Probabilistic vessel axis tracing and its application to vessel segmentation with stream surfaces and minimum cost paths.

We propose a novel framework to segment vessels on their cross-sections. It starts with a probabilistic vessel axis tracing in a gray-scale three-dimensional angiogram, followed by vessel boundary delineation on cross-sections derived from the extracted axis. It promotes a more intuitive delineation of vessel boundaries which are mostly round on the cross-sections. The prior probability density function of the axis tracer's formulation permits seamless integration of user guidance to produce continuous traces through regions that contain furcations, diseased portions, kissing vessels (vessels in close proximity to each other) and thin vessels. The contour that outlines the vessel boundary in a 3-D space is determined as the minimum cost path on a weighted directed acyclic graph derived from each cross-section. The user can place anchor points to force the contour to pass through. The contours obtained are tiled to approximate the vessel boundary surface. Since we use stream surfaces generated w.r.t. the traced axis as cross-sections, non-intersecting adjacent cross-sections are guaranteed. Therefore, the tiling can be achieved by joining vertices of adjacent contours. The vessel boundary surface is then deformed under constrained movements on the cross-sections and is voxelized to produce the final vascular segmentation. Experimental results on synthetic and clinical data have shown that the vessel axes extracted by our tracer are continuous and less jittered as compared with the other two trace-based algorithms. Furthermore, the segmentation algorithm with cross-sections are robust to noise and can delineate vessel boundaries that have level of variability similar to those obtained manually.