Faster segmentation algorithm for optical coherence tomography images with guaranteed smoothness

This paper considers the problem of segmenting an accurate and smooth surface from 3D volumetric images. Despite extensive studies in the past, the segmentation problem remains challenging in medical imaging, and becomes even harder in highly noisy and edge-weak images. In this paper we present a highly efficient graph-theoretical approach for segmenting a surface from 3D OCT images. Our approach adopts an objective function that combines the weight and the smoothness of the surface so that the resulting segmentation achieves global optimality and smoothness simultaneously. Based on a volumetric graph representation of the 3D images that incorporates curvature information, our approach first generates a set of 2D local optimal segmentations, and then iteratively improves the solution by fast local computation at regions where significant improvement can be achieved. It can be shown that our approach monotonically improves the quality of solution and converges rather quickly to the global optimal solution. To evaluate the convergence and performance of our method, we test it on both artificial data sets and 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. Comparing to the 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. Our approach can be easily generalized to multi-surface detection.