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Binary semantic segmentation in computer vision is a fundamental problem. As a model-based segmentation method, the graph-cut approach was one of the most successful binary segmentation methods thanks to its global optimality guarantee of the solutions and its practical polynomial-time complexity. Recently, many deep learning (DL) based methods have been developed for this task and yielded remarkable performance, resulting in a paradigm shift in this field. To combine the strengths of both approaches, we propose in this study to integrate the graph-cut approach into a deep learning network for end-to-end learning. Unfortunately, backward propagation through the graph-cut module in the DL network is challenging due to the combinatorial nature of the graph-cut algorithm. To tackle this challenge, we propose a novel residual graph-cut loss and a quasi-residual connection, enabling the backward propagation of the gradients of the residual graph-cut loss for effective feature learning guided by the graph-cut segmentation model. In the inference phase, globally optimal segmentation is achieved with respect to the graph-cut energy defined on the optimized image features learned from DL networks. Experiments on the public AZH chronic wound data set and the pancreas cancer data set from the medical segmentation decathlon (MSD) demonstrated promising segmentation accuracy and improved robustness against adversarial attacks. 

Multiple-surface segmentation in optical coherence tomography (OCT) images is a challenging problem, further complicated by the frequent presence of weak image boundaries. Recently, many deep learning-based methods have been developed for this task and yield remarkable performance. Unfortunately, due to the scarcity of training data in medical imaging, it is challenging for deep learning networks to learn the global structure of the target surfaces, including surface smoothness. To bridge this gap, this study proposes to seamlessly unify a U-Net for feature learning with a constrained differentiable dynamic programming module to achieve end-to-end learning for retina OCT surface segmentation to explicitly enforce surface smoothness. It effectively utilizes the feedback from the downstream model optimization module to guide feature learning, yielding better enforcement of global structures of the target surfaces. Experiments on Duke AMD (age-related macular degeneration) and JHU MS (multiple sclerosis) OCT data sets for retinal layer segmentation demonstrated that the proposed method was able to achieve subvoxel accuracy on both datasets, with the mean absolute surface distance (MASD) errors of 1.88 ± 1.96μmand 2.75 ± 0.94μm, respectively, over all the segmented surfaces. 

Segmentation of multiple surfaces in optical coherence tomography (OCT) images is a challenging problem, further complicated by the frequent presence of weak boundaries, varying layer thicknesses, and mutual influence between adjacent surfaces. The traditional graph-based optimal surface segmentation method has proven its effectiveness with its ability to capture various surface priors in a uniform graph model. However, its efficacy heavily relies on handcrafted features that are used to define the surface cost for the “goodness” of a surface. Recently, deep learning (DL) is emerging as a powerful tool for medical image segmentation thanks to its superior feature learning capability. Unfortunately, due to the scarcity of training data in medical imaging, it is nontrivial for DL networks toimplicitlylearn the global structure of the target surfaces, including surface interactions. This study proposes to parameterize the surface cost functions in the graph model and leverage DL to learn those parameters. The multiple optimal surfaces are then simultaneously detected by minimizing the total surface cost whileexplicitlyenforcing the mutual surface interaction constraints. The optimization problem is solved by the primal-dual interior-point method (IPM), which can be implemented by a layer of neural networks, enabling efficient end-to-end training of the whole network. Experiments on spectral-domain optical coherence tomography (SD-OCT) retinal layer segmentation demonstrated promising segmentation results with sub-pixel accuracy.