LEARNING LOCALIZED GENERATIVE MODELS FOR 3D POINT CLOUDS VIA GRAPH CONVOLUTION
Point clouds are an important type of geometric data and have widespread use in computer graphics and vision. However, learning representations for point clouds is particularly challenging due to their nature as being an unordered collection of points irregularly distributed in 3D space. Graph convolution, a generalization of the convolution operation for data defined over graphs, has been recently shown to be very successful at extracting localized features from point clouds in supervised or semi-supervised tasks such as classification or segmentation. This paper studies the unsupervised problem of a generative model exploiting graph convolution. We focus on the generator of a GAN and define methods for graph convolution when the graph is not known in advance as it is the very output of the generator. The proposed architecture learns to generate localized features that approximate graph embeddings of the output geometry. We also study the problem of defining an upsampling layer in the graph-convolutional generator, such that it learns to exploit a self-similarity prior on the data distribution to sample more effectively.
The paper proposes a version of GANs specifically designed for generating point clouds. The core contribution of the work is the upsampling operation: in short, it takes as an input N points, and produces N more points (one per input) by applying a graph convolution-like operation.
Pros:
+ The problem of making scalable generative models for point clouds is clearly important, and using local operations in that context makes a lot of sense.
Cons:
- The paper is not particularly well-written, is often hard to follow, and contains a couple of confusing statements (see a non-exhaustive list of remarks below).
- The experimental evaluation seems insufficient: clearly it is possible to come up with more baselines. Even a comparison to other types of generative models would be useful (e.g. variants of VAEs, other types of GANs). There also alternative local graph-convolution-like operations (e.g. tangent convolutions) that are designed for point clouds. In addition, it is quite strange that results are reported not for all the classes in the dataset.
Various remarks:
p.1, “whereby it learns to exploit a self-similarity prior to sample the data distribution”: this is a confusing statement.
p.2, “(GANs) have been shown on images to provide better approximations of the data distribution than other generative models”: This statement is earthier too strong (all other models) or does not say much (some other models)
p.2, “However, this means that they are unable to learn localized features or exploit weight sharing.”: I see the point about no weight sharing in the generator, but feature learning 
p.3, “the key difference with the work in this paper is that PointNet and PointNet++ are not
generative models, but are used in supervised problems such as classification or segmentation.”: Yet, the kind of operation that is used in the pointnet++ is quite similar to what you propose?
p.4: “because the high dimensionality of the feature vectors makes the gridding approach unfeasible.”: but you are actually dealing with the point clouds where each point is 3D?