## 1 Introduction  
Breast cancer is one of the leading causes of death in women around the world and diagnosing breast cancer in its early stages will always remain crucial [1, 2]. Breast ultrasound is widely used in clinical diagnosis for its advantages of safety and low cost. Generally, accurate tumor segmentation is necessary and significant for precise diagnosis using breast ultrasound. However, fully automatic segmentation methods are difficult to obtain accurate results that can meet clinical analysis standards [3]. This is mainly related to the poor quality of the ultrasound images, but also to the limitations of the segmentation model. Compared to automatic segmentation methods that gives results at once, the advantage of interactive segmentation is that the user provides prior knowledge about the object through interactions to guide the refinement of the segmentation result [4]. In a real clinical situation, each patient may have multiple ultrasound images, and it is unrealistic to use manual annotation of tumor boundaries for all of them. Therefore, interactive segmentation tools with fast implementation of high accuracy segmentation have a significant meaning for clinical use. There are three key points of excellent interaction segmentation of medical images: simple type of interactions, efficient interaction information transfer, and the use of prior knowledge. Existing interactive segmentation methods have different types of interactions, which can be divided into providing points [5; 6; 7; 8; 9], scribbles [10; 11; 12; 13; 14; 15; 16], a bounding box (BB), or a polygon box (PB) [11; 17]. Among these ways, providing scribbles, BB and PB require the user to swipe the mouse pointer over the image for a long time, while clicking on points is intuitively the easiest interaction type. Interaction information transfer refers to the way of using user interactions to guide the segmentation. Most of the existing interaction segmentation methods use Gaussian probability maps, distance transforms, etc., to transfer user interaction information to the segmentation mode. However, they cannot utilize both the location information of interaction points and the contextual information of the image. Since human interaction is actually providing prior information to the network, using prior information in the model can reduce the number of user interactions but few ways take advantage of this. Some conventional interactive segmentation methods are based on graph theory. The graph cuts [10] method uses the Gaussian mixture model (GMM) as the underpinning model and needs the user's scribbles for refinement. In this method, a large number of scribbles are needed before getting a satisfactory accuracy. GrabCut [11] requires the user to provide a bounding box to limit the region of interest (ROI) to take less scribbles, but its performance is poor on medical images as graph cuts [10] on account of the same GMM model. The Random walker segmentation method [12] uses random walker as the basic model to attain a refined result. These three methods all require a lot of user interactions due to the poor performance of underpinning model. In 2007, [PERSON] et al. proposed an interactive framework [13] using geodesic distances to convert user-provided scribbles, so that the target could be automatically segmented. This was the first method to use geodesic distance transform for interactive segmentation, while some subsequent methods [14; 15; 16] have improved on this. However, all of them only perform well on images with large differences between foreground and background, because the geodesic distance focuses on the gradient information of the original image. In order to break through the limitations of traditional method, interactive segmentation methods based on CNNs have been proposed. [PERSON] et al. [5] converted user's interaction points into Euclidean distance maps based on foreground and background points.