# EDC-Net: Edge Detection Capsule Network for 3D Point Clouds
## 2 Related Work
### Edge Detection  
Edge detection from point clouds has been attracting a lot of attention in various fields of research, such as robotics, photogrammetry, CAD and urban scene analyses [1; 2; 3; 15]. Conventional methods for edge extraction from point clouds were based on building a mesh [3; 15] or building a graph [13]. Reconstructing point clouds to a mesh or graph is computationally expensive. To overcome this issue, computing the difference of eigenvalues was proposed to extract edges [12]. The same idea was extended based on a segmentation [16] approach. Furthermore, discriminative learning algorithms are employed to extract edges from unorganized point clouds through a point classifier based on the edge versus non-edge points [2]. Moreover, a spatial filtering approach based on fast Fourier transform (FFT) was applied for boundary point detection to cope with the predefined threshold values [14]. Most of the techniques in the field of the edge extraction from point clouds are based on the geometric analysis; however, recently some methods have been proposed by using deep learning approaches [17; 18; 19; 20; 21; 22]. CNNs are employed to define a scalar sharpness field over the smooth underlying the moving least-squares (MLS) surface of a point cloud [22]; this technique is capable of localizing sharp features of the scanned object. An extension of of this technique was proposed in [20] by training a convolutional neural network to derive a sharpness field parametrized over the underlying smooth proxy MLS surface. Furthermore, a combination of reconstruction and edge extraction was proposed in EC-Net [21], which is an edge-aware method based on extracting local patches and training the network to learn edges in patches. EC-Net [21] introduced a deep edge-aware point cloud consolidation framework. The network is trained to reconstruct upsampled 3D point clouds. The first phase of their technique consists of point classification and regression of per-point distances to the edge. Edge points are then detected as the points with a zero point-to-edge distance. PIE-NET [17] is the pipeline of the work; the technique of this pipeline treats point cloud curve inference as a curve proposal process. In this technique, first edges and corners are identified; then the edges are extracted by curve proposal and selection approaches. A geometric attention mechanism was presented in [19] to provide normals estimating and sharp feature lines' properties in a learnable fashion which concentrates merely on geometric properties of point clouds. PCEDNet [18] presented a classification approach of edges in point clouds, where both edges and their surroundings are described. In their work, points are parameterized with a scale-space matrix (SSM) to encode extrinsic geometric properties of a surface surrounding each point of the input point cloud at multiple scales. Their proposed SSM provides information from a neural network to learn the description of edges and use it to efficiently detect them in given point clouds. Unlike the previous approaches, in our proposed method we extract the geometrical features as a means of pre-processing to feed the network, and we define the classification process of edge detection as a point-wise segmentation problem by a capsule network approach.