# EDC-Net: Edge Detection Capsule Network for 3D Point Clouds
## 2 Related Work
### Capsule Network  
The primary idea of capsule networks was initially introduced in [42] as a local component of artificial neural networks in which each capsule learns to recognize an implicitly defined visual entity over a limited domain of viewing conditions. This idea of capsules was developed afterwards into a dynamic routing mechanism between capsules in [23] as CapsNet (capsule networks). In the CapsNet model, capsules are groups of neurons that act together; and the information is stored at the vector level instead of scalar level. CapsNet [23] used the concept of iterative routing-by-agreement and squashing function on the output vector to get the activation capsules. Capsule networks recently proved to be powerful tools for a broad range of problems and have been applied in various lines of research; a thorough review of capsule networks can be found in [24]. Furthermore, the concept of CapsNet recently has been applied in point cloud processing research [25; 26; 27; 28; 29]. 3D Point Capsule Networks [25] proposed an auto-encoder to process sparse 3D point clouds while maintaining spatial arrangements of the input data. The geometric capsules approach is introduced in [26] to learn object representations from 3D point clouds by bundles of geometrically interpretable hidden units based on pose and features. Quaternion equivariant capsule networks [28] proposed to learn a pose-equivariant representation of objects by building a hierarchy of local reference frames where each frame is modeled as a quaternion. 3 DCapsule [29] replaced the common fully connected classifier with a 3D capsule architecture in order to determine the spatial relationship between feature vectors by mapping feature vectors to capsules. DCG-Net [27] employed the agreement voting concept of capsules to build an aggregation neighborhood graph from a raw point cloud for the tasks of segmentation and classification.  
While the aforementioned approaches applied a capsule network for different problems of point cloud processing, our proposed approach concentrates on employing a capsule network for a point-wise segmentation task to detect edges of point clouds. There was recent study that employed capsule networks for the segmentation tasks [43; 44; 45; 46; 47]. Matwo-CapsNet [43] presented a multi-label semantic segmentation technique based on capsule networks. Matwo-CapsNet combines pose and appearance information and encodes them as matrices through a dual routing mechanism. In [44] a segmentation architecture was developed based on capsule networks by improving the expectation-maximization routing algorithm (EM-routing). TraceCaps [45] is a capsule-based network architecture for semantic segmentation problems. It benefits from the part-whole dependencies attribute in capsule layers. TraceCaps derives the probabilities of the class labels for each capsule through a recursive, layer-by-layer procedure to build a segmentation network. SegCaps [46; 47] is a convolutional-deconvolutional capsule network for the task of object segmentation. It extended the idea of convolutional capsules with locally-connected routing and proposed the concept of deconvolutional capsules. Unlike these models that are used for 2D images and for medical image applications, our proposed EDC-Net model merely focuses on 3D point clouds and defines the problem of edge detection as a segmentation task.