Multi-kernel Diffusion CNNs for Graph-Based Learning on Point Clouds

Abstract

Graph convolutional networks are a new promising learning approach to deal with data on irregular domains. They are predestined to overcome certain limitations of conventional grid-based architectures and will enable efficient handling of point clouds or related graphical data representations, e.g. superpixel graphs. Learning feature extractors and classifiers on 3D point clouds is still an underdeveloped area and has potential restrictions to equal graph topologies. In this work, we derive a new architectural design that combines rotationally and topologically invariant graph diffusion operators and node-wise feature learning through 1 × 1 convolutions. By combining multiple isotropic diffusion operations based on the Laplace-Beltrami operator, we can learn an optimal linear combination of diffusion kernels for effective feature propagation across nodes on an irregular graph. We validated our approach for learning point descriptors as well as semantic classification on real 3D point clouds of human poses and demonstrate an improvement from 85% to 95% in Dice overlap with our multi-kernel approach.

Rotation invariant point cloud analysis: Where local geometry meets global topology

“…Inspired by the success of deep learning in 2D computer vision [6,27,12], massive efforts have been widely carried out for point cloud analysis [22], which mainly employ MLP as a basic feature extraction module. Further, to aggregate local information which has been proved to be critical in 2D convolution neural networks, some approaches such as graph-based convolutions [11,30,31] and local max pooling have been developed. However, the previous works include interior drawbacks.…”

DiffusionNet: Discretization Agnostic Learning on Surfaces

“…Similarly to our approach, diffusion for smooth communication has been explored on graphs [Klicpera et al 2019;Xu et al 2019], images [Liu et al 2016], and point clouds [Hansen et al 2018]. In contrast, our method directly learns a diffusion time per-feature (which significantly improves performance, Table 7), incorporates a learned gradient operation, and is applied directly to mesh surfaces.…”

“…A successful set of methods for learning on 3D shapes represented as point clouds was pioneered by the PointNet [Qi et al 2017a] and PointNet++ [Qi et al 2017b] architectures, which have been extended in many recent works, including PointCNN [Li et al 2018], DGCNN [Wang et al 2019], PCNN [Atzmon et al 2018], and KPConv [Thomas et al 2019], to name a few (see also for a recent survey). Moreover, recent efforts have also been made to incorporate invariance and equivariance of the networks with respect to various geometric transformations, e.g., Deng et al [2018], Hansen et al [2018], Li et al [2021], Poulenard et al [2019], Zhang et al [2019], and Zhao et al [2020]. The major advantages of point-based methods are their simplicity, flexibility, applicability in a wide range of settings, and robustness in the presence of noise and outliers.…”