Precomputed Radiance Transfer Research Articles

Precomputed Radiance Transfer for Dynamic Scenes with Diffuse Interreflection

Precomputed Radiance Transfer for Dynamic Scenes with Diffuse Interreflection

A meshless hierarchical representation for light transport

We introduce a meshless hierarchical representation for solving light transport problems. Precomputed radiance transfer (PRT) and finite elements require a discrete representation of illumination over the scene. Non-hierarchical approaches such as per-vertex values are simple to implement, but lead to long precomputation. Hierarchical bases like wavelets lead to dramatic acceleration, but in their basic form they work well only on flat or smooth surfaces. We introduce a hierarchical function basis induced by scattered data approximation. It is decoupled from the geometric representation, allowing the hierarchical representation of illumination on complex objects. We present simple data structures and algorithms for constructing and evaluating the basis functions. Due to its hierarchical nature, our representation adapts to the complexity of the illumination, and can be queried at different scales. We demonstrate the power of the new basis in a novel precomputed direct-to-indirect light transport algorithm that greatly increases the complexity of scenes that can be handled by PRT approaches.

Spherical Piecewise Constant Basis Functions for All-Frequency Precomputed Radiance Transfer

This paper presents a novel basis function, called spherical piecewise constant basis function (SPCBF), for precomputed radiance transfer. SPCBFs have several desirable properties: rotatability, ability to represent all-frequency signals, and support for efficient multiple product. By smartly partitioning the illumination sphere into a set of subregions, and associating each subregion with an SPCBF valued 1 inside the region and 0 elsewhere, we precompute the light coefficients using the resulting SPCBFs. Efficient rotation of the light representation in SPCBFs is achieved by rotating the domain of SPCBFs. We run-time approximate the BRDF and visibility coefficients using the set of SPCBFs for light, possibly rotated, through fast lookup of summed-area-table (SAT) and visibility distance table (VDT), respectively. SPCBFs enable new effects such as object rotation in all-frequency rendering of dynamic scenes and on-the-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.

A framework for precomputed and captured light transport

Several types of methods precompute or capture light transport operators in either virtual or real scenes. Precomputed radiance transfer methods interactively render realistic images of static scenes under dynamic incident illumination, while reflectance field techniques capture an appearance model of a real scene for relighting purposes. In this article we present a unifying mathematical framework for methods that precompute or capture light transport operators, and characterize a large body of earlier work in its terms. The framework is given in the form of an operator equation that extends the rendering equation to account for a constrained space of emissions. The connections between traditional global illumination methods and precomputed transfer techniques become apparent through the explicit equation. Based on insight provided by the unifying view, we outline possibilities for new methods, particularly the wider adaptation of previous, hierarchical finite element techniques for efficient computation of the transport operators.

Real‐time homogenous translucent material editing

Abstract This paper presents a novel method for real‐time homogenous translucent material editing under fixed illumination. We consider the complete analytic BSSRDF model proposed by Jensen et al. [JMLH01], including both multiple scattering and single scattering. Our method allows the user to adjust the analytic parameters of BSSRDF and provides high‐quality, real‐time rendering feedback. Inspired by recently developed Precomputed Radiance Transfer (PRT) techniques, we approximate both the multiple scattering diffuse reflectance function and the single scattering exponential attenuation function in the analytic model using basis functions, so that re‐computing the outgoing radiance at each vertex as parameters change reduces to simple dot products. In addition, using a non‐uniform piecewise polynomial basis, we are able to achieve smaller approximation error than using bases adopted in previous PRT‐based works, such as spherical harmonics and wavelets. Using hardware acceleration, we demonstrate that our system generates images comparable to [JMLH01]at real‐time frame‐rates.

Precomputed Radiance Transfer Field for Rendering Interreflections in Dynamic Scenes

Abstract In this paper, we introduce a new representation – radiance transfer fields (RTF) – for rendering interreflections in dynamic scenes under low frequency illumination. The RTF describes the radiance transferred by an individual object to its surrounding space as a function of the incident radiance. An important property of RTF is its independence of the scene configuration, enabling interreflection computation in dynamic scenes. Secondly, RTFs naturally fit in with the rendering framework of precomputed shadow fields, incurring negligible cost to add interreflection effects. In addition, RTFs can be used to compute interreflections for both diffuse and glossy objects. We also show that RTF data can be highly compressed by clustered principal component analysis (CPCA), which not only reduces the memory cost but also accelerates rendering. Finally, we present some experimental results demonstrating our techniques.

A theory of locally low dimensional light transport

Blockwise or Clustered Principal Component Analysis (CPCA) is commonly used to achieve real-time rendering of shadows and glossy reflections with precomputed radiance transfer (PRT). The vertices or pixels are partitioned into smaller coherent regions, and light transport in each region is approximated by a locally low-dimensional subspace using PCA. Many earlier techniques such as surface light field and reflectance field compression use a similar paradigm. However, there has been no clear theoretical understanding of how light transport dimensionality increases with local patch size, nor of the optimal block size or number of clusters. In this paper, we develop a theory of locally low dimensional light transport, by using Szego's eigenvalue theorem to analytically derive the eigenvalues of the covariance matrix for canonical cases. We show mathematically that for symmetric patches of area A , the number of basis functions for glossy reflections increases linearly with A , while for simple cast shadows, it often increases as √ A . These results are confirmed numerically on a number of test scenes. Next, we carry out an analysis of the cost of rendering, trading off local dimensionality and the number of patches, deriving an optimal block size. Based on this analysis, we provide useful practical insights for setting parameters in CPCA and also derive a new adaptive subdivision algorithm. Moreover, we show that rendering time scales sub-linearly with the resolution of the image, allowing for interactive all-frequency relighting of 1024 x 1024 images.

A theory of locally low dimensional light transport

Blockwise or Clustered Principal Component Analysis (CPCA) is commonly used to achieve real-time rendering of shadows and glossy reflections with precomputed radiance transfer (PRT). The vertices or pixels are partitioned into smaller coherent regions, and light transport in each region is approximated by a locally low-dimensional subspace using PCA. Many earlier techniques such as surface light field and reflectance field compression use a similar paradigm. However, there has been no clear theoretical understanding of how light transport dimensionality increases with local patch size, nor of the optimal block size or number of clusters.

Visual equivalence

Efficient, realistic rendering of complex scenes is one of the grand challenges in computer graphics. Perceptually based rendering addresses this challenge by taking advantage of the limits of human vision. However, existing methods, based on predicting visible image differences, are too conservative because some kinds of image differences do not matter to human observers. In this paper, we introduce the concept of visual equivalence, a new standard for image fidelity in graphics. Images are visually equivalent if they convey the same impressions of scene appearance, even if they are visibly different. To understand this phenomenon, we conduct a series of experiments that explore how object geometry, material, and illumination interact to provide information about appearance, and we characterize how two kinds of transformations on illumination maps (blurring and warping) affect these appearance attributes. We then derive visual equivalence predictors (VEPs): metrics for predicting when images rendered with transformed illumination maps will be visually equivalent to images rendered with reference maps. We also run a confirmatory study to validate the effectiveness of these VEPs for general scenes. Finally, we show how VEPs can be used to improve the efficiency of two rendering algorithms: Light-cuts and precomputed radiance transfer. This work represents some promising first steps towards developing perceptual metrics based on higher order aspects of visual coding.

Visual equivalence

Efficient, realistic rendering of complex scenes is one of the grand challenges in computer graphics. Perceptually based rendering addresses this challenge by taking advantage of the limits of human vision. However, existing methods, based on predicting visible image differences, are too conservative because some kinds of image differences do not matter to human observers. In this paper, we introduce the concept of visual equivalence , a new standard for image fidelity in graphics. Images are visually equivalent if they convey the same impressions of scene appearance, even if they are visibly different. To understand this phenomenon, we conduct a series of experiments that explore how object geometry, material, and illumination interact to provide information about appearance, and we characterize how two kinds of transformations on illumination maps (blurring and warping) affect these appearance attributes. We then derive visual equivalence predictors (VEPs): metrics for predicting when images rendered with transformed illumination maps will be visually equivalent to images rendered with reference maps. We also run a confirmatory study to validate the effectiveness of these VEPs for general scenes. Finally, we show how VEPs can be used to improve the efficiency of two rendering algorithms: Light-cuts and precomputed radiance transfer. This work represents some promising first steps towards developing perceptual metrics based on higher order aspects of visual coding.

Presence and interaction in mixed reality environments

In this paper, we present a simple and robust mixed reality (MR) framework that allows for real-time interaction with virtual humans in mixed reality environments under consistent illumination. We will look at three crucial parts of this system: interaction, animation and global illumination of virtual humans for an integrated and enhanced presence. The interaction system comprises of a dialogue module, which is interfaced with a speech recognition and synthesis system. Next to speech output, the dialogue system generates face and body motions, which are in turn managed by the virtual human animation layer. Our fast animation engine can handle various types of motions, such as normal key-frame animations, or motions that are generated on-the-fly by adapting previously recorded clips. Real-time idle motions are an example of the latter category. All these different motions are generated and blended on-line, resulting in a flexible and realistic animation. Our robust rendering method operates in accordance with the previous animation layer, based on an extended for virtual humans precomputed radiance transfer (PRT) illumination model, resulting in a realistic rendition of such interactive virtual characters in mixed reality environments. Finally, we present a scenario that illustrates the interplay and application of our methods, glued under a unique framework for presence and interaction in MR.

Clustering Environment Lights for an Efficient All-Frequency Relighting

We present a novel precomputed radiance transfer method for efficient relighting under all-frequency environment illumination. Environment illumination is represented as a set of environment lights. Each environment light comprises a direction and an intensity. In a preprocessing step, the environment lights are clustered into several clusters, taking into account only the light directions. By experiment, we confirmed that the environment lights can be clustered into a much smaller number of clusters than their original number. Given any environment illumination, sampled as an environment map, an efficient relighting is then achieved by computing the radiance using the precomputed clusters. The proposed method enables relighting under very high-resolution environment illumination. In addition, unlike previous approaches, the proposed method can efficiently perform relighting when some regions of the given environment illumination change.

Real-time BRDF editing in complex lighting

Current systems for editing BRDFs typically allow users to adjust analytic parameters while visualizing the results in a simplified setting (e.g. unshadowed point light). This paper describes a real-time rendering system that enables interactive edits of BRDFs, as rendered in their final placement on objects in a static scene, lit by direct, complex illumination. All-frequency effects (ranging from near-mirror reflections and hard shadows to diffuse shading and soft shadows) are rendered using a precomputation-based approach. Inspired by real-time relighting methods, we create a linear system that fixes lighting and view to allow real-time BRDF manipulation. In order to linearize the image's response to BRDF parameters, we develop an intermediate curve-based representation, which also reduces the rendering and precomputation operations to 1D while maintaining accuracy for a very general class of BRDFs. Our system can be used to edit complex analytic BRDFs (including anisotropic models), as well as measured reflectance data. We improve on the standard precomputed radiance transfer (PRT) rendering computation by introducing an incremental rendering algorithm that takes advantage of frame-to-frame coherence. We show that it is possible to render reference-quality images while only updating 10% of the data at each frame, sustaining frame-rates of 25-30fps.

All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation

This paper introduces a new data representation and compression technique forprecomputed radiance transfer(PRT). The light transfer functions and light sources are modeled withspherical radial basis functions(SRBFs). A SRBF is a rotation-invariant function that depends on the geodesic distance between two points on the unit sphere. Rotating functions in SRBF representation is as straightforward as rotating the centers of SRBFs. Moreover, high-frequency signals are handled by adjusting the bandwidth parameters of SRBFs. To exploit inter-vertex coherence, the light transfer functions are further classified iteratively into disjoint clusters, and tensor approximation is applied within each cluster. Compared with previous methods, the proposed approach enables real-time rendering with comparable quality under high-frequency lighting environments. The data storage is also more compact than previous all-frequency PRT algorithms.

Rendering Participating Media by Importance Sampling based on Precomputed Radiance Transfer

Rendering Participating Media by Importance Sampling based on Precomputed Radiance Transfer

All-frequency relighting of glossy objects

We present a technique for interactive rendering of glossy objects in complex and dynamic lighting environments that captures interreflections and all-frequency shadows. Our system is based on precomputed radiance transfer and separable BRDF approximation. We factor glossy BRDFs using a separable decomposition and keep only a few low-order approximation terms, each consisting of a purely view-dependent and a purely light-dependent component. In the precomputation step, for every vertex, we sample its visibility and compute a direct illumination transport vector corresponding to each BRDF term. We use modern graphics hardware to accelerate this step and further compress the data using a nonlinear wavelet approximation. The direct illumination pass is followed by one or more interreflection passes, each of which gathers compressed transport vectors from the previous pass to produce global illumination transport vectors. To render at run time, we dynamically sample the lighting to produce a light vector, also represented in a wavelet basis. We compute the inner product of the light vector with the precomputed transport vectors, and the results are further combined with the BRDF view-dependent components to produce vertex colors. We describe acceleration of the rendering algorithm using programmable graphics hardware and discuss the limitations and trade-offs imposed by the hardware.

Local, deformable precomputed radiance transfer

Precomputed radiance transfer (PRT) captures realistic lighting effects from distant, low-frequency environmental lighting but has been limited to static models or precomputed sequences. We focus on PRT for local effects such as bumps, wrinkles, or other detailed features, but extend it to arbitrarily deformable models. Our approach applies zonal harmonics (ZH) which approximate spherical functions as sums of circularly symmetric Legendre polynomials around different axes. By spatially varying both the axes and coefficients of these basis functions, we can fit to spatially varying transfer signals. Compared to the spherical harmonic (SH) basis, the ZH basis yields a more compact approximation. More important, it can be trivially rotated whereas SH rotation is expensive and unsuited for dense per-vertex or per-pixel evaluation. This property allows, for the first time, PRT to be mapped onto deforming models which re-orient the local coordinate frame. We generate ZH transfer models by fitting to PRT signals simulated on meshes or simple parametric models for thin membranes and wrinkles. We show how shading with ZH transfer can be significantly accelerated by specializing to a given lighting environment. Finally, we demonstrate real-time rendering results with soft shadows, inter-reflections, and subsurface scatter on deforming models.

Real-time rendering of plant leaves

This paper presents a framework for the real-time rendering of plant leaves with global illumination effects. Realistic rendering of leaves requires a sophisticated appearance model and accurate lighting computation. For leaf appearance we introduce a parametric model that describes leaves in terms of spatially-variant BRDFs and BTDFs. These BRDFs and BTDFs, incorporating analysis of subsurface scattering inside leaf tissues and rough surface scattering on leaf surfaces, can be measured from real leaves. More importantly, this description is compact and can be loaded into graphics hardware for fast run-time shading calculations, which are essential for achieving high frame rates. For lighting computation, we present an algorithm that extends the Precomputed Radiance Transfer (PRT) approach to all-frequency lighting for leaves. In particular, we handle the combined illumination effects due to low-frequency environment light and high-frequency sunlight. This is done by decomposing the local incident radiance of sunlight into direct and indirect components. The direct component, which contains most of the high frequencies, is not pre-computed with spherical harmonics as in PRT; instead it is evaluated on-the-fly using pre-computed light-visibility convolution data. We demonstrate our framework by the rendering of a variety of leaves and assemblies thereof.

Deferred shadowing for real‐time rendering of dynamic scenes under environment illumination

AbstractEnvironment illumination, which is a complex and distant lighting environment represented by images, is often applied to create photo‐realistic images. However, creating photo‐realistic animations under environment illumination is exceedingly compute intensive. The Precomputed Radiance Transfer (PRT) methods achieve real‐time rendering under environment illumination; however, these methods only have a limited application in animation because the objects in the scene cannot be moved or rotated. In this paper, we propose a method for rendering photo‐realistic animations of dynamic scenes under environment illumination in real time. We notice the fact that when objects are moved or rotated, changes of radiances occur mainly in the regions of shadows cast by other objects. Our method makes a distinction between self‐shadow and shadows cast by other objects and computes these two kinds of shadows efficiently. Copyright © 2005 John Wiley & Sons, Ltd.

A frequency analysis of light transport

We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatment of both space and angle.We show that occlusion, a multiplication in the primal, amounts in the Fourier domain to a convolution by the spectrum of the blocker. Propagation corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As shown by previous work, reflection is a convolution in the primal and therefore a multiplication in the Fourier domain. Our work shows how the spatial components of lighting are affected by this angular convolution.Our framework predicts the characteristics of interactions such as caustics and the disappearance of the shadows of small features. Predictions on the frequency content can then be used to control sampling rates for rendering. Other potential applications include precomputed radiance transfer and inverse rendering.