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Markovian approach for 3D reconstruction of vessels from two views

A method to reconstruct vessel lumens, based on constrained reconstruction of serial cross- sections from two digital angiographic projections, is proposed. Each cross-section is reconstructed by a binary matrix from its two densitometric data projections, with ambiguities on the reconstruction removed by a priori knowledge. A probabilistic approach in which properties of the expected solution are described through a Markov Random Field (MRF) model was chosen to facilitate incorporation of a priori information on the vessel segment to be reconstructed. The best solution amongst all possible ones is obtained by the implementation of an optimization algorithm based on Simulated Annealing. An initial configuration consisting of the ellipse of best fit is constructed and then imposed to guarantee rapid convergence to the optimal solution. This initial configuration is then deformed to be made consistent with projection data while being constrained into a connected realistic shape. The MRF model parameters have been estimated on 2D synthetic slices, from systematic quality reconstruction measurements. The method provides a good reconstruction of complex shapes, and can be applied to single pathologic vessels as well as to branchings. The method thus far has only been validated on peripheral arteries and bifurcations.