Our goal in this article is to propose a fast and easy to implement BRDF modeling method that provides both accurate and compact representations for all types of BRDF, i.e., isotropic or anisotropic. To achieve this objective, we use a Bayesian regression method with a Gaussian process prior which allows obtaining compact BRDF representations in a purely analytical way. For this purpose, we use a generalzed distance covariance kernel which is much better suited to BRDF features than the usual Gaussian kernel. To speed up the processing, we adapt this method to the specificities of BRDFs through an appropriate input data structure and distribution of observations so as to drastically reduce the problem dimensionality through an efficient factorization method. In this way, all calculations at both fitting and rendering steps are reduced to basic matrix products and the computation of a BRDF representation with our modeling method takes only a few seconds. Furthermore, rather than using a systematic approach as in state-of-the-art methods, the size and complexity of the BRDF representation can be adapted to the application requirements as regards the fitting accuracy and rendering constraints. Besides, our BRDF representation can be easily converted to spherical harmonics expansions, which allows easier integration in usual rendering algorithms. We also propose importance sampling methods derived from our BRDF modeling method that leads to fast and easy implementations. Experimental applications of our method to various types of isotropic and anisotropic BRDFs show that state-of-the-art methods can be outperformed in most cases by using a small set of observations for the regression.

Abstract Efficient approximation of incident radiance functions from a set of samples is still an open problem in physically based rendering. Indeed, most of the computing power required to synthesize a photo‐realistic image is devoted to collecting samples of the incident radiance function, which are necessary to provide an estimate of the rendering equation solution. Due to the large number of samples required to reach a high‐quality estimate, this process is usually tedious and can take up to several days. In this paper, we focus on the problem of approximation of incident radiance functions on the sphere. To this end, we resort to a Gaussian Process (GP), a highly flexible function modelling tool, which has received little attention in rendering. We make an extensive analysis of the application of GPs to incident radiance functions, addressing crucial issues such as robust hyperparameter learning, or selecting the covariance function which better suits incident radiance functions. Our analysis is both theoretical and experimental. Furthermore, it provides a seamless connection between the original spherical domain and the spectral domain, on which we build to derive a method for fast computation and rotation of spherical harmonics coefficients.

Spherical Fibonacci grids (SFG) yield extremely uniform point set distributions on the sphere. This feature makes SFGs particularly well-suited to a wide range of computer graphics applications, from numerical integration, to vector quantization, among others. However, the application of SFGs to problems in which further refinement of an initial point set is required is currently not possible. This is because there is currently no solution to the problem of adding new points to an existing SFG while maintaining the point set properties. In this work, we fill this gap by proposing the extensible spherical Fibonacci grids (E-SFG). We start by carrying out a formal analysis of SFGs to identify the properties which make these point sets exhibit a nearly-optimal uniform spherical distribution. Then, we propose an algorithm (E-SFG) to extend the original point set while preserving these properties. Finally, we compare the E-SFG with a other extensible spherical point sets. Our results show that the E-SFG outperforms spherical point sets based on a low discrepancy sequence both in terms of spherical cap discrepancy and in terms of root mean squared error for evaluating the rendering integral.

We propose a theoretical framework, based on the theory of Sobolev spaces, that allows for a comprehensive analysis of quadrature rules for integration over the sphere. We apply this framework to the case of shading integrals in order to predict and analyze the performances of quadrature methods. We show that the spectral distribution of the quadrature error depends not only on the samples set size, distribution and weights, but also on the BRDF and the integrand smoothness. The proposed spectral analysis of quadrature error allows for a better understanding of how the above different factors interact. We also extend our analysis to the case of Fourier truncation-based techniques applied to the shading integral, so as to find the smallest spherical/hemispherical harmonics degree L (truncation) that entails a targeted integration error. This application is very beneficial to global illumination methods such as Precomputed Radiance Transfer and Radiance Caching. Finally, our proposed framework is the first to allow a direct theoretical comparison between quadrature- and truncation-based methods applied to the shading integral. This enables, for example, to determine the spherical harmonics degree L which corresponds to a quadrature-based integration with N samples. Our theoretical findings are validated by a set of rendering experiments.

Abstract This paper proposes optimal quadrature rules over the hemisphere for the shading integral. We leverage recent work regarding the theory of quadrature rules over the sphere in order to derive a new theoretical framework for the general case of hemispherical quadrature error analysis. We then apply our framework to the case of the shading integral. We show that our quadrature error theory can be used to derive optimal sample weights (OSW) which account for both the features of the sampling pattern and the bidirectional reflectance distribution function (BRDF). Our method significantly outperforms familiar Quasi Monte Carlo (QMC) and stochastic Monte Carlo techniques. Our results show that the OSW are very effective in compensating for possible irregularities in the sample distribution. This allows, for example, to significantly exceed the regular convergence rate of stochastic Monte Carlo while keeping the exact same sample sets. Another important benefit of our method is that OSW can be applied whatever the sampling points distribution: the sample distribution need not follow a probability density function, which makes our technique much more flexible than QMC or stochastic Monte Carlo solutions. In particular, our theoretical framework allows to easily combine point sets derived from different sampling strategies (e.g. targeted to diffuse and glossy BRDF). In this context, our rendering results show that our approach overcomes MIS (Multiple Importance Sampling) techniques.

Abstract Quasi‐Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g. illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low‐discrepancy sequences and map them to the hemisphere. However such an approach is suboptimal as these sequences do not account for the spherical topology and their discrepancy properties on the unit square are impaired by the spherical projection. In this paper we present a strategy for producing high‐quality QMC sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to illumination integrals, are very simple to generate and consistently outperform existing approaches, both in terms of root mean square error (RMSE) and image quality. Furthermore, only a single pattern is required to produce an image, thanks to a scrambling scheme performed directly in the spherical domain.

The Monte Carlo method has proved to be very powerful to cope with global illumination problems but it remains costly in terms of sampling operations. In various applications, previous work has shown that Bayesian Monte Carlo can significantly outperform importance sampling Monte Carlo thanks to a more effective use of the prior knowledge and of the information brought by the samples set. These good results have been confirmed in the context of global illumination but strictly limited to the perfect diffuse case. Our main goal in this paper is to propose a more general Bayesian Monte Carlo solution that allows dealing with nondiffuse BRDFs thanks to a spherical Gaussian-based framework. We also propose a fast hyperparameters determination method that avoids learning the hyperparameters for each BRDF. These contributions represent two major steps toward generalizing Bayesian Monte Carlo for global illumination rendering. We show that we achieve substantial quality improvements over importance sampling at comparable computational cost.

Abstract Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of k‐means clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving the efficiency and accuracy of LPCA. We propose a novel SortCluster LPCA algorithm that significantly reduces the cost of the point‐cluster classification stage, achieving a speed‐up of up to 20. To improve the approximation accuracy, we investigate different initialization schemes for LPCA and find that the k‐means++ algorithm [ AV07 ] yields best results, however at a high computation cost. We show that similar ideas that lead to the efficiency of our SortCluster LPCA algorithm can be used to accelerate k‐means++. The resulting initialization algorithm is faster than purely random seeding while producing substantially more accurate data approximation.

Abstract Most Monte Carlo rendering algorithms rely on importance sampling to reduce the variance of estimates. Importance sampling is efficient when the proposal sample distribution is well‐suited to the form of the integrand but fails otherwise. The main reason is that the sample location information is not exploited. All sample values are given the same importance regardless of their proximity to one another. Two samples falling in a similar location will have equal importance whereas they are likely to contain redundant information. The Bayesian approach we propose in this paper uses both the location and value of the data to infer an integral value based on a prior probabilistic model of the integrand. The Bayesian estimate depends only on the sample values and locations, and not how these samples have been chosen. We show how this theory can be applied to the final gathering problem and present results that clearly demonstrate the benefits of Bayesian Monte Carlo.

Although compression of 3D content has been a widely studied topic, adaptive streaming of large virtual scenes is progressively becoming the standard way to share collaborative environments, due to the growing complexity of the shared data. The classical 'download and play' paradigm associated to standalone compression is leaving place to interactive refinements of regions-of-interest, provided given polygon budget and network capability. With the increasing number of applications and potential clients sharing reusable data, the traditional client / server architecture is likely to be over passed by less server-centered protocols, in order to distribute the complex tasks of identifying the selected data to be streamed. In this paper, we present the design and performances of a platform exploiting peer-to-peer transmission and show how the whole setting can be implemented using the MPEG-4 AFX standards.

The general craze for virtual environments, the potential of augmented reality applications and the announced revolution of the Internet world (Web 2.0, Web 3D.0) are key points for the emergence of an 'ambient' Web which will make it possible for users to communicate, collaborate, entertain, work and exchange content. In this context, content storage, delivery, and reproduction are among the essential points for the deployment of a highly scalable platform of wide reality. In this paper, we propose a self-scalable peer-to-peer architecture for the navigation in network-based virtual worlds. To reach this goal, we propose a fully distributed and adaptive streaming method that quickly adapts the reproduced content according to user interaction. Our content delivery strategy has been implemented and tested on a dedicated simulator with a large 3D city model. The presented results show the efficiency of our strategy in very critical conditions.

The general craze for virtual environments, the potential of augmented reality applications and the announced revolution of the Internet world (Web 2.0, Web 3D.0) are key points for the emergence of an 'ambient' Web which will make it possible for users to communicate, collaborate, entertain, work and exchange content. In this context, content storage, delivery, and reproduction are among the essential points for the deployment of a highly scalable platform of wide reality. In this paper, we propose a self-scalable peer-to-peer architecture for the navigation in network-based virtual worlds. To reach this goal, we propose a fully distributed and adaptive streaming method that quickly adapts the reproduced content according to user interaction. Our content delivery strategy has been implemented and tested on a dedicated simulator with a large 3D city model.

The ever increasing speed of Internet connections has led to a point where it is actually possible for every end user to seamlessly share data on Internet. Peer-to-peer (P2P) networks are typical of this evolution. The goal of our paper is to show that thanks to self-adaptive assignment techniques, server-less P2P networks can efficiently deal with very large environments such as met in the geo-visualisation area. Our method takes advantage of a hierarchical and progressive data structure that describes the environment. In order to assess the global efficiency of this P2P technique, we have implemented a dedicated real time simulator. Experimentation results are presented using a hierarchical LOD model of a very large urban environment

The ever increasing speed of Internet connections has led to a point where it is actually possible for every end user to seamlessly share data on Internet. Peer-To-Peer (P2P) networks are typical of this evolution. The goal of our paper is to show that server-less P2P networks with self-adaptive assignment techniques can efficiently deal with very large environments such as met in the geovisualization domain. Our method allows adaptative view-dependent visualization thanks to a hierarchical and progressive data structure that describes the environment. In order to assess the global efficiency of this P2P technique, we have implemented a dedicated real time simulator. Experimentation results are presented using a hierarchical LOD model of a very large urban environment.

Wavelet methods for geometry encoding is a recently emerged superset of multiresolution analysis which has proven to be very efficient in terms of compression and adaptive transmission of three-dimensional (3-D) content. The decorrelating power and space/scale localization of wavelets enable efficient compression of arbitrary meshes as well as progressive and local reconstruction. Recent techniques based on zerotree compression have shown to be among the best lossy mesh compression methods, while remaining compatible with selective transmission of geometric data at various levels of detail. While some progressive reconstruction schemes have been proposed in the past, we show in this paper that this representation, recently proposed in the MPEG4 standard, can be efficiently used to perform real-time, view-dependent reconstruction of large meshes. The proposed system combines algorithms for local updates, cache management, and server/client dialog. The local details management is an improvement of progressive reconstructions built on top of hierarchical structures. It enables fast, homogeneous accommodation and suppression of wavelet coefficients at any level of subdivision, with time complexity independent of the size of the reconstructed mesh. The cache structure wisely exploits the hierarchical character of the received data, in order to avoid redundant information transmission. The whole system enables the client to have total control on the quality of navigation according to its storage and processing capabilities, whatever the size of the mesh.

Wavelet methods for geometry encoding is a recently emerged superset of multiresolution analysis which has proven to be very efficient in term of compression and adaptive transmission of 3D content. The decorrelating power and space/scale localization of wavelets enable efficient compression of arbitrary meshes as well as progressive and local reconstruction. Recent techniques based on zerotree compression have shown to be among the best lossy mesh compression methods, while remaining compatible with selective transmission of geometric data at various level of detail. While some progressive reconstruction schemes have been proposed in the past, we show in this paper that this representation, recently proposed in the MPEG4 standard, can be efficiently used to perform real-time, view-dependent reconstruction of large meshes. The proposed system combines algorithms for local updates, cache management and server/client dialog. The local details management is an improvement of progressive reconstructions built on top of hierarchical structures. It enables fast, homogeneous accommodation and suppression of wavelet coefficients at any level of subdivision, with time complexity independent of the size of the reconstructed mesh. The cache structure wisely exploits the hierarchical character of the received data, in order to avoid redundant information transmission. The whole system enables the client to have total control on the quality of navigation according to its storage and processing capabilities, whatever the size of the mesh.

The goal of the MOVIE very large-scale integration chip is to facilitate the development of software-only solutions for real-time video processing applications. This chip can be seen as a building block for single-instruction, multiple-data processing, and its architecture has been designed so as to facilitate high-level language programming. The basic architecture building block associates a subarray of computation processors with an I/O processor. A module can be seen as a small linear, systolic-like array of processing elements, connected at each end to the I/O processor. The module can communicate with its two nearest neighbors via two communication ports. The chip architecture also includes three 16-bit video ports. One important aspect in the programming environment is the C-stolic programming language. C stolic is a C-like language augmented with parallel constructs, which allow the differentiation between the array controller variables (scalar variables) and the local variables in the array structure (systolic variables). A statement operating on systolic variables implies a simultaneous execution on all the cells of the structure. Implementation examples of MOVIE-based architectures dealing with video compression algorithms are given.

The MPEG-2 video coding standard offers great latitude in implementation and covers a wide variety of applications. The DVFLEX video encoder allows one to take advantage of this flexibility by making the whole coding loop including the bitstream generation, software programmable. The DVFLEX architecture is basically an array of linearly-connected processing modules. These modules are based on the MVP (TMS320C80) and include dedicated I/O ports for video, bitstream and inter-processor communications. All these I/O ports allow the processing to be performed in parallel with I/Os. The processing workload is distributed among these modules on an image region per processor basis. As for the on-chip MVP processors, tasks assignment is much more constrained because of the bitstream handling problems. Although suboptimal, the solution we describe is simple and gives satisfactory results. However, the on-chip to off-chip memory I/Os have to be carefully handled so as to keep the processors busy.

This paper shows how a real-time simulator of moving pictures compression algorithms can be rapidly assembled using a basic building block, here called MOVIE (MOdule for Video Experimentation). The internal architecture of the MOVIE VLSI chip can be compared to a small systolic machine made of a 32-bit I/O processor, a reduced linear array of 16-bit computation processors and data video input/output mechanisms. Externally, the chip is provided with four 16-bit bidirectional data ports and three 16-bit bidirectional data video port. Several MOVIE chips can be easily clustered to allow the size of the linear array of computation processors to be increased. The MOVIE chip is fully programmable in a high level language in order to make program developments easier.

The MPEG-1 (ISO-11172) video compression standard allows considerable latitude in codec design in both aspects of processing algorithms and hardware. This flexibility is difficult to exploit because it implies hours of computer simulation to find a good compromise between the application requirements, the picture quality, and the hardware complexity. To cope with this problem, we have developed an MPEG-1 programmable coding testbed that allows real time experimentation of the coding process in a wide range of application profiles. The coder architecture is highly modular and consists of several processing units which communicate through high speed video data paths and low speed transputer links for control data. Each of these processing units has an MIMD architecture made up of a linear structure of processing modules. These processing modules combine transputers for the control tasks and DSPs for intensive computing tasks (or block matching accelerators for the motion estimation unit). The power of the current version of the system is sufficient to process MPEG SIF video format in real time. The implementation of other low bit rate video compression applications is currently being considered.

It has long been observed that the keenness of sight is lower for diagonal directions than for horizontal or vertical ones. This anisotropy of the human eye response can be exploited by using a non-orthogonal sampling pattern with a reduced sampling density. After an introduction to the two-dimensional sampling theory, it is shown that quincunx sampling is well suited to this characteristic. Then a sampling scheme based on this approach is described. This effectively leads to halving the sampling density and thereby the computing time of ray-traced pictures.

The use of Monte-Carlo integration together with stochastic sampling is very useful for dealing with the scattering phenomena that occur in the propagation and reflection of light. In this paper, these techniques have been applied to the implementation of a physicsbased global illumination model. The theoretical basis of this approach is presented briefly and various applications to realistic image rendering are then described. This concerns the rendering of penumbra and scattered reflection effects, antialiasing and accurate color modelling through spectral integration. For all these applications, both theoretical and implementation aspects are developed and it is shown that stochastic techniques can provide very simple and efficient algorithms.

30-picture synthesis systems used for instance in the audiovisual field or networked services require the implementation of easy-to-use aids to composition. This particular composition software realizes the sizing and locating of even complex CSG objects in a simple and direct manner. The Ray-casting method is used for display and designation.

Recently published papers have shown that, with appropriate intersection algorithms, the rendering of many procedural objects is possible with all the advantages offered by the ray-tracing techniques. In the case of stochastic surfaces, the intersection can be computed by a recursive subdivision technique. The efficiency of this algorithm depends essentially on the bounding volume whose size and shape are directly related to the stochastic characteristics of these surfaces. After a brief review of the rendering of stochastic surfaces and the bounding volume selection problem, two types of bounding volume are studied, describing how their intersection with a ray can be computed and how their size can be derived from the stochastic characteristics. The efficiency then, of these bounding volumes are compared.

Abstract Ray‐casting techniques provide a very general framework in which many problems can be solved in a much easier way than with conventional methods. This is particularly true for the illumination model when a high level of realism is required. Another interesting feature of ray‐casting is its ability to display a wide class of algebraic surfaces with a minimum of approximation. Both aspects are developed in this paper where a full lighting model, based on a theoretical approach, is presented. Then, an algorithm for the display of surfaces of revolution is described. Computation time is the major drawback of ray‐tracing. Special purpose parallel processors seem to offer a good price/performance ratio compared to the use of supercomputers.