Despite extensive studies in the past, the problem of segmenting globally optimal single and multiple surfaces in 3D volumetric images remains challenging in medical imaging. The problem becomes even harder in highly noisy and edge-weak images. In this paper we present a novel and highly efficient graph-theoretical iterative method with bi-criteria of global optimality and smoothness for both single and multiple surfaces. Our approach is based on a volumetric graph representation of the 3D image that incorporates curvature information. To evaluate the convergence and performance of our method, we test it on a set of 14 3D OCT images. Our experiments suggest that the proposed method yields optimal (or almost optimal) solutions in 3 to 5 iterations. To the best of our knowledge, this is the first algorithm that utilizes curvature in objective function to ensure the smoothness of the generated surfaces while striving for achieving global optimality. Comparing to the best existing approaches, our method has a much improved running time, yields almost the same global optimality but with much better smoothness, which makes it especially suitable for segmenting highly noisy images.
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