel, cone-beam projections are usually obtained in a rotational acquisition mode with a fixed step in rotational angle.…”