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標題: 以立體血管顯像術重健三維血管模型的新方法
New Methods to Reconstruct 3-D Blood Vessel Models from Stereoscopic Magnetic Resonance Angiography
作者: 郭蕾欣
Kuo, Lei-Hsin
關鍵字: MRA;磁振造影血管顯影術;projection;blood vessel;reconstruction;投影;血管;重建
出版社: 電機工程學系

Magnetic resonance angiography (MRA) is an imaging technique to show the blood vessels without all the other tissues. There are two approaches to acquire an image of MRA. One is to project the 3-D vessels onto 2-D plane; the other is to directly obtain the complete 3-D information. The advantage of 3-D MRA is that one can view the data from arbitrary direction. However, the scan time is usually very long. To shorten the scan time, 2-D MRA is used, but the depth of information will be sacrificed. Therefore, we researched on the subject of reconstructing 3-D vessels from two projective MRA images.
Stereoscopic magnetic angiography utilizes two images by projecting blood vessels onto 2-D plane in two angles. For digital subtraction angiography (DSA), the pixel value is the integration of the attenuation value in the path of the X-ray. We can use this property to derive the shape of the vessels by solving the integrals. On the other hands, there are many imaging parameters in MRA(such as T1, T2, proton density, and so on). Therefore, it is difficult to obtain the relation between the shape of the vessels and the pixel intensity. For this reason, we attempt to reconstruct the shape of the vessels by geometry. We assume that blood vessels are tilted circular tube and the shape of blood vessels on every cross-section is approximately an ellipse. Based on these assumptions, we developed an algorithm to estimate the parameters of the ellipse from the boundaries of the projective images. The reconstructed ellipses are then taken as the 3-D shape of the vessels.
To describe of an ellipse, we needed its semiaxis lengths together with its rotation angles with respect to the coordinate system. While this representation was intuitive, it proved inconvenient for reconstruction as it led to complicated equations. Alternatively, we represented an ellipse using a symmetric matrix. This representation ed to a simple linear relationship between the ellipse and its orthogonal projection.
In the thesis, eighty images of MRA were used to demonstrate the capability of our algorithm. From these images, we used fifty images to make two projective images. The two projections are 150 apart. We used our algorithm to estimate all the ellipses and reconstructed the 3-D model of the vessels, and then we compared the boundaries of the original projective images with the boundaries of the re-projective images of the reconstructed 3-D model, the average error is 0.1011.
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