Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks that generalizes poorly to arbitrary rotations. In this paper, we introduce a novel convolution operator for point clouds that achieves rotation invariance. Our core idea is to use low-level rotation invariant geometric features such as distances and angles to design a convolution operator for point cloud learning. The well-known point ordering problem is also addressed by a binning approach seamlessly built into the convolution. This convolution operator then serves as the basic building block of a neural network that is robust to point clouds under 6-DoF transformations such as translation and rotation. Our experiment shows that our method performs with high accuracy in common scene understanding tasks such as object classification and segmentation. Compared to previous and concurrent works, most importantly, our method is able to generalize and achieve consistent results across different scenarios in which training and testing can contain arbitrary rotations. Our implementation is publicly available at our project page.

The NSF Digital Clay project is focused on the design, prototyping, integration, and validation of a computer-controlled physical device capable of taking any of a wide range of possible shapes in response to changes in a digital 3D model or to changes in the pressure exercised upon it by human hands. Although it clearly is a natural and unavoidable evolution of 3D graphical user interfaces, its unprecedented capabilities constitute a major leap in technologies and paradigms for 3D display, for 3D input, and for collaborative 3D design. In this paper, we provide an overview of the Digital Clay project and discuss the challenges, design choices, and initial solutions for a new finger sculpting interface designed for the Digital Clay and prototyped using conventional 3D I/O hardware.