Abstract:
Three-dimensional reconstruction of blood vessel networks from a pair of x-ray images is a problem that has occupied the medical vision community for some time. Previous solutions have used a priori information about the blood vessel networks. These solutions have had some success reconstructing the blood vessel networks around the heart, but not those within the brain. This is because the networks in the brain exhibit greater variation in both structure and shape, which makes representing the a priori information a difficult problem. This thesis describes a representation of blood vessel networks, that catalogues the structural and shape variations. We show how this representation can be used to solve the correspondence problem posed by reconstruction from only a pair of x-rays. Our solution has several unique features: first it is not wholly based upon x-ray data; second it is able to produce several solutions. In addition, it has a very good time complexity. The entire system is of polynomial time complexity, unlike other matching techniques which have exponential time complexity. We back these claims with practical results using both real and simulated data.
