It is also known, and it is practically shown that the use of a unposition number system in residual classes (RNS) allows you to drastically increase the speed of the computer system (CS). There are various approaches and difficulties regarding to the assessment of the reliability of the CS in RNS. So, the existing options of mathematical models do not always satisfy a comprehensive assessment of the reliability of the CS in RNS. The variant of mathematical model of reliability of CS, that functions in RNS, is considered in the article, based on the use of a mathematical model of structural sliding backup in the case of a loaded mode of operation of the backup elements, which is used in the positional binary number system (PBNS). A calculation and comparative security of the trooped computing structure (TCS) analysis was carried out in PBNS with an ideal majority element and the CS in RNS with an ideal reliability machine. The results of analysis showed the following. At the initial stage of the functioning of computational systems, reliability, by probability of trouble-free operation, the CS in RNS with two control bases above the reliability of the trooked positional computing structure, widely used in the PDS and with a smaller addition of an additional equipment insertion. It supposes the effective use of RNS for the increase of reliability of CS and computing devices on the initial stage of their functioning. For example, for the increase of reliability the practical use of unposition code structures is possible in RNS in the side digital calculable complexes of ballistic rockets and in the computing devices of pilotless aircrafts of brief action.

This article discusses asynchronous techniques with spreading sequences (codes) that are statistically uncorrelated for arbitrarily random starting points. We provide improved codes for the spread-spectrum multiple-access asynchronous techniques. The article provides methods for generating improved codes, as well as estimates of their parameters. We investigate the cross-correlation of codes for arbitrarily random starting points. The comparative analysis shows that with a slight increase in the correlation modulus, we can significantly increase the cardinality of the spreading codes. This useful property can be used in future radio control systems and future smart grids to implement soft capacity, i.e. the base station can increase the subscriber capacity with a slight decrease in the quality of service.

Although Monte Carlo path tracing is a simple and effective algorithm to synthesize photo-realistic images, it is often very slow to converge to noise-free results when involving complex global illumination. One of the most successful variance-reduction techniques is path guiding, which can learn better distributions for importance sampling to reduce pixel noise. However, previous methods require a large number of path samples to achieve reliable path guiding. We present a novel neural path guiding approach that can reconstruct high-quality sampling distributions for path guiding from a sparse set of samples, using an offline trained neural network. We leverage photons traced from light sources as the primary input for sampling density reconstruction, which is effective for challenging scenes with strong global illumination. To fully make use of our deep neural network, we partition the scene space into an adaptive hierarchical grid, in which we apply our network to reconstruct high-quality sampling distributions for any local region in the scene. This allows for effective path guiding for arbitrary path bounce at any location in path tracing. We demonstrate that our photon-driven neural path guiding approach can generalize to diverse testing scenes, often achieving better rendering results than previous path guiding approaches and opening up interesting future directions.

We propose NeuMIP, a neural method for representing and rendering a variety of material appearances at different scales. Classical prefiltering (mipmapping) methods work well on simple material properties such as diffuse color, but fail to generalize to normals, self-shadowing, fibers or more complex microstructures and reflectances. In this work, we generalize traditional mipmap pyramids to pyramids of neural textures, combined with a fully connected network. We also introduce neural offsets, a novel method which enables rendering materials with intricate parallax effects without any tessellation. This generalizes classical parallax mapping, but is trained without supervision by any explicit heightfield. Neural materials within our system support a 7-dimensional query, including position, incoming and outgoing direction, and the desired filter kernel size. The materials have small storage (on the order of standard mipmapping except with more texture channels), and can be integrated within common Monte-Carlo path tracing systems. We demonstrate our method on a variety of materials, resulting in complex appearance across levels of detail, with accurate parallax, self-shadowing, and other effects.

Path guiding is a promising technique to reduce the variance of path tracing. Although existing online path guiding algorithms can eventually learn good sampling distributions given a large amount of time and samples, the speed of learning becomes a major bottleneck. In this paper, we accelerate the learning of sampling distributions by training a light-weight neural network offline to reconstruct from sparse samples. Uniquely, we design our neural network to directly operate convolutions on a sparse quadtree, which regresses a high-quality hierarchical sampling distribution. Our approach can reconstruct reasonably accurate sampling distributions faster, allowing for efficient path guiding and rendering. In contrast to the recent offline neural path guiding techniques that reconstruct low-resolution 2D images for sampling, our novel hierarchical framework enables more fine-grained directional sampling with less memory usage, effectively advancing the practicality and efficiency of neural path guiding. In addition, we take advantage of hybrid bidirectional samples including both path samples and photons, as we have found this more robust to different light transport scenarios compared to using only one type of sample as in previous work. Experiments on diverse testing scenes demonstrate that our approach often improves rendering results with better visual quality and lower errors. Our framework can also provide the proper balance of speed, memory cost, and robustness.

Rendering specular material appearance is a core problem of computer graphics. While smooth analytical material models are widely used, the high-frequency structure of real specular highlights requires considering discrete, finite microgeometry. Instead of explicit modeling and simulation of the surface microstructure (which was explored in previous work), we propose a novel direction: learning the high-frequency directional patterns from synthetic or measured examples, by training a generative adversarial network (GAN). A key challenge in applying GAN synthesis to spatially varying BRDFs is evaluating the reflectance for a single location and direction without the cost of evaluating the whole hemisphere. We resolve this using a novel method for partial evaluation of the generator network. We are also able to control large-scale spatial texture using a conditional GAN approach. The benefits of our approach include the ability to synthesize spatially large results without repetition, support for learning from measured data, and evaluation performance independent of the complexity of the dataset synthesis or measurement.

Abstract Recently, deep learning approaches have proven successful at removing noise from Monte Carlo (MC) rendered images at extremely low sampling rates, e.g., 1–4 samples per pixel (spp). While these methods provide dramatic speedups, they operate on uniformly sampled MC rendered images. However, the full promise of low sample counts requires both adaptive sampling and reconstruction/denoising. Unfortunately, the traditional adaptive sampling techniques fail to handle the cases with low sampling rates, since there is insufficient information to reliably calculate their required features, such as variance and contrast. In this paper, we address this issue by proposing a deep learning approach for joint adaptive sampling and reconstruction of MC rendered images with extremely low sample counts. Our system consists of two convolutional neural networks (CNN), responsible for estimating the sampling map and denoising, separated by a renderer. Specifically, we first render a scene with one spp and then use the first CNN to estimate a sampling map, which is used to distribute three additional samples per pixel on average adaptively. We then filter the resulting render with the second CNN to produce the final denoised image. We train both networks by minimizing the error between the denoised and ground truth images on a set of training scenes. To use backpropagation for training both networks, we propose an approach to effectively compute the gradient of the renderer. We demonstrate that our approach produces better results compared to other sampling techniques. On average, our 4 spp renders are comparable to 6 spp from uniform sampling with deep learning‐based denoising. Therefore, 50% more uniformly distributed samples are required to achieve equal quality without adaptive sampling.

Abstract Distribution effects such as diffuse global illumination, soft shadows and depth of field, are most accurately rendered using Monte Carlo ray or path tracing. However, physically accurate algorithms can take hours to converge to a noise‐free image. A recent body of work has begun to bridge this gap, showing that both individual and multiple effects can be achieved accurately and efficiently. These methods use sparse sampling, GPU raytracers, and adaptive filtering for reconstruction. They are based on a Fourier analysis, which models distribution effects as a wedge in the frequency domain. The wedge can be approximated as a single large axis‐aligned filter, which is fast but retains a large area outside the wedge, and therefore requires a higher sampling rate; or a tighter sheared filter, which is slow to compute. The state‐of‐the‐art fast sheared filtering method combines low sampling rate and efficient filtering, but has been demonstrated for individual distribution effects only, and is limited by high‐dimensional data storage and processing. We present a novel filter for efficient rendering of combined effects, involving soft shadows and depth of field, with global (diffuse indirect) illumination. We approximate the wedge spectrum with multiple axis‐aligned filters, marrying the speed of axis‐aligned filtering with an even more accurate (compact and tighter) representation than sheared filtering. We demonstrate rendering of single effects at comparable sampling and frame‐rates to fast sheared filtering. Our main practical contribution is in rendering multiple distribution effects, which have not even been demonstrated accurately with sheared filtering. For this case, we present an average speedup of 6× compared with previous axis‐aligned filtering methods.