# Boundary-Inner Disentanglement Enhanced Learning for Point Cloud Semantic Segmentation
## 1 Introduction  
Semantic information is the key to understanding the virtual scene constructed by a point cloud [1] in applications such as indoor navigation [2], autonomous driving [3], and cultural heritage [4]. Advances in the current semantic segmentation networks are due to various delicate designs of local aggregation operators (LAOs), which generally take the features and coordinates of the center point and its neighboring points as input, outputting the transformed feature for the center point [5]. Nevertheless, most LAOs aggregate the features of all neighboring points equally, thus smoothing the extracted features on the semantic boundary, which results in a bad contour for final semantic segmentation. Here, the semantic boundary refers to the transitional area between objects with different categories. For example, the joint where the window meets the wall can be defined as the boundary (the points not on the boundary make up the inner areas), as shown in the red regions in Figure 1.  
There are a few boundary-related methods for point cloud semantic segmentation [6, 7, 8, 9, 10, 11, 12]. IAF-Net [6] adaptively selects indistinguishable points such as boundary points and improves the segmentation performance of these points through multistage loss. JSENet [7] adds a semantic edge detection stream, which outputs the semantic edge map and jointlylearns the semantic segmentation and semantic edge. BoundaryAwareGEM [8] constitutes a boundary prediction module to predict the boundary, utilizing the predicted boundary to generate LAO aggregate features with discrimination. PushBoundary [9] consists of two streams for prediction of the boundary and the direction of the interior, thus guiding boundaries to their original locations. Most of these methods rely on additional boundary prediction modules, thus increasing model complexity. Unlike existing works, this paper is motivated by the goal of improving the segmentation accuracy of boundary points without requiring additional modules and learning parameters. It is well known that endowing a point cloud with boundary information can help improve the overall segmentation accuracy [12]. The boundary information can change the segmentation result by affecting features learned by the network. To explore the role of the boundary, this paper analyzes the change in feature similarity between the boundary point and its neighboring points utilizing the boundary information. Specifically, for every boundary point, its neighboring points are partitioned into four collections in terms of two factors: whether they are on the boundary, and whether their categories are the same as the center point. Then, the entanglement between the boundary point and each collection of neighboring points is measured, representing their proximity in the representation space. Results show that the boundary can weaken the boundary-inner entanglement, where \"boundary-inner\" represents the boundary point and its neighboring points in inner areas. It is shown that reducing the boundary-inner entanglement is beneficial for improving the segmentation accuracy. Therefore, to improve the segmentation accuracy of boundary points, a lightweight Boundary-Inner Disentanglement Enhanced Learning (BIDEL) framework is proposed, which can maximize the boundary-inner feature distinction through a newly defined boundary loss function \(L_{BIDEL}\). Boundary information is only utilized in the loss function at the training stage; thus, BIDEL does not need additional modules for explicit boundary prediction. Experiments with two classic baselines across three datasets demonstrate that BIDEL can assist the baseline in obtaining a better accuracy of boundary points and small objects. In summary, the following key contributions are highlighted:  
1. This paper shows that reducing boundary-inner entanglement is beneficial for overall semantic segmentation accuracy. 2.