The problem is simple enough. Given a point-cloud perform segmentation and classification and improving the state-of-art by incorporating local information of each point.
How is it Solved
The authors propose an incremental extension of the popular Graph CNN model read here named as Edge Convolution that is tailored for their task. Further because point-clouds inherently is not a graph. Hence the lack of an adjacency matrix needed for graph-convolutions. They propose Dynamic Graph CNN, i.e., dynamic connections between points.
Edge Convolution: A Graph-CNN layer consists of finding the features of a node ( a point in the point cloud here ) at the next time step as a function of that point and its neighbours. Its defined as a simple summation of weights multiplied into the features in Graph-CNN while here it is defined as .
Here the function h() is modelled using a neural network. The reason for using a function of is that contributes towards the globalposition of the point and towards its relation with other points.
The aggregation function used here is the max operation.
Dynamic GraphCNNs: Point Cloud even though has some geometric properties is not a graph inherently. Hence in this work, the neighbors of a node are defined at each pass using K-nearest neighbors. This means that the connections between nodes can change from one iteration to another leading to the name Dynamic GraphCNN.