# EDC-Net: Edge Detection Capsule Network for 3D Point Clouds
## 1 Introduction  
Point cloud data is a fundamental class of 3D data--a type of raw data from various 3D sensor devices. Point clouds are playing an important role in the computer vision community due to their rich geometric information and the proliferation of 3D sensors. Furthermore, a wide range of applications in robotics, autonomous-driving and virtual/augmented reality can directly be obtained the 3D point cloud data. The importance of 3D point cloud data stems from their depth information and geometric structure; 2D imagery yields a lot of ambiguities because of the lack of this information. Edges in 3D point clouds are considered as remarkably meaningful features due to their capability of representing the topological shape of a set of points. Extracting edges from 3D point clouds is one of the fundamental shape understanding methods which is able to describe the abstract features of a point set. Edges offer an intuitive and low dimensional representation of point clouds. Therefore, extracting edges from point clouds provides a smaller chunk of data while preserving the feature information of shapes in point clouds. There are several applications of edge extraction in photogrammetry, CAD (computer-aided design) and urban scenes analyses [1; 2; 3]. The proliferation of algorithms for reconstructing 3D objects, e.g., [4; 5], is an affirmation of the importance of the 3D information in the unreachable cases to the 3D sensors. Deep learning algorithms have proven their robustness in various lines of research; however, there are still many challenges in applying CNNs (convolutional neural networks) for 3D point clouds since they are sets of unordered 3D points without any spatial order and regular structure. PointNet [6] and PointNet++ [7] have made fundamental improvements in this case to train a model directly through the 3D point clouds. Recently, many network architectures [8; 9; 10; 11] were inspired by these pioneer techniques [6; 7]. However,applying CNNs for the edge detection problem in point clouds is still challenging. The majority of edge detection techniques are based on signal processing and local geometry properties [1; 2; 3; 12; 13; 14; 15; 16], although recently there was some research that applied deep learning techniques for edge detection from point clouds [17; 18; 19; 20; 21; 22]. In this paper, we introduce a novel approach for edge detection from point clouds based on the main concepts of capsule networks [23]. Capsule networks recently have proven excellent performance in the several applications [24], and to the best of our knowledge, we are the first to apply capsule networks for the edge detection task of 3D point clouds. The key difference in our proposed method compared with the recent CNN-based edge detection methods [17; 18; 19; 20; 21; 22] is the usage of capsule networks for edge detection. The remarkable advantage of capsule networks is based on the information that is stored at the vector level instead of scalar. Capsules are groups of neurons that act together for storing the information at the vector level. The nature of neurons in the conventional CNNs is scalar and additive, and this makes the neurons ambivalent to the spatial relationships of neurons within the kernel of the previous layer in any given layer of a network. In capsule networks the information at the neuron level is stored as vectors in lieu of scalars. These sets of neurons are defined as capsule types. Dynamic routing between capsules exploits the agreement between these capsule vectors to extract part-to-whole relationships. These vectors contain information about spatial orientation. This is a very notable factor in point clouds since the capsule layers are capable of disentangling geometrical features of point clouds. This is the reason that capsule networks recently attracted attention in 3D point cloud applications [25; 26; 27; 28; 29]; none of them, however, applied capsule networks for edge detection task.