## 5 Deep-Learning-Based Methods for Point Cloud Understanding
### Point-Based Methods
[100] presented kernel point convolution (KP-Conv) for flexible and deformable convolutions on sparse point clouds, as shown on the right of Figure 16. This method is inspired by image-based convolution, but instead of kernel pixels, it uses a set of kernel points to define the volume, where a linear correlation function applies each kernel weight. For greater flexibility, the number of kernel points is not fixed, and the positions of the kernel points are formulated as an optimization problem of the best coverage in a sphere space and trained to fit the point cloud geometry. [PERSON] et al. [144] (FG-Net) published a general deep learning framework for large-scale point clouds to tackle issues (noise, outliers, and dynamically changing environments) associated with methods, designed for small point clouds. They introduce a deformable convolution for modeling local object structures with kernels that dynamically adapt to geometries. Pointwise attention aggregation is used to capture the distributed contextual information in spatial locations and semantic features across a long spatial range. [PERSON] et al. [145] showed how to improve the segmentation results of a well-known ConvNet baseline model [140] by applying contrastive boundary learning (CBL) to enhance feature discrimination between points across boundaries. Experiments demonstrate that CBL can help to improve predictions, especially in cluttered regions, and reduce classification artifacts. The CBL framework is not limited to ConvNet architecture but can be coupled to any other multi-stage backbone, as results with the RandLA-Net backbone [146] have shown. **Point-based graph neural networks** (GNNs) allow a natural representation of data (point cloud and mesh) within non-Euclidean space. The nature of these data does not imply familiar properties, such as an orthonormal coordinate system, vector space structure, or shift invariance. Consequently, basic operations such as convolution, which are taken for granted in the Euclidean case, are not even well defined in non-Euclidean domains [147]. In recent decades, researchers have been working on how to conduct convolutional operations on graphs. Graph convolutional network (GCN) models are neural networks that can leverage the graph structure and aggregate node information from the neighborhoods in a convolutional fashion [148]. [PERSON] and [PERSON] [149] suggested a superpoint graph (SPG) (Figure 17) constructed from simple yet meaningful shapes, which partition from the global point cloud by local geometric features (linearity, planarity and scattering, and verticality). Superedges interconnect superpoints in a global graph to capture the spatial context information, which is then exploited by a GCN. [PERSON] et al. [150] proposed a dynamic graph CNN (DGCNN), an EdgeConv-based model to group points in Euclidean and semantic space over potentially long distances. The EdgeConv module applies to the dynamically updated graphs in each network layer. [PERSON] and [PERSON] [151] published the PyramNet architecture  
Figure 16: **Left: pixel-wise convolution with kernel size \(3\times 3\). Center: Pointwise convolutions: For each point, nearest neighbors are searched and binned into kernel cells before convolving with kernel weights. Graphic originally shown in [138]. Right: Kernel point convolution 2D example. Input points with a constant scalar feature (in grey) are convolved through a KPConv that is defined by a set of kernel points (in black) with filter weights on each point. The graphic was originally shown in [100]. **  
as a combination of a graph embedding module (GEM) and a pyramid attention network (PAN). To improve local feature expression ability, GEM utilizes a covariance matrix to replace the Euclidean distance. The PAN combines features of different resolutions and different semantic strengths from four convolution kernels to improve segmentation. [PERSON] et al. [152] used graph attention convolution (GAC) with learnable kernel shapes to adapt to the structure of the objects.