Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis

We introduce a data-driven approach to complete partial 3D shapes through a combination of volumetric deep neural networks and 3D shape synthesis. From a partially-scanned input shape, our method first infers a low-resolution -- but complete -- output. To this end, we introduce a 3D-Encoder-Predictor Network (3D-EPN) which is composed of 3D convolutional layers. The network is trained to predict and fill in missing data, and operates on an implicit surface representation that encodes both known and unknown space. This allows us to predict global structure in unknown areas at high accuracy. We then correlate these intermediary results with 3D geometry from a shape database at test time. In a final pass, we propose a patch-based 3D shape synthesis method that imposes the 3D geometry from these retrieved shapes as constraints on the coarsely-completed mesh. This synthesis process enables us to reconstruct fine-scale detail and generate high-resolution output while respecting the global mesh structure obtained by the 3D-EPN. Although our 3D-EPN outperforms state-of-the-art completion method, the main contribution in our work lies in the combination of a data-driven shape predictor and analytic 3D shape synthesis. In our results, we show extensive evaluations on a newly-introduced shape completion benchmark for both real-world and synthetic data

ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans

We introduce ScanComplete, a novel data-driven approach for taking an incomplete 3D scan of a scene as input and predicting a complete 3D model along with per-voxel semantic labels. The key contribution of our method is its ability to handle large scenes with varying spatial extent, managing the cubic growth in data size as scene size increases. To this end, we devise a fully-convolutional generative 3D CNN model whose filter kernels are invariant to the overall scene size. The model can be trained on scene subvolumes but deployed on arbitrarily large scenes at test time. In addition, we propose a coarse-to-fine inference strategy in order to produce high-resolution output while also leveraging large input context sizes. In an extensive series of experiments, we carefully evaluate different model design choices, considering both deterministic and probabilistic models for completion and semantic inference. Our results show that we outperform other methods not only in the size of the environments handled and processing efficiency, but also with regard to completion quality and semantic segmentation performance by a significant margin.Comment: Video: https://youtu.be/5s5s8iH0NF

Representing three-dimensional cross fields using 4th order tensors

This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on \mbox{SO}(3) are presented. The relationship of the new formulation with spherical harmonics is exposed. This paper is quite theoretical. Due to pages limitation, few practical aspects related to the computations of cross fields are exposed. Nevetheless, a global smoothing algorithm is briefly presented and computation of cross fields are finally depicted

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection