Globally optimal 3D graph search incorporating both edge and regional information: application to aortic MR image segmentation
Qi Song, Xiaodong Wu, Xin Dou, Milan Sonka · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
We present a novel method for incorporating both edge and regional image information in a 3-D graph-theoretic approach for globally optimal surface segmentation. The energy functional takes a ratio form of the "onsurface" cost and the "in-region" cost. We thus introduce an optimal surface segmentation model allowing regional information such as volume, homogeneity and texture to be included with boundary information such as intensity gradients. Compared to the linear combination as in the standard active contour energies, this ratioform energy is parameter free with no bias toward either a large or small region. Our method is the first attempt to use a ratio-form energy functional in graph search framework for high dimensional image segmentation, which delivers a globally optimal solution in polynomial time. The globally optimal surface can be achieved by solving a parametric maximum flow problem in the time complexity of computing a single maximum flow. Our new approach is applied to the aorta segmentation of 15 3-D MR aortic images from 15 subjects. Compared to an expert-defined independent standard, the overall mean unsigned surface positioning error was 0.76± 0.88 voxels. Our experiments showed that the incorporation of the regional information was effective to alleviate the interference of adjacent objects.