Computer Science

This paper describes a novel approach for on demand volumetric texture synthesis based on a deep learning framework that allows for the generation of high quality 3D data at interactive rates. Based on a few example images of textures, a generative network is trained to synthesize coherent portions of solid textures of arbitrary sizes that reproduce the visual characteristics of the examples along some directions. To cope with memory limitations and computation complexity that are inherent to both high resolution and 3D processing on the GPU, only 2D textures referred to as "slices" are generated during the training stage. These synthetic textures are compared to exemplar images via a perceptual loss function based on a pre-trained deep network. The proposed network is very light (less than 100k parameters), therefore it only requires sustainable training (i.e. few hours) and is capable of very fast generation (around a second for 256 3 voxels) on a single GPU. Integrated with a spatially seeded PRNG the proposed generator network directly returns an RGB value given a set of 3D coordinates. The synthesized volumes have good visual results that are at least equivalent to the state-of-the-art patch based approaches. They are naturally seamlessly tileable and can be fully generated in parallel.

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D constrained, 3D constrained and 3D Restricted Delaunay refinement problems respectively. Our algorithms take a 2D planar straight line graph (PSLG) or 3D piecewise linear complex (PLC) G as input, and generate quality meshes conforming or approximating to G . The implementation of our algorithms shows that they are the first to run an order of magnitude faster than current state-of-the-art counterparts in sequential and parallel manners while using similar numbers of Steiner points to produce triangulations of comparable qualities. It thus reduces the computing time of mesh refinement from possibly hours to a few seconds or minutes for possible use in interactive graphics applications.

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.

In this paper, we present the implicit representation of one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation we construct the rotationally invariant measure of deviation from the specified symmetry. The spherical harmonics we consider have some applications in the area of directional fields design due to their ability to represent mutually orthogonal axes in 3D space not relatively to their order and orientation.

S-patches have many nice mathematical properties. It is known since their first appearance, that any regular S-patch can be exactly converted into a trimmed rational Bézier surface. This is a big advantage compared to other multi-sided surface representations that have to be approximated for exporting them into CAD/CAM systems. The actual conversion process, however, remained at a theoretical level, with bits and pieces scattered in multiple publications. In this paper we review the entirety of the algorithm, and investigate it from a practical aspect.

A neural implicit outputs a number indicating whether the given query point in space is inside, outside, or on a surface. Many prior works have focused on _latent-encoded_ neural implicits, where a latent vector encoding of a specific shape is also fed as input. While affording latent-space interpolation, this comes at the cost of reconstruction accuracy for any _single_ shape. Training a specific network for each 3D shape, a _weight-encoded_ neural implicit may forgo the latent vector and focus reconstruction accuracy on the details of a single shape. While previously considered as an intermediary representation for 3D scanning tasks or as a toy-problem leading up to latent-encoding tasks, weight-encoded neural implicits have not yet been taken seriously as a 3D shape representation. In this paper, we establish that weight-encoded neural implicits meet the criteria of a first-class 3D shape representation. We introduce a suite of technical contributions to improve reconstruction accuracy, convergence, and robustness when learning the signed distance field induced by a polygonal mesh -- the _de facto_ standard representation. Viewed as a lossy compression, our conversion outperforms standard techniques from geometry processing. Compared to previous latent- and weight-encoded neural implicits we demonstrate superior robustness, scalability, and performance.

A debate in the scientific literature has arisen regarding whether the orb depicted in Salvator Mundi, which has been attributed by some experts to Leonardo da Vinci, was rendered in a optically faithful manner or not. Some hypothesize that it was solid crystal while others hypothesize that it was hollow, with competing explanations for its apparent lack of background distortion and its three white spots. In this paper, we study the optical accuracy of the Salvator Mundi using physically based rendering, a sophisticated computer graphics tool that produces optically accurate images by simulating light transport in virtual scenes. We created a virtual model of the composition centered on the translucent orb in the subject's hand. By synthesizing images under configurations that vary illuminations and orb material properties, we tested whether it is optically possible to produce an image that renders the orb similarly to how it appears in the painting. Our experiments show that an optically accurate rendering qualitatively matching that of the painting is indeed possible using materials, light sources, and scientific knowledge available to Leonardo da Vinci circa 1500. We additionally tested alternative theories regarding the composition of the orb, such as that it was a solid calcite ball, which provide empirical evidence that such alternatives are unlikely to produce images similar to the painting, and that the orb is instead hollow.

This work introduces progressive spatio-temporal filtering, an efficient method to build all-frequency approximations to the light transport distribution into a scene by filtering individual samples produced by an underlying path sampler, using online, iterative algorithms and data-structures that exploit both the spatial and temporal coherence of the approximated light field. Unlike previous approaches, the proposed method is both more efficient, due to its use of an iterative temporal feedback loop that massively improves convergence to a noise-free approximant, and more flexible, due to its introduction of a spatio-directional hashing representation that allows to encode directional variations like those due to glossy reflections. We then introduce four different methods to employ the resulting approximations to control the underlying path sampler and/or modify its associated estimator, greatly reducing its variance and enhancing its robustness to complex lighting scenarios. The core algorithms are highly scalable and low-overhead, requiring only minor modifications to an existing path tracer.

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.

This paper presents a light-weight, high-quality texture synthesis algorithm that easily generalizes to other applications such as style transfer and texture mixing. We represent texture features through the deep neural activation vectors within the bottleneck layer of an auto-encoder and frame the texture synthesis problem as optimal transport between the activation values of the image being synthesized and those of an exemplar texture. To find this optimal transport mapping, we utilize an N-dimensional probability density function (PDF) transfer process that iterates over multiple random rotations of the PDF basis and matches the 1D marginal distributions across each dimension. This achieves quality and flexibility on par with expensive back-propagation based neural texture synthesis methods, but with the potential of achieving interactive rates. We demonstrate that first order statistics offer a more robust representation for texture than the second order statistics that are used today. We propose an extension of this algorithm that reduces the dimensionality of the neural feature space. We utilize a multi-scale coarse-to-fine synthesis pyramid to capture and preserve larger image features; unify color and style transfer under one framework; and further augment this system with a novel masking scheme that re-samples and re-weights the feature distribution for user-guided texture painting and targeted style transfer.