Efficient Optimal Surface Detection: Theory, Implementation and Experimental Validation

In this paper, a novel polynomial-time algorithm is described for solving the optimal net surface detection problem on proper ordered multi-column graphs in N -D space (N ≥ 3). The method is applied to searching for optimal object boundaries with arbitrary smoothness constraints in volumetric medical images. By simple transformations, such optimal surface detection problems can be simplified to a problem of computing the minimum s-t cuts in the transformed graphs. An efficient implementation for the 3-D case that can achieve near real-time performance on moderate-sized datasets is presented. We further examine our technique in experiments by segmenting the cylindrical surfaces of human airways from pulmonary volumetric CT images, and compare the results to those produced by previous methods. By allowing full specifications of the costfunction and smoothness constraints without degrading the performance, the new algorithm is more flexible than traditional methods and guarantees global optimality. The multi-dimensional nature of the algorithm maintains continuity in higher dimensions.