Efficient convex optimization-based curvature dependent contour evolution approach for medical image segmentation

Markov random field (MRF) based approaches are extensively used in image segmentation applications, which often produce segmentation results with a boundary of minimal length/surface and tending to pass along image edges, yet affected by boundary shrinkage or bias in the absence of proper image edge information to drive the segmentation. In this paper, we propose a novel curvature re-weighted boundary smoothing term and introduce a new convex optimization-based contour/surface evolution method for medical image segmentation. The proposed curvature-based term generates the optimal solution with low curvatures and helps to avoid boundary shrinkage and bias. This is particularly useful for segmenting medical images, in which noisy and poor image quality exists widely and the shapes of anatomical objects are often smooth and even convex. Moreover, a new convex optimization-based contour evolution method is applied to propagate the initial contour to the object of interest efficiently and robustly. Distinct from the traditional methods for contour evolution, the proposed algorithm provides a fully time-implicit contour evolution scheme, which allows a large evolution step-size to significantly speed up convergence. It also propagates the contour to its globally optimal position during each discrete time-frame, which improves the algorithmic robustness to noise and poor initialization. The fast continuous max-flow-based algorithm for contour evolution is implemented on a commercially available graphics processing unit (GPU) to achieve a high computational performance. Experimental results for both synthetic and 2D/3D medical images showed that the proposed approach generated segmentation results efficiently and increased the accuracy and robustness of segmentation by avoiding segmentation shrinkage and bias.