Three Dimensional Reconstruction of Blood Vessels from Stereoscopic Magnetic Resonance Angiography
Magnetic resonance angiography (MRA) was an imaging technique to show the blood vessels but suppress signals from all the other tissues. There were two approaches to acquire an image of MRA. One was done in two-dimension (2-D) by projecting the three-dimensional (3-D) vessels onto 2-D plane. The other was to directly obtain the complete 3-D information. The advantage of 3-D MRA was that one can view the data from arbitrary direction. However, the scan time was usually very long for 3-D MRA. When the scan time was limited, we must use 2-D MRA and the depth information was lost. The depth information could be partially recovered using stereoscopic angiography, i.e., acquiring two 2-D images from different viewing angles. In addition to the stereoscopic views, stereoscopic angiography could also be used to reconstruct the 3-D shapes of the vessels. However, 3-D reconstruction was used more frequently in digital subtraction X-ray angiography (DSA). The main reason was that pixel intensity was directly related to the integration of the attenuation value along the path of the X-ray in DSA. Therefore, we could derive the vessel shape by solving the integrals from the two views. On the other hands, there were many imaging parameters in MRA (T1 , T2, and proton density). Therefore, it was difficult to obtain the relation between the vessel shape and the pixel intensity. For this reason, we attempted to reconstruct the shape of the vessels simply from the edge information of the two views. We assumed that the shape of the vessel on every cross-section was an ellipse. Then, we developed an algorithm to estimate the parameters of the ellipse from the boundaries of the projective images. A 3-D MRA data set was used to test the capability of our algorithm. From these data, we made two projective images. The two projections were 30o apart. We employed our algorithm to estimate all the ellipses and reconstruct the 3-D model of the vessels. Comparing the boundaries of the original projective images with the boundaries of the reconstructed 3-D model, the average error was 0.1011 pixels.