3D point cloud is an efficient and flexible representation of 3D structures. Recently, neural networks operating on point clouds have shown superior performance on tasks such as shape classification and part segmentation. However, performance on these tasks are evaluated using complete, aligned shapes, while real world 3D data are partial and unaligned. A key challenge in learning from unaligned point cloud data is how to attain invariance or equivariance with respect to geometric transformations. To address this challenge, we propose a novel transformer network that operates on 3D point clouds, named Iterative Transformer Network (IT-Net). Different from existing transformer networks, IT-Net predicts a 3D rigid transformation using an iterative refinement scheme inspired by classical image and point cloud alignment algorithms. We demonstrate that models using IT-Net achieves superior performance over baselines on the classification and segmentation of partial, unaligned 3D shapes. Further, we provide an analysis on the efficacy of the iterative refinement scheme on estimating accurate object poses from partial observations.
We propose a novel point signature based on the properties of the heat diffusion process on a shape. Our signature, called the Heat Kernel Signature (or HKS), is obtained by restricting the well-known heat kernel to the temporal domain. Remarkably we show that under certain mild assumptions, HKS captures all of the information contained in the heat kernel, and characterizes the shape up to isometry. This means that the restriction to the temporal domain, on the one hand, makes HKS much more concise and easily commensurable, while on the other hand, it preserves all of the information about the intrinsic geometry of the shape. In addition, HKS inherits many useful properties from the heat kernel, which means, in particular, that it is stable under perturbations of the shape. Our signature also provides a natural and efficiently computable multi-scale way to capture information about neighborhoods of a given point, which can be extremely useful in many applications. To demonstrate the practical relevance of our signature, we present several methods for non-rigid multi-scale matching based on the HKS and use it to detect repeated structure within the same shape and across a collection of shapes. In our recent work [1], [2], we proposed Point Feature Histograms (PFH) as robust multi-dimensional features which describe the local geometry around a point p for 3D point cloud datasets. In this paper, we modify their mathematical expressions and perform a rigorous analysis on their robustness and complexity for the problem of 3D registration for overlapping point cloud views. More concretely, we present several optimizations that reduce their computation times drastically by either caching previously computed values or by revising their theoretical formulations. The latter results in a new type of local features, called Fast Point Feature Histograms (FPFH), which retain most of the discriminative power of the PFH. Moreover, we propose an algorithm for the online computation of FPFH features for realtime applications. To validate our results we demonstrate their efficiency for 3D registration and propose a new sample consensus based method for bringing two datasets into the convergence basin of a local non-linear optimizer: SAC-IA (SAmple Consensus Initial Alignment). We introduce the Wave Kernel Signature (WKS) for characterizing points on non-rigid three-dimensional shapes. The WKS represents the average probability of measuring a quantum mechanical particle at a specific location. By letting vary the energy of the particle, the WKS encodes and separates information from various different Laplace eigenfrequencies. This clear scale separation makes the WKS well suited for a large variety of applications. Both theoretically and in quantitative experiments we demonstrate that the WKS is substantially more discriminative and therefore allows for better feature matching than the commonly used Heat Kernel Signature (HKS). As an application of the WKS in shape analysis we show results on shape matching.