Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference

We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF inference problems. The core of our method is a very efficient bounding procedure, which combines scalable semidefinite programming (SDP) and a cutting-plane method for seeking violated constraints. In order to further speed up the computation, several strategies have been exploited, including model reduction, warm start and removal of inactive constraints. We analyze the performance of the proposed method under different settings, and demonstrate that our method either outperforms or performs on par with state-of-the-art approaches. Especially when the connectivities are dense or when the relative magnitudes of the unary costs are low, we achieve the best reported results. Experiments show that the proposed algorithm achieves better approximation than the state-of-the-art methods within a variety of time budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page

Tubular Structure Segmentation Using Spatial Fully Connected Network with Radial Distance Loss for 3D Medical Images

This paper presents a new spatial fully connected tubular network for 3D tubular-structure segmentation. Automatic and complete segmentation of intricate tubular structures remains an unsolved challenge in the medical image analysis. Airways and vasculature pose high demands on medical image analysis as they are elongated fine structures with calibers ranging from several tens of voxels to voxel-level resolution, branching in deeply multi-scale fashion, and with complex topological and spatial relationships. Most machine/deep learning approaches are based on intensity features and ignore spatial consistency across the network that are otherwise distinct in tubular structures. In this work, we introduce 3D slice-by-slice convolutional layers in a U-Net architecture to capture the spatial information of elongated structures. Furthermore, we present a novel loss function, coined radial distance loss, specifically designed for tubular structures. The commonly used methods of cross-entropy loss and generalized Dice loss are sensitive to volumetric variation. However, in tiny tubular structure segmentation, topological errors are as important as volumetric errors. The proposed radial distance loss places higher weight to the centerline, and this weight decreases along the radial direction. Radial distance loss can help networks focus more attention on tiny structures than on thicker tubular structures. We perform experiments on bronchus segmentation on 3D CT images. The experimental results show that compared to the baseline U-Net, our proposed network achieved improvement about 24% and 30% in Dice index and centerline over ratio