## 1 Introduction
The five-channel image (original RGB channels and two distance transform map) was used as the input of a full convolutional network (FCN) to obtain the segmentation result. Euclidean distance transform is concerned with the location information of interaction points and cannot utilize image contexts information. BIFSeg [6] uses an image segmentation method similar to GrabCut [11]. The user first draws a boundary box as the input for CNN to obtain an initial result. Then, image-specific fine-tuning conducts CNN to improve segmentation results. DeepIGeoS [7] firstly proposes using geodesic distance maps as part of the input for CNNs. Geodesic distance maps can reflect the grayscale texture information of the original image by calculating the shortest distance from the full image to a specific point, so that CNNs can identify mis-segmentations of foreground and background from the input data to refine the segmentation result. However, it is sensitive to the contrast and spatial information of the image, and lacks the importance of clearly indicating the location information of the interaction point. For example, in the case of blurred tumor boundary, the geodesic distance near the boundary does not change significantly due to the small image gray gradient change, while the Euclidean distance is only related to the locations of interactions and not influenced by the quality of the original image. This means that the Euclidean distance is more effective than the geodesic distance in pointing out the misalignment area. Therefore, there is an urgent need for a method that combines the advantages of both distance transforms. In this paper, we proposed a one-stage interactive segmentation framework for breast ultrasound image based on the above three key points. Compared with existing two-stage interactive segmentation networks [6, 7] to refine the result of automatic segmentation network, our method has several advantages. First, our method can use the same CNN network (I-net) to obtain the automatic segmentation and refined results in turn. We trained I-net on automatic segmentation task to ensure that it could provide an initial segmentation when inputting the only original image. Second, our method has more effective interaction information transfer. We proposed a weighted distance transform combined geodesic distance and Euclidean distance transforms, which means the distance map could reflect both the texture information near the object area and the location information of the interaction points in the whole image. Third, our method can reduce the number of interactions for the use of prior information in the training phase. We referred to the proposed framework as the interactive segmentation using weighted distance transform (WDTSeg). The main contributions of the proposed method are as follows:  
(1) We proposed a one-stage interactive segmentation framework for breast ultrasound image segmentation, which is the first method to use a network to get both automatic and interactive segmentation. The training process was greatly simplified because no additional automatic segmentation network was required to provide the initial results;  
(2) We proposed to convert user interactions into maps with weighted distance transform which combines geodesic distance and Euclidean distance transforms. This combination can effectively convey both location information of interaction points and exploit image contexts knowledge;  
(3) We proposed a shape-aware compound loss function using the prior knowledge of breast tumors in the training phase to reduce the number of interactions. The compound loss function improved the accuracy of model segmentation while avoiding oscillation and overfitting in the training process.