## 3 Methodology
### Point-Sampling Method  
In the field of image analysis, images are often regarded as regular grids of pixels (points). Their feature vectors are hidden representations on the regular grid of an image. In the task of image semantic segmentation, pixels are upsampled uniformly on the hidden representations and then mapped to a set of labels. These labels will be used as output masks to indicate the predicted category at each pixel. The render method does not calculate labels uniformly on the hidden representation but adaptively selects uncertain points to calculate their labels. We adopt the idea of the classic subdivision [33] strategy to render high-resolution images from low-resolution features. This strategy only calculates some locations where the values are significantly different from their neighbors. The values at other locations are obtained by interpolating the existing results. This process, named **point-sampling** method in this paper, restores features from low-resolution by calculating the labels of uncertain points. The point-sampling method is used to replace upsampling method in the 3D ANU-Net architecture and to solve the boundary blur problem. The point-sampling process is described in Figure 4, which consists of the following steps:  
1. The encoder-decoder architecture (black arrows) takes an input image and extracts features from encoder (green arrows and grids). 2. The lightweight coarse decoder yields a coarse mask prediction for target object (red arrows) and up-samples features (blue arrows and grids) using bilinear interpolation. 3. To improve the coarse mask, the point-sampling method selects a set of uncertain points (red dots) from coarse prediction. 4. A simple multilayer perception is used to extract the point-features of each point independently and predicts their labels. 5. The point features are mapped to the size of the encoder feature (dashed gray arrows), and the features at the corresponding position are replaced (dashed red arrows) to obtain the point-sampling features (red grids). 6. The encoder features are concatenated with the up-sampling feature and point-sampling features after passing through the attention gate. 7. The concatenated features are input into the fine decoder (black arrows) to obtain the fine prediction result. Compared with the original up-sampling method, the point-sampling method increases the selection of uncertain points (step 3) and the extraction of point features (step 4). Therefore, how to flexibly and adaptively select uncertain points in the image and to extract corresponding point features to enhance segmentation has become the key of the proposed method. **Point selection strategy:** The main idea of our selection strategy is that uncertain points are also difficult to classify and belongs to the middle area in the probability distribution. After the coarse mask was predicted by a coarse decoder, there are N most uncertain points on the image plane. We believe that the selection of the most uncertain points should not only focus on uncertain areas (e.g., the boundaries between different classes) but also should retain a certain degree of uniform coverage. Such a design can achieve the greatest degree of accurate segmentation and can enhance anti-interference abilities. To achieve the goal, we referred to the following principles in [34] for point selection and balance. In this way, we obtained the fine predicted mask from low resolution. * Overgeneration: first, randomly sample KN points from a uniformlydistributed point set. These KN will be used to overgenerate candidate points, and k should be greater than 1. * Important sampling: then, we will coarsely predict the segmentation class of the above KN and then perform interpolation, calculate the uncertainty estimation of all points on the segmentation task, and select the top \(\beta\)N points with the highest uncertainty. These points are considered important points. * Unimportant sampling: after removing the abovementioned important points from KN, \((1-\beta)\)N points remain.