Figure 1025
Tracking by eigensnakes.
10.9 Extraction of Three-Dimensional Measurements from Angiograms
Presently, medical imaging techniques (in particular, angiograms) are not only supposed to give qualitative information, but also quantitative measurements about the objects to be analyzed. Whereas the technique of angiogram was developed to obtain images from the coronary vessels from different views, measurements of the vessels became necessary very soon thereafter. This is the case with the determination of stent size. When the selected stent is too large, the vessel becomes too rigid, and the lesion is not treated. Obtaining the length of stenosis is of vital importance for the success in this kind of intervention. To obtain these measurements, a view of the affected vessel is taken and the length of the lesion is inferred. The imprecision in the system calibration, as well as the foreshortening due to the view, make these measurements inexact and unreliable. To cope with this, it is necessary to address the problem of a three-dimensional reconstruction of the vessel from two x-ray views (see Figure 10.26).
There are two main approaches to reconstruct the vessel centerline in space:
1. Bottom-up strategy: the user marks the corresponding points in angiograms, and their three-dimensional point is recovered and marked by the user (see Figure 10.27),
FIGURE 10.27 (See color insert.)
A bottom-up strategy to reconstruct vessel centerline is based on user-defined corresponding points in x-ray images.
2. Top-down strategy: a three-dimensional curvilinear model is considered that deforms in space so that its projections approximate the vessel in the x-ray images as well as possible.
Different works have been presented in the literature that follow the bottom-up strategy. Dumay et al. [72] describe a method for the reconstruction of a point using two views. Wahle et al. [73] address three-dimensional reconstruction of skeletons of the coronary tree from biplane views. Wunderlich et al. [74] present a procedure to obtain the length of a lesion after its reconstruction from biplane angiograms.
Now consider the problem of three-dimensional reconstruction of vessel centerlines following the bottom-up strategy.
Given an angiogram device (see Figure 10.21), the angles by which the left-right movement of a system can be defined with respect to the patient determine the rotational angles. The angles by which the movement of a system can be defined toward the head of the patient (cranial (CR) direction) or the feet (caudal (CA) direction) determine the angulation angles. With the imaging equipment, the heart can be displayed under x-ray exposure from a left anterior oblique (LAO) view to a right anterior oblique (RAO) view, with either a cranial or caudal angulation. Rotational angles are denoted by a and angulation angles by p. For the frontal and lateral rotation angles, a > 0 represent LAO views and a < 0 represent RAO views; angulation angles p > 0 represent caudal views and p < 0 represent cranial views. Both rotational degrees of freedom are shown in Figure 10.28a and b.
The projection axes of both systems intersect in the isocenter [72]. Once fixed at position i of the fluoroscope, the acquisition parameters are predetermined
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