Three-dimensional elliptical reconstruction for stereoscopic magnetic resonance angiography

Stereoscopic MRA acquires a pair of blood vessel projections at two different viewing angles. Previously, we have developed two algorithms to reconstruct 3-D blood vessels from stereoscopic MRA. The assumption we made was that blood vessels were tilting circular tubes and the shape of the vessel on every cross-section was an ellipse. Since an ellipse can be represented in either algebraic form or parametric form, our previous algorithms reconstructed the ellipses by representing them in these two forms. In this paper, we further improved the accuracy of our previous algorithms by an order through two enhancements. The first improvement we made was a better method to estimate the rotation angle of the major axis of an ellipse. Instead of using the center of two adjacent ellipses to estimate the rotation angle as in our previous method, the new method used the projection lengths of the two views to estimate the angle. The second improvement we made was the equation to describe the relationship between the major/minor axes and the projection lengths. In our experiments, the average estimation error for the parametric algorithm was improved from 0.471 pixels to 0.066 pixels. The average error for the algebraic algorithm was improved from 0.101 pixels to 0.014 pixels.