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Medical instrument segmentation in 3D ultrasound is essential for image-guided intervention. However, to train a successful deep neural network for instrument segmentation, a large number of labeled images are required, which is expensive and time-consuming to obtain. In this article, we propose a semi-supervised learning (SSL) framework for instrument segmentation in 3D US, which requires much less annotation effort than the existing methods. To achieve the SSL learning, a Dual-UNet is proposed to segment the instrument. The Dual-UNet leverages unlabeled data using a novel hybrid loss function, consisting of uncertainty and contextual constraints. Specifically, the uncertainty constraints leverage the uncertainty estimation of the predictions of the UNet, and therefore improve the unlabeled information for SSL training. In addition, contextual constraints exploit the contextual information of the training images, which are used as the complementary information for voxel-wise uncertainty estimation. Extensive experiments on multiple ex-vivo and in-vivo datasets show that our proposed method achieves Dice score of about 68.6%-69.1% and the inference time of about 1 sec. per volume. These results are better than the state-of-the-art SSL methods and the inference time is comparable to the supervised approaches., Comment: Accepted by IEEE JBHI