Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models that act directly on point clouds is critical, especially when efficiency considerations or noise preclude the possibility of expensive denoising and meshing procedures. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent success of convolutional neural networks for image analysis suggests the value of adapting insight from CNN to the point cloud world. We propose a new neural network module EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. Beyond proposing this module, we provide extensive evaluation and analysis revealing that EdgeConv captures and exploits fine-grained geometric properties of point clouds.

Monte Carlo methods are commonly used for robust rendering of scenes with volumetric participating media. The efficiency of these approaches is directly linked to the manner in which random sampling decisions are made during light path construction. Notably, path construction is influenced by scattering direction and distance sampling, Russian roulette, and splitting strategies. We present a new volumetric path construction technique where all these sampling decisions are guided by a cached estimate of the adjoint light transport solution. Our sampling strategy is based on the theory of zero-variance transport estimators, and it accounts for the spatial and directional variation in volumetric transport. Specifically, we construct paths incrementally by sampling collision distances proportionally to the product of transmittance and the adjoint transport solution (i.e., in-scattered radiance). Scattering directions are likewise sampled according to the product of the phase function and the incident radiance estimate. Combined with an adaptive Russian roulette and splitting strategy tailored to volumes, we demonstrate about an order-of-magnitude variance reduction compared to modern uni-directional methods. Consequently, our approach can render scenes that are otherwise intractable for such methods, while still retaining their simplicity (compared to, e. g., bi-directional methods).

In this paper we present a novel dictionary learning framework designed for compression and sampling of light fields and light field videos. Unlike previous methods, where a single dictionary with one dimensional atoms is learned, we propose to train a multi dimensional dictionary ensemble (MDE). We show that learning an ensemble in the native dimensionality of the data promotes sparsity, hence increasing the compression ratio and sampling efficiency. To make maximum use of correlations within the light field data sets, we also introduce a novel non-local pre-clustering approach that constructs an aggregate MDE (AMDE). The pre-clustering not only improves the image quality, but also reduces the training time by an order of magnitude in most cases. The decoding algorithm supports efficient local reconstruction of the compressed data, which enables efficient real-time playback of high resolution light field videos. Moreover, we discuss the application of AMDE for compressed sensing. A theoretical analysis is presented which indicates the required conditions for exact recovery of point-sampled light fields that are sparse under AMDE. The analysis provides guidelines for designing efficient compressive light field cameras.

Advances in multimaterial 3D printing have the potential to reproduce various visual appearance attributes of an object in addition to its shape. Since many existing 3D file formats encode color and translucency by RGBA textures mapped to 3D shapes, RGBA information is particularly important for practical applications. In contrast to color (encoded by RGB), translucency (encoded by A) is neither linked to any measurable physical nor perceptual quantity and is, therefore, open for interpretation. In this paper, we propose a rigorous definition for A suitable for graphical 3D printing which links both optical material properties and perceptual uniformity for human observers. By deriving our definition from the absorption and scattering coefficients of virtual reference materials with an isotropic phase function, we achieve two important properties. First, a simple adjustment of A is possible, which preserves the translucency appearance if an object is rescaled for printing. Second, determining A for a real material can be achieved by minimizing a distance function between light transport measurements of this material (conducted by commercial spectrophotometers) and simulated measurements of the reference materials. Finally, we derive from visual experiments an embedding of A into a nearly perceptually-uniform scale of translucency for the reference materials.

This paper describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data on a curved manifold. More precisely, it extends a vector field defined over any region to the rest of the domain via parallel transport along shortest geodesics. This basic operation enables fast, robust algorithms for extrapolating level set velocities, inverting the exponential map, computing geometric medians and Karcher/Fréchet means of arbitrary distributions, constructing centroidal Voronoi diagrams, and finding consistently ordered landmarks. Rather than evaluate parallel transport by explicitly tracing geodesics, we show that it can be computed via a short-time heat flow involving the connection Laplacian. As a result, transport can be achieved by solving three prefactored linear systems, each akin to a standard Poisson problem. Moreover, to implement the method we need only a discrete connection Laplacian, which we describe for a variety of geometric data structures (point clouds, polygon meshes, etc.). We also study the numerical behavior of our method, showing empirically that it converges under refinement, and augment the construction of intrinsic Delaunay triangulations (iDT) so that they can be used in the context of tangent vector field processing.

Imaging objects obscured by occluders is a significant challenge for many applications. A camera that could ``see around corners'' could help improve navigation and mapping capabilities of autonomous vehicles or make search and rescue missions more effective. Time-resolved single-photon imaging systems have recently been demonstrated to record optical information of a scene that can lead to an estimation of the shape and reflectance of objects hidden from the line of sight of a camera. However, existing non-line-of-sight (NLOS) reconstruction algorithms have been constrained in the types of light transport effects they model for the hidden scene parts. We introduce a factored NLOS light transport representation that accounts for partial occlusions and surface normals. Based on this model, we develop a factorization approach for inverse time-resolved light transport and demonstrate high-fidelity NLOS reconstructions for challenging scenes both in simulation and with an experimental NLOS imaging system.