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Nuclei segmentation is a fundamental task in histopathology image analysis. Typically, such segmentation tasks require significant effort to manually generate accurate pixel-wise annotations for fully supervised training. To alleviate such tedious and manual effort, in this paper we propose a novel weakly supervised segmentation framework based on partial points annotation, i.e., only a small portion of nuclei locations in each image are labeled. The framework consists of two learning stages. In the first stage, we design a semi-supervised strategy to learn a detection model from partially labeled nuclei locations. Specifically, an extended Gaussian mask is designed to train an initial model with partially labeled data. Then, selftraining with background propagation is proposed to make use of the unlabeled regions to boost nuclei detection and suppress false positives. In the second stage, a segmentation model is trained from the detected nuclei locations in a weakly-supervised fashion. Two types of coarse labels with complementary information are derived from the detected points and are then utilized to train a deep neural network. The fully-connected conditional random field loss is utilized in training to further refine the model without introducing extra computational complexity during inference. The proposed method is extensively evaluated on two nuclei segmentation datasets. The experimental results demonstrate that our method can achieve competitive performance compared to the fully supervised counterpart and the state-of-the-art methods while requiring significantly less annotation effort.