Fast globally optimal single surface segmentation using regional properties
Xin Dou, Xiaodong Wu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
Efficient segmentation of globally optimal surfaces in volumetric images is a central problem in many medical image analysis applications. Intra-class variance has been successfully utilized, for instance, in the Chan-Vese model especially for images without prominent edges. In this paper, we study the optimization problem of detecting a region (volume) bounded by a smooth terrain-like surface, whose intra-class variance is minimized. A novel polynomial time algorithm is developed. Our algorithm is based on the shape probing technique in computational geometry and computes a sequence of O(n) maximum flows in the derived graphs, where n is the size of the input image. Our further investigation shows that those O(n) graphs form a monotone parametric flow network, which enables to solving the optimal region detection problem in the complexity of computing a single maximum flow. The method has been validated on computer-synthetic volumetric images. Its applicability to clinical data sets was demonstrated on 20 3-D airway wall CT images from 6 subjects. The achieved results were highly accurate. The mean unsigned surface positioning error of outer walls of the tubes is 0.258 ± 0.297mm, given a voxel size of 0.39 x 0.39 x 0.6mm3.