State of the Art in Global Illumination for Interactive ...resources.mpi-inf.mpg.de/anim/EG_STAR/EGCGF02.pdf · “02C 200 page C. Damez et al. / Global Illumination for Interactive

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Volume 21 (2003), number 4 pp. 55–77 COMPUTER GRAPHICS forum

State of the Art in Global Illumination for InteractiveApplications and High-quality Animations

Cyrille Damez, Kirill Dmitriev and Karol Myszkowski

Max-Planck-Institut fur Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrucken, Germany

AbstractGlobal illumination algorithms are regarded as computationally intensive. This cost is a practical problem whenproducing animations or when interactions with complex models are required. Several algorithms have beenproposed to address this issue. Roughly, two families of methods can be distinguished. The first one aims atproviding interactive feedback for lighting design applications. The second one gives higher priority to the qualityof results, and therefore relies on offline computations. Recently, impressive advances have been made in bothcategories. In this report, we present a survey and classification of the most up-to-date of these methods.

ACM CSS: I.3.7 Computer Graphics—Three-Dimensional Graphics and Realism

1. Introduction

Synthesis of images predicting the appearance of the realworld has many important engineering applications includ-ing product design, architecture and interior design. Evenless rigorous applications, such as visual effects, film pro-duction, or computer games benefit greatly from an increasein realism. One of the major components of such predic-tive image synthesis is the simulation of the interaction oflight with objects in the scene. The ever-increasing process-ing power and memory size, as well as recent algorithmicdevelopments, have made global illumination computationsaffordable even for complex scenes.

A vast majority of the existing global illuminationalgorithms were designed for rendering static scenes.In practice this means that when such algorithms areused for a dynamic scene, all computations have to berepeated from scratch even when only minor changesare performed. The use of those algorithms in practical,real-life applications is therefore limited. Indeed, the costof redundant computations is excessive for core computergraphics applications such as the production of animatedsequences or interactive rendering.

In recent years, several new algorithmic solutions havebeen proposed that explicitly address the problem of globalillumination computations in interactive applications or forhigh-quality animations. Significant effort has been devotedto the reduction of required resources. Indeed, consideringthe large number of frames necessary even for a briefmovie sequence, shortening the production time carries animportant economic value for the movie industry. Moreover,the ability to provide a fast feedback to the user in responsefor interactive changes in the scene greatly improves theusability of lighting simulation algorithms.

Another important issue is temporal aliasing inanimations. Many typical errors in lighting computation andreconstruction cannot be perceived by the human observerwhen they are coherent in the temporal domain. However,they may cause unpleasant flickering and shimmeringeffects when this coherence is lost. Such artifacts are moredifficult to combat efficiently if temporal processing ofglobal illumination is not performed. In such a case, thetraditional approach of reinforcing the accuracy of globalillumination computation for each frame proves extremelyinefficient. Moreover, it is very difficult to locally controlthe perceivability of temporal aliasing. Clearly, temporalcoherence in the scene changes must be taken into account

c© The Eurographics Association and Blackwell Publishing Ltd2003. Published by Blackwell Publishing, 9600 Garsington Road,Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148,USA. 55

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56 C. Damez et al. / Global Illumination for Interactive Applications and High-quality Animations

in modern global illumination algorithms to make thempractical.

If one considers the recent resurgence of this topic inthe computer graphics literature, it seems that both thehardware and the algorithms at hand are now mature enoughto consider lighting simulations for animated environmentsas feasible. This state-of-the-art report is therefore intended:

• to define a classification of global illuminationtechniques in animated scenes, developed in Section 2;

• to recall and discuss the most up-to-date development inthis field. We discuss interactive and offline global illu-mination algorithms in Sections 3 and 4, respectively;

• to evaluate the respective performances, pros and consof these new approaches: in Section 5 we provide acomparison taking into account some relevant criteria,describing their strengths and weaknesses in practicalapplications. Also, we speculate on possible directionsof further research.

2. Classification of Methods Discussed in the Report

Global illumination algorithms for animations must bedesigned to deal efficiently with many different types ofchanges in the scene. The most typical scene changes mayinvolve:

• the camera — its position and orientation in the scene,the viewing direction, the viewing angle,

• surface attributes — light reflectance and transmissioncharacteristics†, textures,

• light sources — their positions in the scene, spatialdimensionalities and shapes, goniometric diagrams,

• the geometry — moving rigid objects, articulated fig-ures, shape animation.

While not exhaustive, this list gives an idea of thechallenges imposed on a versatile global illuminationalgorithm. In practice, many algorithms are specialized tohandle only a subset of such scene changes. A commonexample of specialized algorithms are walkthroughtechniques dedicated for efficient handling of cameraanimation, a difficult problem in itself for non-diffuseenvironments. A good survey of interactive renderingtechniques for such environments was presented byHeidrich [1] (refer to Sections 2–4 of his report).

In this state-of-the-art report we focus on general purposealgorithms. As a consequence, specialized walkthroughtechniques are not discussed in this report. The commondenominator for most of the algorithms we detail in this

† We do not take into account volumetric effects in this report.

report is their ability to handle modifications in the scenegeometry. Visibility changes between objects in the scenemake it one of the most expensive aspects of the globalillumination computation.

Global illumination algorithms for animated scenes canbe grouped in two categories, with different scopes ofapplication:

• The interactive methods, which are designed to tradethe image quality for the response speed. Their mainobjective is to provide a fast response for frame-to-frame changes in the environment. A fixed frame rateis required by some applications, which splits theillumination update into equal time intervals and resultsin progressive refinement of resulting images.

• The offline methods, for which complete knowledgeof trajectories and upcoming events is required. Thosemethods are usually aimed at producing high qualityanimations. In this case, differences in the renderingtime of particular frames are perfectly acceptable.

Since the working hypothesis for the former methodsis less restrictive, any interactive method can in theory beapplied in place of an offline method, i.e. in a non-interactiveapplication, whereas the contrary generally is not possible.However, the quality of the animations they provide, aswe show in the report, usually cannot match their offlinecounterparts. The temporal coherence of lighting can alsobe exploited much better when longer image sequencesare considered. This requires the knowledge of changes inthe environment in advance, which is impossible in theinteractive scenario.

For the sake of completeness, we chose to mention inthis state-of-the-art report even pioneering animated globalillumination algorithms, though we mainly focus on the mostrecent ones. For the same reason we briefly mention sometechniques dedicated for efficient display of the lightingsimulation results during the rendering phase. This topicwas extensively covered for interactive solutions by Heidrich[1] (refer to Section 5 of his report) and an interestedreader can find there a more detailed discussion of relevanttechniques. In this report we discuss more extensively onlythose rendering solutions, which explicitly emphasize onthe temporal coherence between the subsequent animationframes.

3. Interactive Methods

For many applications, such as lighting design, it is desirableto be able to move one or more objects, or change theirlocal reflection properties, and witness as fast as possiblethe effects of such modifications on the scene appearance.Without an appropriate, interactive enough feedback, finetuning of the lighting is a tedious process. Unfortunately,

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C. Damez et al. / Global Illumination for Interactive Applications and High-quality Animations 57

such modifications of the scene, because of the very natureof global illumination, may change the appearance of everysurface in the scene. The methods reviewed in this sectionusually address this problem by trying to determine aminimum set of recomputation to be made to provide theuser a “precise enough” feedback, while still maintaining a“sufficient” frame rate.

Two separate problems can be distinguished:

• First, the actual simulation of global illumination hasto be performed and updated with respect to theuser changes. Relevant methods will be reviewed inSections 3.1 and 3.2. We start with the incrementalalgorithms that evolved from the finite element radiositymethod in Section 3.1. We proceed to a review of ahybrid approach in Section 3.2 relying both on finiteelement radiosity and stochastic particle shooting, Wediscuss stochastic methods in Sections 3.3–3.5.

• Then the results of the simulation also have to be dis-played. Straightforward hardware polygon rasterizationcan be used if only diffuse reflections are taken intoaccount, but as soon as specular reflections are to be sim-ulated, more sophisticated display methods are calledfor. Therefore, we describe real-time display approachesthat can be applied to global illumination solutions in

Sections 3.6 and 3.7, although they do not address thequestion of how global illumination is to be computed.

3.1. Interactive Update of Radiosity Solutions

The radiosity method [2] and its derivations [3–6] allow theefficient computation of global illumination in diffuse envi-ronments. Therefore, those methods are particularly suitedfor applications such as lighting design or walkthroughs ofarchitectural models.

However, for the radiosity methods, changes in the sur-faces reflectances require new iterations to compute the re-propagation of light in the scene. Moreover, geometric mod-ifications in the scene imply an expensive reevaluation ofmany form factors, and as a consequence light needs to berepropagated until convergence. Various independent algo-rithms based on the radiosity method have been proposed toaddress these issues.

Incremental Progressive Radiosity. Chen [7] and Georgeet al. [8] independently proposed two similaralgorithms, based on progressive radiosity [3] whichallow the update of a converged radiosity solutionafter the displacement of an object in the followingway: First, the radiosity of the dynamic object isrepropagated toward all static surfaces. Then, onestatic mesh element is chosen. Its radiosity is shot atthe dynamic object, and the opposite of its radiosityis shot at the surfaces that are inside the shadow

volume cast by the dynamic object. This process isrepeated iteratively until a satisfying approximation iscomputed. Muller et al. [9] later extended progressiveradiosity further, building shadow-lists to speed upmodified interactions computation. Unfortunately,as all require a computation time which is quadraticwith respect to the number of mesh elements, thosealgorithms are limited to simple scenes only.

Dynamic Hierarchical Radiosity. Hierarchical radiositywas first introduced by Hanrahan et al. [4] to reducethe cost of radiosity computations. This method isbased on the use of a hierarchical mesh, representingthe surface’s radiosity at various precision levels. Lightexchanges between elements are represented by a linkstructure that specifies at which level of precision theform factor computation and light gathering should beperformed. This method can be naturally extended tohandle dynamic scenes, as the link structure makes iteasier to localize the form factors that have potentiallybeen affected by the changes in the geometry.

Forsyth et al. [10] first proposed an extension of hi-erarchical radiosity for interactive scenes, in which agiven link can be occluded or validated (if the dynamicobject passes between the corresponding sender and re-ceiver), promoted or pushed down the hierarchy. How-ever this algorithm does not provide any simplificationmechanism. As a consequence, the size of the mesh iscontinuously increasing as the interactive session goeson, which makes it impractical for long interactive ses-sions. To overcome this drawback Shaw [11] proposedan alternative link structure allowing to “unrefine” themesh, through the use of special shadow links keepingtrack of blocker information, and a method to localizeocclusion caused by the dynamic object using motionvolumes.

However, even though these approaches provide sig-nificant improvements over the progressive radiositymethod presented earlier, they still need a couple ofseconds to update even very simple scenes. Moreover,as pointed out by Drettakis and Sillion [12], they lack amechanism to offer a consistent trade-off between ac-curacy and speed to be able to reach interactive framerates with fairly complex scenes.

Line-Space Hierarchy. In order to achieve interactiveframe rates, Drettakis and Sillion [12] proposed toaugment the hierarchical radiosity link structure withshafts [13] that represent the set of line segmentsjoining two linked hierarchical elements. Traversingthe link structure to test for intersections of shaftsby the bounding box of the dynamic object allowsto rapidly identify interactions that have to berecomputed, further refined or simplified.

The line-space hierarchy method also gives the user


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control over the time vs. quality trade-off. A budgetlimit of links allowed for refinement has to be fixedwith respect to the desired frame rate. Similarly,the update of modified links is controlled in orderto guarantee a certain frame rate. As the hierarchyof objects in the line-space hierarchy algorithmuses clustering [5,6], a consistent solution is alwayscomputed. No matter how fast the frame rate requiredis, the set of active links in the hierarchy alwaysaccounts for the complete line space. Of course, whenfast updates are required, all interactions will be placedat a rather high level. The computed solution willtherefore be a rather crude approximation.

However, when the scene becomes more complex,or the requested precision is high, the weightof the link hierarchy becomes overwhelming.The memory required for the storage of shafts isparticularly significant. In order to reduce the memoryrequirements of the line-space hierarchy algorithm,Schoeffel et al. [14] proposed to clean up the linkhierarchy by removing shafts. Shafts that are likely tobe needed in the next couple of frames are predictedby a simple movement extrapolation scheme and builtby a separate process. This reduces the adverse effecton performance that would be caused by “on-the-fly”reconstruction of shafts. Typical memory savings rangefrom 80% to 90%. When the dynamic object is movedalong a continuous path with a “ reasonable” speed(which admittedly might not always be the case duringinteractive design sessions), a performance similar tothe original line-space algorithm can be obtained.

3.2. Incremental Update of Glossy Global Illumination

Hierarchical radiosity is one of the most efficient global illu-mination method for diffuse scenes. However, the computa-tional cost and memory requirements of deterministic, finiteelement methods for glossy surfaces are too high for practi-cal applications, despite being proved feasible for scenes oflimited complexity [15–17]. In particular, the explicit stor-age in memory of a directional representation of outgoingradiances for all mesh elements prevents the use of thesemethods for scenes whose complexity corresponds to indus-try requirements, even on todays most expensive high-endhardware. On the other end, various non-deterministic meth-ods [18–20] have demonstrated their efficiency for comput-ing lighting effects involving specular reflections and refrac-tions, such as caustics, but are far less efficient when it comesto diffuse interactions.

To keep the best from both worlds, Granier et al. [21]proposed a unified hierarchical algorithm that cleanly sepa-rates purely diffuse light paths from those involving specularreflections and/or refractions. The former are computed bya classical hierarchical radiosity approach, while the latter

are handled using stochastic particle shooting. Clever use ofshafts allows limitation of this stochastic shooting to por-tions of line space where they are really needed. For a properintegration of both methods within the hierarchical radios-ity paradigm, particles’ energies are added at an appropriatelevel in the hierarchical mesh during the push–pull traversal.

Rapid updates [22] of solutions computed by the unifiedhierarchical algorithm are possible using a frameworksimilar to the one of the line-space hierarchy (see Section3.1). In this algorithm, all transfers to diffuse surfaces arerecorded in the mesh or in caustic textures and displayedusing straightforward polygon rasterization hardware.Automatic methods to choose between particle storage inmesh or in textures are provided, as well as means to restrictthe texture size. Specular paths to the eye are interactivelydisplayed using the Render Cache method (refer to Section3.6).

To obtain fast updates during object motion, the numberof particles resent during object motion has to be reduced.As for diffuse transfer in the line-space hierarchy algorithm,the particle paths that are affected by the dynamic objectmovement have to be quickly identified. This is doneusing an octree which is subdivided up to a user-specifiedmaximum depth around the dynamic object position. Linksthat are used to transfer particles are inserted in the octreecells they traverse (in hash tables for quicker access) withthe corresponding receiver element. During object motion,the octree is consulted to access the affected links. Onlya small, user controllable percentage of them is reemitted.Figure 1 shows a typical caustic quality degradation duringobject motion.

This algorithm allows updates of global illuminationsolutions including specular effects within a couple secondsper frame. As a comparison, the initial frame solution forthe example scene of Figure 1 took 35 min to compute.However, this method is controlled using several user fixedthresholds. There is no automatic method yet to choose theirvalue to guarantee a given frame rate. This strongly reducesits usability.

3.3. Radiosity Computation Using Graphics Hardware

In the previous sections we discussed algorithms which relycompletely on software-based computations and for whichgraphics hardware is used only at the image display stage.However, the rapidly improving speed and functionalityof graphics hardware makes it more and more attractiveto relegate some expensive computation from the CPU tographics hardware [1].

In this section we discuss two example algorithms inwhich the radiosity computation is supported by graphicshardware. First, we briefly overview an algorithm proposedby Udeshi and Hansen [23] which is a hybrid of hardware


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Figure 1: Update of caustic textures during object motion. From left to right: initial position with good quality, two intermediatepositions with degraded quality (3 s/frame), final image quality 20 s. after the end of motion. (Images courtesy of Xavier Granierand George Drettakis.)

progressive radiosity and ray tracing. Then, we discuss theinstant radiosity algorithm developed by Keller [24] whichuses the graphics hardware to rapidly compute an estimateof the illumination based on a quasi-random walk photontracing pass.

Hybrid Hardware Radiosity and Ray Tracing. Udeshiand Hansen [23] use graphics hardware to obtain thedirect illumination on diffuse surfaces. Shadows arecomputed using a shadow volume algorithm improvedby the authors. Also, approximate one-bounce diffuseinterreflection computation is performed, in whichbright directly illuminated surface elements becomesecondary (virtual) light sources. A single-planeversion of the hemi-cube algorithm is used to computethe form factors. However, visibility is not taken intoaccount for virtual lights, which may lead to incorrectindirect illumination. The CPU is mostly involvedin ray tracing of pixels through which specular andrefractive objects can be seen. The authors report anachievement of several frames per second on a graphicsupercomputer (64 processors and eight graphicspipelines) for scenes of moderate complexity.

Instant Radiosity. Keller [24] proposes an algorithm thatuses the CPU in a first pass, and classical OpenGLlighting functions in a second pass. First, photonsare emitted from light sources and are traced in thescene to produce an approximation of the diffuseradiance on object surfaces in this scene. Insteadof the classical random walk terminated by RussianRoulette, a quasi-random walk algorithm, based onfractional absorption, is used [25]. The algorithmapplies knowledge of the average diffuse reflectivity ρ

of the scene to restrict the length of photon paths ina physically plausible way. Let for instance N be thetotal number of walks the user wants to generate. Thenexactly �ρN� walks will have length equal to 1, �ρ2 N�walks will have length equal to 2, �ρ3 N� - length equalto 3, and so on. The maximum walk length will then beequal to �logρ(1/N )�. All photons start with the sameenergy. When a photon hits the surface, its energy is

scaled by a factor fd (y)/ρ, where fd (y) is the diffusereflectivity at the point of intersection.

As a result of the photon tracing stage, anapproximation of the diffuse radiance is obtained.Graphics hardware is then cleverly used to render theimage with shadows. Each photon hit point on thescene surfaces is treated as a virtual point light source.Since standard graphics hardware can render only onelight source with shadows at a time, the accumulationbuffer is used to sum up the individual images. Theluminance of every pixel is usually affected by manyphotons, thus a very crude radiance approximation isenough. Keller shows that a number of quasi-randomwalks varying from 32 to 128 already yields visuallysmooth images.

Two problems of the algorithm are discussed in [24].Since only a crude approximation of radiance isgenerated, a good spatial distribution of photons isrequired to achieve plausible results. Partially thisproblem is solved by applying uniform quasi-randomsequences for photon shooting. However, in the regionswhere the contribution of a single photon is too strong(e.g. close to its hit point), objectionable bright spotscan appear. This problem is hidden by OpenGL, whichclamps intensity values to the 0–1 range, limiting theeffect of such artifacts. The second problem is that eachphoton, colored by a texture, has a large influence onthe overall color of the scene.

Dynamic environments are handled by explicitlystoring an individual image, corresponding to eachquasi-random walk. Every time a walk is renewed, itsimage is replaced by a new one. The current N imagesare then accumulated and displayed, thus implicitlyperforming temporal antialiasing. This, however,restricts the number of quasi-random walks since alarge amount of memory is required to store individualimages, and the accumulation of images for all randomwalks is costly for large N .

The indisputable advantage of the approach is that a


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solution is obtained with pixel precision. Images thusavoid visually objectionable artifacts, such as lightleaks, inherent to finite element approaches. However,as in the case of the radiosity methods discussed inSection 3.1 and the hybrid approach of Section 3.2,this algorithm relies on hardware rendering to build theimages. As a consequence, specular surfaces, such asmirrors, cannot be displayed. Also, for small N (whichmay be necessary to maintain interactive frame rates),some parts of quickly moving objects may accumulateinsufficient indirect illumination. These issues aresuccessfully addressed by using a distributed raytracing technique, which we describe in Section 3.5.

3.4. Selective Photon Tracing

In the instant radiosity algorithm [24] discussed in theprevious section, photon paths are successively replacedby new ones to update lighting in dynamic environments.Ideally, at first only the photon paths, which clearly interferewith dynamic objects in the scene should be replaced. Also,since Instant Radiosity is a view-dependent algorithm, imagerecalculation is required for any change of the cameraparameters. In this section we discuss an algorithm calledselective photon tracing (SPT) developed by Dmitriev et al.[26] which addresses those important issues.

The SPT algorithm uses graphics hardware to computedirect lighting with shadows using the shadow volumealgorithm in a way similar to Udeshi and Hansen [23](refer to Section 3.3). Using the functionality of moderngraphics hardware Dmitriev et al. can process up to fourlight sources with goniometric diagrams per one renderingpass. The indirect lighting is computed asynchronouslyusing quasi-random photon tracing (similar to Keller [25])and density estimation techniques (similar to Volevich[27]). The indirect lighting is reconstructed at vertices ofa precomputed mesh and can be readily displayed usinggraphics hardware for any camera position. The most uniquefeature of the SPT algorithm is exploiting the temporalcoherence of illumination by tracing photons selectively intothe scene regions that require illumination update.

In the SPT algorithm, pseudo-random sequences,typically used in photon shooting, are replaced by thequasi-random Halton sequence [28]. This proves to beadvantageous. Firstly, as shown by Keller [25], quasi-random walk algorithms converge faster than classicalrandom walk ones. Secondly, a periodicity property ofthe Halton sequence [29] provides a straightforward wayof updating indirect illumination as the scene changes.Let us briefly discuss this periodicity property, which isfundamental for efficient searching of invalid photon pathsin dynamic scenes.

The Halton sequence generation is based on the radical

(a) (b)

Figure 2: Structure of photon paths, corresponding to quasi-random points with similar coordinates: (a) similarity of firsttwo coordinates, (b) similarity of first four coordinates.

inverse function [28] h, applied to an integer i . If hi j is thej th coordinate of the Halton point with index i , it can beshown that [26]

|hi j − h(i+m Ng) j | <1

bkj

, if Ng = lbkj . (1)

where b j is a base, used to compute the j th coordinate ofHalton points, k, l, and m are integers such that k ≥ 0

and l > 0. For instance, setting Ng = bk00 bk1

1 bk22 bk3

3 yieldspoints in which the first four coordinates closely match. Thecloseness of this match is governed by the correspondingpowers k0, k1, k2, k3 (the larger power values are selectedthe closer match is obtained). If the scene surfaces andBSDFs are reasonably smooth, quasi-random points withsimilar coordinates produce photons with similar paths,which is depicted in Figure 2.

By selecting quasi-random points with such an intervalNg , that the similarity of coordinates j = 0 and 1 is assured,photons are emitted coherently inside a pyramid with itsapex at light source position. However, those photons do notreflect coherently (Figure 2a). By additionally increasing Ngto obtain a similarity of coordinates j = 2 and 3, photonsare selected so that they reflect coherently inside a morecomplex bounding shape, as shown in Figure 2b.

The lighting computation algorithm considers a pool ofphotons of fixed size Z for the whole interactive session.The photons are traced during the initialization stage. Thenthe paths which become invalid due to changes in thescene are selectively updated. This is performed by tracingphotons for the previous scene configuration with negativeenergy and tracing photons for the new scene configurationwith positive energy. For detecting the invalid photon pathsthe so-called pilot photons, which constitute 5–10% of Z ,are emitted in the scene. For each pilot photon i whichhits a dynamic object and therefore requires updating, theremaining photons in the pool Z with similar paths in the


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(a) (b)

Figure 3: Example frames with global illumination effects obtained using selective photon tracing for scenes composed of (a)12 400 and (b) 377 900 triangles. On a 1.7 GHz Dual P4 Xeon computer with an NVIDIA GeForce3 64 MB video card theframe rates 8 fps. and 1.1 fps. have been achieved, respectively. In order to remove all visible artifacts in lighting distributionresulting from object changes in the scene, 4–8 s of the selective photon update computation are usually required.

scene can be found immediately by adding the offsets m Ngto i , where m are integers such that i + m Ng < Z (refer toEquation 1).

The frame rate in an interactive session using the SPT al-gorithm is mostly determined by the OpenGL performance.For rendering with shadows from multiple light sources withgoniometric diagrams, frame rates ranging from 1.1 to 8fps. are reported (refer to Figure 3). Indirect illumination isupdated incrementally and the result of each update is imme-diately delivered to the user. Most lighting artifacts createdby outdated illumination are removed in the first 4–8 s afterthe scene change. If photons are updated in a random order atleast 2–4 times longer computations are needed to obtain im-ages of similar quality. Better performances can be expectedfor more complex scenes, or when user modifications havemore localized consequences. The unique feature of SPT isthat while the temporal coherence in lighting computationsis strongly exploited, no additional data structures storingphoton paths are required.

In the case study examples (refer to Figure 3) providedby Dmitriev et al. [26] the coherence of photons wasconsidered only up to their second bounce. This provedto be sufficient to efficiently update the illumination forthe studied scenes. When such a coherence for a highernumber of bounces is required, the number of coherentphoton groups Ng increases exponentially. This results in aproportional increase of the photon pool size Z . Interactiveupdate of such an increased pool of photons might not befeasible on a single PC-class computer. The major problemwith the algorithm proposed by Dmitriev et al. is lack ofadaptability of the mesh used to reconstruct the indirectillumination in the scene. Also, only point light sources areexplicitly handled in their hardware-supported algorithm for

the direct illumination computation.

Selective photon tracing can be used in the context ofoffline global illumination computation as well. In particular,this technique seems to be attractive in all those applicationswhich require local reinforcement of computations based onsome importance criteria. An example of such an applicationis the efficient rendering of high-quality caustics, whichusually requires a huge number of photons. After identifyingsome paths of caustic photons, more coherent particlescan easily be generated using this approach. The drawbackof many existing photon based methods is that too manyparticles are sent into well illuminated scene regions witha simple illumination distribution, and too few photonsreach remote scene regions. This deficiency could easily becorrected using the SPT approach, by skipping the tracingof redundant photons and properly scaling the energy of theremaining photons.

3.5. Interactive Global Illumination Using a DistributedRay-Tracing Engine

Remarkable advances in ray tracing speed have recentlybeen made. Through the exploitation of image and objectspace coherence, and better use of computational resources,such as processor caches and SIMD instructions, ray tracingat interactive speed was proven feasible [30,31]. Though forsmall scenes it still cannot outperform graphics hardware ona single PC, comparable performance can be obtained forthe rendering of complex scenes which are composed ofhundreds of thousands of triangles. Moreover, ray tracingis fairly easy to parallelize, which makes it possible toachieve even greater performance on a cluster of PCs. Thoseremarkable improvements in ray tracing performance madeit possible to develop an interactive global illumination


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(a) (b)

Figure 4: Example frames with global illumination effects obtained using distributed ray-tracing engine for scenes composedof a) 300 000 and b) 34 000 triangles. On a cluster of 16 CPUs (Athlon1800+) the frame rates 1.5 fps. and 1.84 fps. have beenachieved, respectively. To fully eliminate all visible image artifacts resulting from changes of the view direction or other changesin the scene 1–2 s of the computation are usually required. (Images courtesy of Ingo Wald, Thomas Kollig, Carsten Benthin,Alexander Keller, and Philipp Slusallek.)

system, which extends the earlier discussed instant radiosityapproach to handle more general lighting effects at evenhigher speed [32].

Similarly to the instant radiosity algorithm [24], in the ap-proach proposed by Wald et al. [32] a coarse representationof radiance is generated by shooting particles from the lightsources and treating their hit points as virtual point lightsources. The computations are distributed over a cluster ofPCs. Each PC generates its own set of quasi-random walksand as a result considers a different set of virtual lights. Sincea single PC is not powerful enough to compute full resolu-tion images with acceptable frame rate, each client computesonly selected samples of the final image. The image plane issplit into image tiles and the same (fixed) sample pattern ischosen for all tiles using the interleaved sampling technique[33]. The samples within each tile are computed by differentPCs, which means that neighboring samples are obtained fordifferent sets of virtual lights.

Though such image tiling solves the network bandwidthproblem, it results in structured noise, since sample valuescomputed on different PCs may differ significantly. Toremove this noise, discontinuity buffering is used. The ideais to apply a 3 × 3 neighbor filter to each pixel, by takinginto account only those pixels that represent scene surfaceswith similar normal vectors and depth values (measuredwith respect to the observer). This selection of similarpixels for filtering purposes is important to avoid excessivesmearing of fine geometric details, e.g. object silhouettes.The proposed criteria of pixel similarity do not preventthe blurring of sharp shadow boundaries, which cannot bedistinguished from the noise in reconstructed lighting. Wald

et al. demonstrated that their 3×3 discontinuity buffer workswell in practice and effectively removes noise caused byinterleaved sampling.

The algorithm proposed by Wald et al. can render manyimportant lighting effects such as diffuse interreflections,specular reflection and refraction, and even caustics (refer toFigure 4b). The latter effect is obtained using an approachsimilar to photon mapping, in which photons are shotfrom light sources in the direction of specular objects thatare expected to cast caustics. To speed up the causticscomputation, the kd-tree structure, typically used forphotons lookup, is replaced by a uniform grid. Instead ofn-nearest neighbor queries, all photons inside a sphere of afixed radius are collected and used to estimate pixel color.The caustics computation is embedded into the generalparallelization strategy. The whole pool of caustic photonsis distributed evenly among all computers of the cluster.Image tiles, delivered by each client, include both diffuseand caustic illumination and are filtered by the server.Noise, caused by an insufficient number of caustic photonsis partially removed by the discontinuity buffer procedure,described above. 500–1500 caustic photons per light sourceare shown to be sufficient for the generation of good lookingcaustics (refer to Figure 4b).

The proposed approach solves many problems, inherentto the Instant Radiosity algorithm. For example, objectsreflected in mirrors are now rendered without any problem,and caustics can be computed as well. Like instant radiosity,this algorithm is an unbiased Monte Carlo scheme (exceptfor the biased photon mapping part) for which the lightingcomputation is performed on a per pixel basis. This prevents


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discretization errors and enables rendering of parametricgeometry. Since a full illumination recomputation is doneafter each object or camera movement, there is no outdatedillumination. Such a recomputation, however, involves hugecomputational efforts and requires a cluster of PCs tosupport interactive frame rates. The temporal coherencebetween frames is preserved by using the same randomnumbers sequences and low discrepancy points for eachframe during interaction. The server capacity of collectingthe image tiles currently limits the frame rate to 5–6 fps. atvideo resolution. The caustic photon paths must be explicitlyspecified in this algorithm, which might be difficult toachieve in an automatic way for the secondary and higherorder caustics.

The method has a strong potential to be used in offlinerendering applications. The authors report that high-qualitystill images can be achieved after 1–2 s of computation.

3.6. Reconstructing Illumination from a Sparse Set ofSamples

As acknowledged in the previous sections, high qualityglobal illumination methods allowing specular effectsare usually computationally intensive. In particular, theinteractive methods reviewed earlier usually rely on raytracing to display specular paths to the eye. Maintaininginteractive frame rates when taking into account such view-dependent specular effects usually requires a considerableamount of processing power (see Section 3.5). Moreover,if updating the geometry requires a couple of seconds,interactive fine tuning of objects positions becomes tedious.

Extending the work of Bergman et al. [34] and Bishop etal. [35], the algorithms reviewed in this section propose todecouple global illumination computations from geometricprojections and image rendering. As such, these algorithmsare not actual global illuminations algorithms: they do notaim at computing the illumination, but at providing aninterface for the interactive display and update of globalillumination solutions, when the actual underlying algorithmcannot provide the required frame rate.

Given a sparse set of high quality illumination samplescomputed asynchronously by a separate process (typicallyPath Tracing [18,36,37]) the illumination is progressivelyreconstructed, either in image space (see Section 3.6.1)or in object space (see Section 3.6.2). Therefore, whenperforming a change, these algorithms always offer a veryfast feedback even if the resulting image accuracy may bepoor. Eventually, when no changes are performed, the outputwill be refined until the maximum quality is obtained.

3.6.1. Reconstruction in Image Space

Walter et al. [38,39] proposed a mechanism based onpoint reprojection and progressive, adaptive sampling of the

illumination to provide fast feedback for the interactive useof a pixel or ray based renderer (e.g. ray tracing or anyother special case of bi-directional path tracing). Images aregenerated by reprojecting samples previously stored in theso-called Render Cache. A depth culling heuristic is usedto remove a large number of points that should have beenoccluded. Linear interpolation between reprojected pointsand filtering on 3 × 3 neighborhood are used to fill in theremaining gaps in the image. An additional filtering pass andthe use of predictive sampling reduce the amount of visualartifacts in intermediate images.

Samples in the Render Cache age at a constant rate,and are progressively replaced in the cache by newer ones.New samples are requested in areas most likely to change.A priority image is generated, based on the samples’ ageand the number of neighboring samples used during theinterpolation step (in order to give higher priority to imageregions which have been generated using a lower densityof samples from the cache in the previous frame). Anerror diffusion dithering algorithm is used to transformthe greyscale priority image into a binary image, encodingwhether a sample for a given pixel is to be generated or not.This dithering ensures that the sample distribution is uniformin similar priority regions.

Several heuristics are used to identify samples thatare likely to be invalid. For instance, the authors advisepremature aging of those in the neighborhood of a pixelthat has suddenly changed color. However, this color changeheuristic can be falsely triggered by Monte Carlo noise.In this case, when using a stochastic global illuminationmethod, it is therefore necessary to provide an estimate ofthe noise floor that is to be expected from the samplingprocess.

When the rendered sequence of images offers enough timecoherence the quality of intermediate images is sufficient togive the user a clear idea of what is happening. However,the artifacts caused by the progressive update of objects orshadow positions may sometimes be distracting. Moreover,when the desired image is rapidly changing (e.g. when thecamera is quickly moving, or when stepping through a wall),most samples collected from the previous frame are invalid,and the display needs some time to be correctly updated. Dueto the fact that the samples are requested according to thelast frame computed, some screen areas cannot be coveredby samples, for certain camera motions (e.g. backward). Asa result, the intermediate reconstructed images will not coverthe whole screen.

As the illumination samples can be computedasynchronously, multiple rendering processes can beused in parallel. Obviously, as more samples are providedto build the image, the aforementioned artifacts areconsequently reduced. The authors also show that animplementation carefully optimized for current industry


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standard processors, paying particular attention to memoryaccess coherence, makes the performance scalable withhigher display resolutions. Frame rates of about 12 fps. arereported on a single 1.7 GHz processor for ray tracing witha 512 × 512 resolution.

The performance of the Render Cache is linearly depen-dent on the resolution of the display. As noted previously,when the sample density is not sufficient, the reconstructedintermediate images may not cover the whole screen, whichwill cause holes in the images. As a consequence, renderinghigher resolution images requires more samples to be com-puted if such holes are to be avoided.

3.6.2. Reconstruction in Object Space

In order to avoid the holes that can be witnessed with pointbased approaches such as the Render Cache, reconstructionin object space, using a polygonal mesh and classicalrasterising hardware to display it, seems to be a reasonablealternative.

In order to allow interaction with objects in the scene,and at the same time ensure that the objects’ geometricrepresentation is always correct, Tole et al. [40] proposeda new object-space caching structure: the Shading Cache.As in the Render Cache approach, high quality illuminationsamples are provided by a separate asynchronous process.Those samples are used to progressively update theshading of patch vertices in a 3D mesh. As this polygonalmesh is displayed using the graphic pipeline, interactivemodification of the scene geometry is always possible inreal time. However, the shading of surfaces may be incorrectfor intermediate images, and is progressively updated totake into account the objects’ new configuration.

This algorithm starts from an unrefined mesh, all geo-metric primitives in the scene formed of one single patch.This mesh is progressively refined, either to provide a betterquality for the current camera and objects position, or to takeinto account modifications in the scene. As in the RenderCache algorithm, updates are made according to new illumi-nation samples that are requested based on a priority image.In the Shading Cache algorithm, this priority image consistsof the difference between the maximum and minimum tone-mapped color of each patch in the current view. However, inthis case, patches, instead of points in image space, are tobe selected for update. Therefore, here the sample selectioncannot rely on the dithering of a greyscale image. Instead,greyscale values are normalized and used as probabilities toselect a given patch in the current view for update. A floodfilling algorithm is provided to ensure that small patcheswith high priority, such as sharp shadow borders, have fairenough chances to be selected.

Selected patches can be updated either by re-evaluatingtheir vertices, or by subdividing them in four and evaluatingthe children’s vertices. Subdivision of patches is possible

until they reach sub-pixel size. To ensure that the size of themesh remains reasonable, patches that have not contributedto the images for several frames, because they moved out ofthe field of view or their projected area has become smallerthan a pixel, are removed. Double buffering is used to avoidconcurrent accesses to the vertex array by the progressiverefinement loop and the display process.

To take into account the potentially changing view-dependent appearance of specular surfaces, aging is usedto progressively recompute their illumination. The agingspeed of surfaces is attributed using a perceptually uniformgloss scale [41]. As a consequence, patches whose shadingchanges more rapidly with the viewpoint are updated moreoften.

In order to provide fast updates of the illumination, as inGranier and Drettakis’ unified algorithm (see Section 3.2), amaximum subdivision depth has to be fixed during object orcamera motion. When the motion stops, refinement can becontinued up to pixel level.

As the shading samples are computed by separate, inde-pendent processes, this algorithm can easily benefit frommultiprocessing. On a setup consisting of nine dual 1.7 GHzPentium IV, for scenes composed of up to 10 000 primi-tives, updating the geometry can be done at 40–60 fps., whilethe illumination update to maximum quality may require10–20 s. Performance comparisons provided by the authorsshow that the Shading Cache requires ten times less sampleson average than the Render Cache to effectively render animage. This allows much faster updates of illumination inresponse to user changes, when a very high-quality, slowsample renderer is used.

3.7. Other High-Quality Display Methods

In the previous section we discussed a number of solutionswhich make possible efficient image display with glossy andspecular effects through progressive refinement of sparselydistributed samples in image space (Section 3.6.1) or objectspace (Section 3.6.2). An interesting alternative is offered bythe use of rapidly developing graphics hardware (note thatin Section 3.3 we also discuss the use of graphics hardwarebut in a different context of the lighting computation forradiosity algorithms). Thanks to the speed and flexibility ofcurrent graphic cards, many of those effects can be producedalmost instantly without the need of progressive refinement.

In this section we only briefly overview hardware-supported techniques for the rendering of glossy andspecular effects. More elaborate discussion of thosetechniques can be found in a specialized survey on similartopics presented by Heidrich [1] and in recent books onreal-time techniques [42,43].

Pioneering work on the rendering of mirror reflectionsfor planar surfaces using multipass pipeline rendering was


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done by Diefenbach [44,45] and Wojdala et al. [46].In their methods every mirror plane requires a separaterendering pass, using the mirror reflection of the realobserver parameters as the camera position. Higher levelsof reflections, i.e. a mirror reflected in another mirrorand so on, can be easily computed by recursion of thebasic algorithm. Handling light refraction is more complexbecause it involves a non-linear transformation, whichcannot be directly implemented on graphics hardware.However, Snell’s law can be well approximated for paraxialrays (small incidence angles) using the tangent law [45],which results in a linear transform.

For handling curved surfaces, a better performance canbe achieved using the standard environment mapping tech-nique, for which hardware implementation is now availableon most graphics cards. Complex reflectance models can berendered using this technique through their decompositioninto simpler parts which can be evaluated in multipass ren-dering with alpha blending [47]. Using prefiltered environ-ment maps [47–49] a complete global illumination of an ob-ject in the scene can be rendered with realtime performance.Each entry of the prefiltered map contains an outgoing ra-diance value in a given direction, which is precomputed asa BRDF weighted integral of irradiance incoming from thewhole scene.

For dynamic environments it is essential to update pre-filtered maps at interactive speed. Kautz et al. [50] use hard-ware accelerated convolution operations to efficiently filterthe map for the Phong reflectance model, which is feasi-ble due to radial symmetries inherent for this model. Thecostly convolution operation can be avoided based on pre-filtering technique proposed by Ramamoorthi and Hanrahan[51]. They assumed that the irradiance function is smoothand continuous, so that only 9 spherical harmonics coeffi-cients are enough to give accurate approximation of irradi-ance for diffusely reflecting surfaces. Those coefficients canbe computed in linear time with respect to the number ofpixels in the map. It is therefore possible to prefilter envi-ronment maps for diffuse objects on the fly.

All these techniques properly consider only illuminationby distant objects. Recently, Sloan et al. [52] introduceda transfer function, which maps incoming radiance tooutgoing radiance and can be precomputed for anyrigid object. The function can be used to render self-interreflection and self-shadowing effects on-the-fly for oneobject illuminated by dynamic, local, and low frequencylighting. The self-transfer function can also be generalizedto a neighborhood-transfer function in order to find thelocal influence of a given object on the illumination ofneighboring objects.

For rendering of glossy effects, interactive ray tracing[30,31] is a viable solution as well. As we discussed inSection 3.5 ray tracing can be an algorithm of choice

especially for complex scenes. Also, ray tracing is veryflexible in handling various types of geometry and datastructures for storing lighting information.

4. Offline methods

In the previous section we discussed interactive global il-lumination and rendering solutions, which usually trade theimage quality for the response speed. In this section we focuson offline solutions used in the final production of high qual-ity animations. Such high quality is required in applicationssuch as entertainment, advertisement, education, engineer-ing, architecture, urban planning, and many others. Addingglobal illumination effects in the aforementioned applica-tions greatly improves their capacity to reproduce reality andtherefore their credibility.

A vast majority of the algorithms reviewed in this sectionrely on the a priori knowledge of all modifications in thescene to ensure an uniform image quality, both spatially andtemporally. The main objective of those methods is to exploitthe spatio-temporal coherence of illumination distributionin the subsequent animation frames in order to improve thecomputation efficiency and reduce the temporal aliasing.

Again, as in Section 3 two separate problems can bedistinguished:

• First, the actual simulation of global illumination has tobe performed according to the animation script, whichdescribes all changes in the scene as a function of time.Relevant methods will be reviewed in Sections 4.1–4.5. We start with the offline solutions evolving fromdeterministic (Section 4.1) and stochastic (Section 4.2)radiosity algorithms, extended into the time domain.We discuss a method to reduce flickering when usingthe photon mapping algorithm [19,53] for animations(Section 4.3). We then proceed to a review of the image-based framework for lighting computation in animations(Section 4.4). Finally, we discuss some applications ofhuman perception models to improve the efficiency ofdensity estimation and irradiance cache computationsfor dynamic environments (Section 4.5).

• Second, the results of the global illumination compu-tation also have to be carefully displayed to obtain thehigh quality animation frames. Basically all algorithmsdiscussed in Sections 4.1–4.5 have inherent problems tostore the results of the global illumination computationwith a spatial resolution that is suitable for their immedi-ate display for an arbitrary camera view. The algorithmof choice to improve the spatial resolution of lightingdetails for a given camera view is the so-called finalgathering. During the final gathering stage, the global il-lumination computation is not explicitly performed, butrather the results of such a computation at selected sam-ple points in object space are summed. Nevertheless, for


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Figure 5: Example stills from a 500 frames long animation computed using space-time hierarchical Radiosity. The scenewas built using 35 000 input surfaces. Rendering was approximately 20 times faster than a frame per frame computation, butrequired 7 times more memory.

the sake of completeness of this report, we review inSection 4.6 some final gathering solutions. However, welimit ourselves only to those solutions which exploit thetemporal coherence between frames.

4.1. Offline Radiosity Algorithms for Animations

As recalled previously in Section 3.1, finite element meth-ods, such as the radiosity methods, are best suited to thecomputation of view independent global illumination solu-tions when all surfaces are considered diffuse. Please referto Section 3.1 for a brief reminder of the principle of thosemethods.

The first attempts at efficiently using radiosity methodsto compute high-quality animations focused on adaptingthe full-matrix and progressive radiosity algorithm to takeadvantage of time coherence. Baum et al. [54] proposedto project the bounding box of the moving objects onhemicubes to determine the form-factors that need to beupdated. More recently, Pueyo et al. [55] proposed to followthe principle of cell animations and compute every frameas the sum of a fixed image and a frame-dependent one.As a consequence, this method requires that the cameraposition should be fixed. Since these methods are basedon full-matrix or progressive radiosity, they are somewhatinefficient when compared to hierarchical algorithms, andscale poorly when the complexity of the produced meshexceeds several thousand patches.

The space-time hierarchical radiosity method is aimed atcomputing the radiosity function for every point of a diffusescene composed of rigid objects, all potentially moving(including the primary light sources), for every possibletime of a given finite time interval. Like the dynamichierarchical radiosity and the line-space hierarchy, it is basedon hierarchical radiosity (see Section 3.1).

However, instead of solving a sequence of equations(one for each frame of the animation), this algorithmproposes to solve one integral equation that models all light

exchanges between the surfaces of the scene during thewhole animation interval. Therefore, instead of updating thehierarchical spatial mesh on a frame-by-frame basis, thismethod builds a mixed spatial and temporal mesh whichdescribes the variation of radiosity on all surfaces, duringall the animation. As in the classical hierarchical radiosity,this refinement is performed as a side effect of the linkrefinement procedure.

As this method is a straightforward extension of theclassical hierarchical radiosity algorithm, it can benefit frommost of the additions that have been proposed throughthe last decade. For instance, it has been shown [56]that the space-time hierarchical radiosity can successfullyuse a clustering approach, and therefore deal with scenescomposed of tens of thousands of polygons, and waveletsbasis to improve the temporal continuity of the solutions andreduce the overall weight of the mesh.

However, this similarity also causes this method to sufferfrom the same problem as the classical hierarchical radiosityalgorithm. In particular, meshing artifacts become obvious,both in the spatial and temporal dimensions, if a properreconstruction pass or final gathering is not applied. Usingelements with radiosity varying linearly over time greatlyimproves the solution’s temporal continuity [56].

The speedup can vary from 2 (for a simple 3 s. animationin a scene composed of less than 100 polygons) to almost20 (for the 24 s. animation shown in Figure 5), whilemoderately complex scenes (about 104 input surfaces) willlead to a typical acceleration factor of 6 to 8. However,the memory used to compute the animation (compared tothe memory needed for one frame) will be multiplied by afactor varying typically between 7 to 12. Clearly, a method toreduce the RAM requirements (e.g. allowing to cache largeunused portions of the mesh on disk) is called for [57].


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4.2. Multi-Frame Lighting Method

This algorithm, presented by Besuievsky et al. [58,59], alsoaims at computing view independent radiosity solutionsfor diffuse animated scenes, where all motions are knownin advance. All objects, including light sources, can beanimated.

It is a finite-element method that uses Monte Carloestimates of the diffuse light transport [60]. Global lines arelines that are cast independently from surface positions, witha uniform density all over the scene. They can be generatede.g. by joining random pairs of points taken in a spherebounding the whole scene.

The multi-frame lighting method benefits from timecoherence by using the same set of global lines for the wholeanimation. Global lines are tested for intersection onceagainst all static objects, and against every frame position ofthe dynamic objects. Visibility lists are built for each globalline. Static and dynamic lists are then merged and sorted forevery frame, and used to perform the light transfer [60].

As a result, the longer the animation, and the higher theratio of static surfaces versus the total number of surfaces,the better this method performs [59]. The algorithm stores inmemory the radiosities for all mesh elements and all frames.Therefore the memory consumption of the algorithm growsquickly, whereas the increase of the speedup ratio withthe length of the animation is bounded. The authors reportthat a good compromise between memory consumption andspeedup can be obtained by splitting the animations insegments of about 60 frames. In this case, typical speedupreported, when compared to a frame-by-frame computation,ranges from 7 to 25. Solutions for a possible distributedprocessing version of this algorithm are also presented [59],though they have not been actually implemented.

A major limitation of this method is that it does not allowadaptive meshing. As a consequence, the same mesh is usedthrough all the animation. High spatial frequency variationsof the radiosity function (e.g. sharp shadow boundaries)are poorly reconstructed. If a very dense mesh is used,the overall memory consumption of the algorithm and thecomputing time will raise dramatically as more lines areneeded to avoid noise artifacts. For static images, this issuehas been addressed using hierarchical approaches [61,62].Such hierarchical methods have not been extended to thecase of animated scenes yet.

4.3. Photon Mapping

The photon mapping algorithm proposed by Jensen [19,53]is commonly used for the global illumination computationboth in academia as well as in industry. The method workswell even for complex environments and all possible lightpaths can be easily simulated. In particular, the method

outperforms all other techniques in high-quality renderingof caustic effects. The method consists of two stages:

(1) lighting simulation through photon tracing,

(2) rendering with recomputation of direct lighting andview-dependent specular effects.

In the first stage of this method photons are traced fromlight sources toward the scene and photon hit points are reg-istered in a kd-tree structure, the so-called photon map. Themap is used in the rendering stage for lighting reconstructionusing nearest neighbor density estimation [63]. Soft indirectlighting is reconstructed using the irradiance cache [64,65]and final gathering [53,66,67] techniques. Such an indirectreconstruction is required because a direct rendering of dif-fuse illumination based on the density estimation of photonsleads to poor image quality [53]. Irradiance caching and finalgathering techniques for animations are discussed in Sec-tion 4.6.

While the density estimation and irradiance cachingintroduce some bias into the reconstructed lighting functionthe resulting images are of very high quality. In particular,the stochastic noise which is a common problem for manyalgorithms based on Monte Carlo integration is effectivelyreduced below a perceivable level.

When using the photon map algorithm to render anima-tions, the first stage is so fast (when compared to the light-ing reconstruction pass) that photons can be easily recom-puted for each frame. Attempts at reusing photons for severalframes were done in order to perform motion blur [68] andto improve the temporal coherence of the irradiance cache[69].

To reduce the flickering of the lighting reconstructed fromthe photon map the same random numbers are used forthe generation of the photon paths [70]. Since in dynamicenvironments the photon paths can change from frameto frame a random number sequence must be associatedwith each photon path independently from other photons.This simple approach reduces the variance of lightingreconstructed directly from photon maps (e.g. caustics) bya factor of 10 or more [70]. The photon temporal coherenceis less important for slowly varying indirect lighting.

4.4. Image-Based Method Handling DynamicEnvironments

Frame-to-frame changes in lighting are often slow, and forthe indirect lighting, usually quite smooth as well. Based onthis observation, the global illumination can be computedonly for a limited number of images, and then reconstructedusing those images for an arbitrary camera position and anarbitrary moment in time. A significant step toward thisgoal was done by Nimeroff et al. [71] who proposed apowerful range-image based framework for handling global


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illumination in dynamic environments. In this frameworkimages for arbitrary camera locations can be interpolatedwithin a “view-space” spanned by the base range images.Nimeroff et al. discuss two major problems that must beaddressed in this framework:

(1) Where to place the camera in order to cover the wholescene and ensure the highest possible quality of theresulting images?

(2) How to choose the snapshots of global illumination inthe temporal domain to capture its changes in dynamicenvironments?

For the initial step, Nimeroff et al. propose to place thekeyframe cameras at the corners of the “view-space” and tocompute the corresponding base images. For simplicity only2D placement of the camera in the scene is investigated,and the vertical positioning of camera is ignored. Thequality is evaluated by computing the percentage of pixelswhose item buffer identifiers are identical for all theseimages. If the percentage is below a predefined thresholdvalue, the space is subdivided and additional keyframecameras are inserted. This quality criterion captures wellthe occlusion relations between objects in the scene and isswiftly computed using graphics hardware. However, thiscriterion might be unreliable for several global illuminationeffects. For example, for scenes with mirrors and transparentobjects the distortion of reflected/refracted patterns is notestimated, while it can be quite significant in the derivedimages due to interpolation. Also, the distortion of texturepatterns is ignored.

Direct and indirect lighting are handled asynchronouslyand are sparsely sampled in time. To reconstruct the globalillumination, they are interpolated between independentlyselected base images. The time steps for recomputing thelighting are found by recursive subdivision. At each timestep the lighting is calculated for a number of vertices usingwavelet radiosity. Then the differences between the corre-sponding vertices are computed. If differences larger thanan assumed threshold are found for a certain percentage ofvertices the time sequence is subdivided. Since such subdivi-sions are decided independently for direct and indirect light-ing, it may happen that significant differences in the indirectlighting cause a subdivision, while those differences mightbe washed out in the resulting images by the direct lighting[72]. As a result, the criterion driving the time sequence sub-division might be too conservative. Also, tone reproduction[73] is not applied to the resulting lighting. This is difficultin the view-independent framework proposed by Nimeroffet al. because the eye adaptation conditions cannot be es-tablished. Both effects can affect the visibility of changes inlighting.

The interpolation of lighting between two time stepsis an important feature of Nimeroff’s framework. Thecontinuity of changes in the lighting distribution between

time steps eliminates popping effects, which may resultfrom switching between two distinct lighting distributionsas in [74] (refer to Section 4.5). However, the accuracy oflighting reconstruction fluctuates between frames, achievingthe highest level for the keyframes, and then graduallydecreasing for inbetween frames.

4.5. Perception-Guided Animation Rendering

Nimeroff et al. [71] proposed a simple energy-based metricto guide the keyframe placement in order to reduce the errorof interpolated lighting for inbetween frames. However, itis not clear whether for a given error threshold the lightingdistribution errors are perceivable or not. Ideally, someperception-based animation quality metrics are required thatcan decide whether the errors introduced by exploiting thetemporal coherence are below the sensitivity level of humanobservers. Such error metrics are common in digital videocompression and broadcasting applications (refer to a surveyof such metrics resulting from the research performed by theVideo Quality Experts Group [75]).

Myszkowski et al. [76] proposed a perception-basedspatiotemporal animation quality metric (AQM) whichwas designed specifically for handling synthetic animationsequences. We briefly overview the most importantcharacteristics of the AQM and we discuss its applicationto guide the global illumination computation for dynamicenvironments [77] in Section 4.5.1.

The human visual system model used in the AQM can beconsidered as a quite advanced one, however, it is limited tothe modeling of the early stages (from the retina and to thevisual cortex V1) of the visual path. Since gains by addingfurther extensions to such early vision models are rathersmall [78], some attempts of using higher level perceptualand cognitive elements have been introduced in the contextof animation. Yee et al. [74] showed successful applicationsof visual attention models to improve the efficiency of globalillumination and rendering computation. We discuss thissolution in Section 4.5.2.

4.5.1. Animation Quality Metric

The AQM is an objective metric of image quality, whichtakes as input two animation frames and generates a map ofperceivable differences between those frames. Based on themap it is possible to predict how strong and where on screenthe differences between frames can be seen. The centralpart of the AQM is a model for the spatiovelocity contrastsensitivity function (CSF), which specifies the detectionthreshold for a stimulus as a function of its spatial andtemporal frequencies [79]. Also, visual masking is modeled,which affects the detection threshold of a stimulus as afunction of the interfering background stimulus which hassimilar spatial frequency characteristic [80]. The AQMmodels temporal and spatial mechanisms (channels), which


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are used to represent the visual information at various scalesand orientations, in a similar way as the primary visualcortex does [81].

Myszkowski et al. used the AQM to decide upon thecomputation stopping condition for the density estimationphoton tracing (DEPT) algorithm [27]. The DEPT is similarto other stochastic solutions in which photons are tracedfrom light sources towards surfaces in the scene. The energycarried by every photon is deposited at the hit point locationson those surfaces [63,82,83]. A simple photon bucketing ona dense triangular mesh is performed, and every photon isdiscarded immediately after its energy is distributed to themesh vertices. Efficient object space filtering substantiallyreduces visible noise. Excessive smoothing of the lightingfunction can be avoided by adaptively controlling the localfilter support, which is based on stochastically derivedestimates of the local illumination error [27,83].

Myszkowski et al. extend the DEPT algorithm to handleanimated objects, and the proposed extensions could beeasily applied to other stochastic algorithms such as photonmapping [19]. Direct lighting is assumed to be computedfor each frame. Initially, the indirect lighting function issparsely sampled in space for all frames (not just for fixedkeyframes [71,74]) within a given animation segment. Then,based on the obtained results, a decision is made whetherthe segment can be expanded/contracted in the temporaldomain. Since the validity of samples may depend on theparticular region in the scene for which indirect lightingconditions change more rapidly, different segment lengthsare chosen locally for each mesh element (used to storephoton hits), based on the variations of the lighting function.Energy-based statistical measures of such local variationsare used to calculate the number of preceding and followingframes for which samples can be safely used for a givenregion. More samples are generated if the quality of theframes obtained for a given segment length is not sufficient.

The perception-based AQM is used to choose an averagenumber of photons per frame for each segment to preventperceivable degradation of animation quality. The twoanimation frames, which are required as the AQM input, areobtained by splitting all temporally processed photons intotwo halves and generating the corresponding frames I1(K )

and I2(K ). Since the AQM test is costly it is performed onlyfor the central frames K in each animation segment. Thesame mesh is used for the indirect lighting reconstructionin I1(K ) and I2(K ), so the solution bias is the same forboth compared frames. Effectively the AQM is used tomeasure the perceivable differences between frames I1(K )

and I2(K ), which result from the stochastic noise. TheAQM provides a conservative stopping condition for photontracing when the noise falls below the sensitivity level of thehuman observer. Tracing more photons cannot improve theperceived quality of the indirect lighting reconstruction dueto limitations in the spatial mesh resolution.

As the final step of the photon-based lighting reconstruc-tion, spatial filtering [27] is performed for those scene re-gions in which a sufficient number of samples cannot becollected in the temporal domain. For the final renderingthe indirect lighting is reconstructed using the techniquesaforementioned, while specular effects and direct lightingare computed for every frame separately by ray tracing.

In the algorithm proposed by Myszkowski et al. sparsesampling of indirect lighting is performed for every frame,and the final lighting reconstruction is based on the pro-cessing of lighting distributions for a number of subsequentframes placed along the animation path. Thus, at each mo-ment of time a similar level of accuracy of indirect lightingcan be obtained. Such a framework is less prone to per-ceivable errors, and the probability of overlooking some im-portant lighting events between keyframes is substantiallyreduced. The reported speedup of indirect lighting compu-tation is over 20 times for tested scenes [77] and the re-sulting animation quality is much better than in the tradi-tional frame-by-frame approach. While only scenes com-posed of less than 100 000 triangles have been tested, a sim-ilar speedup can be expected for more complex scenes be-cause collecting photons in the temporal domain is alwayscheaper than shooting them from scratch for each frame.

The main drawback of this algorithm is the limited accu-racy of indirect lighting reconstruction, which is imposed bythe spatial resolution of the mesh used for collecting pho-tons. Obviously, the mesh resolution can be set arbitrarilyfine and more photons can be traced, however, some localadaptation of the mesh density driven by the lighting distri-bution would be far more efficient. For example, it is verydifficult to obtain high quality caustics using the algorithmdeveloped by Myszkowski et al. .

Recently, a plug-in for the animation package 3D StudioMax was developed using a similar approach. The maindifference is that in the original algorithm, photons arecollected from both previous and following frames, whereasthe new approach only considers photons collected fromframes preceding the current one. Also, the spatio-temporalprocessing of photons is improved by applying an adaptivenearest neighbors algorithm, which operates both in thespace and time domains. Figure 6 shows example animationframes obtained using the plug-in with and without thetemporal photon processing for the same number of tracedphotons per frame. The differences in quality are even morepronounced in the context of animations, when additionallyflickering effects can be seen in the case shown in Figure 6b.

4.5.2. Visual Attention Modeling

In this section we discuss a technique which uses visualattention modeling at the stage of lighting simulation toimprove the computation performance. A basic idea is toreinforce the computation in those image regions that attractmore attention of the observer.


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(a) (b)

Figure 6: Example animation frames (a) with and (b) without temporal processing for about 80 000 photons per frame. Ananimation segment length of 31 frames was considered for the temporal photon processing. The average time of the indirectlighting computation per frame was less than 3 s.

(a) (b)

Figure 7: Spatiotemporal error tolerance map processing. (a) An input frame with dynamic objects rendered for a movingcamera and (b) the corresponding spatiotemporal error tolerance map obtained using the spatiovelocity CSF processing.Brighter areas on the map denote areas where less effort should be spent in computing the lighting solution. (Images courtesyof Hector Yee, Sumant Pattanaik, and Donald Greenberg.)

Yee et al. [74] proposes an interesting application of avisual attention model to improve the efficiency of indirectlighting computations in the RADIANCE system [84] fordynamic environments. A saliency map of the human visualsystem sensitivity based on the visual attention model[85] and spatiovelocity CSF [76,79] is created (Figure 7shows an example of the spatiotemporal error tolerancemap resulting from the spatiovelocity CSF processing fora selected animation frame). The saliency map (refer toFigure 8a) is used to control the irradiance caching forsecondary lighting in the RADIANCE system on a per pixelbasis. For less salient image regions greater errors can betolerated, and the indirect lighting can be interpolated for alarger neighborhood. This makes caching more efficient atthe expense of blurring details in the lighting distribution.The reported speedup of irradiance caching falls into therange 3–9 times.

Further speedup is obtained by computing the indirectlighting only for selected keyframes and re-using theobtained lighting for the remaining inbetween frames.Interpolation of indirect lighting between the keyframes isnot performed and the same number of inbetween frames(between each pair of keyframes) is always used. Sincethere is no verification of the validity of applying the samekeyframe lighting to the inbetween frames, some poppingeffects due to switching the lighting between keyframes canbe perceived. To reduce this effect, Yee et al. sampled theindirect lighting more densely, e.g. every 10 frames.

The technique proposed by Yee et al. significantlyimproves the performance of the RADIANCE system foranimation rendering applications. However, variability inthe selection of the regions of interest (ROI) for differentobservers, or even for the same observer from session tosession, can lead to some degradation of the animation


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(a) (b)

Figure 8: Example saliency map (a) computed using the Itti model [85] for an animation frame shown in (b).

quality. This is the case for those image regions thatwere not considered as important attractors of the visualattention in the saliency map. Yee et al. reports that suchdegradations of quality could be perceived when the sameanimation sequence is viewed more than once by the sameobserver. For those applications which require high-qualityanimations, possibly viewed many times by a large numberof observers, the approach proposed by Yee et al. mightnot be suitable. Yee et al. also ignore visual maskingwhich plays an important role in hiding imperfections ofreconstructed lighting [80].

4.6. High-Quality Display by Final Gathering Methods

Most of the mesh-based and photon mapping offline meth-ods generally require a second pass to obtain high-qualityimages from the solution they computed. This second pass,when operating on a frame-by-frame basis, proves signifi-cantly more expensive than the first one. The algorithm ofchoice for the final high-quality rendering is the so-calledfinal gathering [5,66,67,86]. Usually the direct lighting isexplicitly computed for each pixel, and the indirect lightingis obtained through the integration of incoming radiances,which is very costly.

Those costs can be reduced by using the irradiance cachedata structures [64,65] to store irradiance samples sparselyin object space. The cached values are used to interpolatethe indirect lighting for each pixel and are computed lazily.The irradiance cache technique efficiently removes shadingartifacts which are very difficult to avoid if the indirectlighting is directly reconstructed based on the radiosity meshor the photon maps. Note that irradiance caching may causepopping artifacts for dynamic scenes due to changes incached lighting as well as changes of in the cache locationsin object space [69].

However, the price to be paid for this high quality lightingreconstruction is long computation times, which are mostlycaused by the irradiance integration that is repeated formany sample points in the scene. More efficient versionsof final gathering have been recently proposed specificallyfor hierarchical radiosity with clustering [87,88]. All thesefinal gathering approaches ignore temporal processing andtherefore are suitable only for the efficient rendering ofwalkthrough animations in static environments.

Recently, Martin et al. [89] proposed a final gatheringalgorithm for animated hierarchical radiosity. The temporalcoherence in the radiosity solution is obtained using the line-space hierarchy [12,14,22], which is designed to identifyefficiently links affected by changes in the scene and redis-tributing the lighting energy for the current scene configura-tion (we review the related techniques in Section 3.1).

Because of the final gathering step only a coarse globalradiosity solution [67] is computed. The temporal changesin the lighting are updated by comparing the previousand current radiosity solutions. The radiosity solution forvisible surfaces is stored in a hierarchical tree of texturesrepresenting the space-time illumination. Therefore, for eachvisible surface patch a texture movie is created and displayedduring rendering in a given time interval.

The resolution of textures is adaptively chosen so thatat least one texel stores lighting information for each pixelin the final frame. Martin et al. found that usually aroundten times more texels than pixels are sufficient to obtainhigh quality final frames. The texture size is upper boundedand scene independent because the textures are maintained(resp. are newly created) only for the surfaces that remainvisible (resp. just became visible) in the current frame,and are destroyed immediately when those surfaces becomeinvisible. The texel lighting is computed during the gathering


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step using the hierarchical radiosity links. They are classifiedas good if the gathered lighting error is within given bounds,and bad otherwise. For good links a final gather step is notrequired, and resulting lighting is accumulated in a textureusing linear interpolation within a given patch. For eachshooter polygon associated with a bad link the graphicshardware is used to estimate the visibility of texels in areceiver patch using the projective shadows technique. Inthe temporal domain bad links are classified as static ordynamic. The costly visibility computation is performedonce for a given time interval for static links, and is repeatedfor each frame for dynamic links.

The final gathering method proposed by Martin et al.leads to significant rendering speedup (1.7–7 times in theexamples given by the authors). However, the method sharestypical drawbacks of hierarchical radiosity solutions such aspoor handling of non-Lambertian surfaces and significantstorage costs required by the link data structures. Those costsare even more significant in the presented solution becausethe history of links is also stored, e.g. links are not deletedwhen refined for possible reuse in different time intervals.Also, in Martin et al. ’s implementation surface clustering isnot supported, which increases the quantity of stored linkseven further.

5. Summary and Conclusion

In this section we present a summary of algorithms discussedin this report in the form of concise Tables 1 and 2. Weintentionally omit some of the algorithms (often pioneeringones that we reviewed for the sake of report completeness)if a more recent algorithm uses a similar approach, withimproved results. As in the remainder of this report, wedistinguish between interactive and high-quality offlineglobal illumination algorithms.

The criteria we use for comparison within the two setsof method are quite similar, the only difference beingthe criterion chosen for measuring speed. For interactivemethods (Table 1), the frame rate achieved at a givenhardware platform is used as a measure of the algorithmefficiency. We provide the frame rate numbers and CPUcharacteristics as reported by the authors of respectivepublications. Note that those numbers can be misleadingwhen used for a direct comparison between the performanceof different algorithms since they were obtained for differentscenes and different levels of image quality. For offlinemethods (Table 2), we report the speedup in respect to anequivalent frame by frame computation. Again a precautionshould be taken when comparing the speedup factorsbetween the presented algorithms because they are allreported with respect to different base algorithms. Thus, allframe rate and speedup numbers presented in Tables 1 and 2should be merely considered as a quick reference to theperformance figures reported by the authors of respective

algorithms. Any definitive conclusions concerning thesealgorithms should not be drawn based merely on thenumbers.

As acknowledged earlier in this report, several newalgorithms aiming at computing global illumination inanimated scenes have been proposed in the past couple ofyears. Obviously, even if significant progresses have beenmade, neither a seamless, truly real time, nor a reliablehigh quality, artifact free global illumination algorithm hasbeen proposed. There is still room for improvement for thealgorithms we presented in this report, all of which have theirown set of strengths and weaknesses.

Often, the artifacts generated by these algorithms are sim-ilar to the one caused by their “static” counterparts. For ex-ample, almost all mesh-based methods we presented in thisreport suffer from meshing artifacts that cause aliasing andpoor shadow boundary reconstruction. Similarly, stochasticmethods suffer from noise both in the spatial and in the tem-poral dimensions. Some successful solutions to reduce tem-poral aliasing in the lighting distribution manifesting as pop-ping and flickering artifacts have been proposed, e.g. explicitphoton processing in the temporal domain [68,77], usingthe same random numbers or low discrepancy sequences foreach frame [32,70]. However, those solutions are usually lessefficient for quickly changing lighting conditions (e.g. mov-ing light sources) or highly dynamic environments in whichmany photon paths is changed from frame to frame. Also,those techniques have not been fully integrated with tech-niques combating other aspects of temporal aliasing causedby changes in the visibility and texturing [91,92].

The algorithms we presented in this report indeed achieveimpressive results. However, their ultimate objectives (real-time or affordable artifact-free global illumination for an-imated scenes) obviously have not been reached yet. Forexample, we think that further investigations will be worthpursuing for a better use of temporal coherence in order toreduce flickering artifacts in high quality global illumina-tion. For interactive design scenarios, new methods to pro-gressively add high frequency lighting details on request alsoseem to be called for.

Acknowledgements

We would like to thank the authors of discussed papers whoprovided us with images illustrating their work. Thanks alsoto all those who read early drafts of the paper - PhilippeBekaert, Katja Daubert, Jorg Haber, Vlastimil Havran, JanKautz, Annette Scheel, Philipp Slusallek, and Ingo Waldfor their helpful comments and suggestions. This work wassupported in part by the European Community within thescope of the RealReflect project IST-2001-34744 “Realtimevisualization of complex reflectance behavior in virtualprototyping” .


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Table 1: Comparison of interactive algorithms (refer to Section 3).

LightingEffectsHandled

Average SceneComplexity

Frame Rate Artifacts Additional notes

SPT Diffuse 105 Polygons 1 fps.(dual P41.7 GHz)

Meshing artifacts + Delayedillumination update (0.1 fps.)

Only point light sources

DRT All 105 Polygons 1.5 fps.(8 dualAthlon1800+)

Overestimated lighting nearphoton impact + Delayedillumination update (0.5 fps.)

Requires a PC cluster

UHA All 104 Primitives 0.25 fps.(P3 733 Mhz)

Meshing artifacts Requires a static solutionprecomputation

RC All 104 Polygons 0.5 fps.(dual P41.7 GHz)

Stale points + Holes in images Requires a couple of minutes toobtain full quality static images

SC All 104 Polygons 45 fps.(9 dual P41.7 GHz)

Meshing artifacts + Delayedillumination update (0.1 fps.)

Requires a PC cluster

Table 2: Comparison of offline algorithms (refer to Section 4).

LightingEffectsHandled

Average SceneComplexity

Speedup(average)

Artifacts Additional notes

STHR Diffuse 104 Polygons ×7 Meshing artifacts + Popping Very high memory requirements(up to 500 MB)

MFLM Diffuse 103 Polygons ×12 Blurred shadow boundaries

ISI All 104 Polygons ×10 Possible artifacts in texturing andspecular effects

May require many base imagesfor specular effects

TFPT Diffuse 104 Polygons ×20 Meshing artifacts Less popping than with a frameby frame computation

SSVA All 104 Polygons ×8 Popping Possible quality problems whensubmitted to different viewers

TPR Diffuse 102 Polygons ×5 Popping may be visible whenswitching texture precision

High memory requirements + Nosurface clustering

SPT: Selective Photon Tracing [26], Section 3.4DRT: Global Illumination based on

Distributed Ray Tracing [32], Section 3.5UHA: Unified Hierarchical Algorithm [21,22], Section 3.2RC: Render Cache [38,39], Section 3.6.1SC: Shading Cache [40], Section 3.6.2

STHR: Space-Time Hierarchical Radiosity [57,90], Section 4.1MFLM: Multi-Frame Lighting Method [59], Section 4.2ISI: Image Space Interpolation [71], Section 4.4TFPT: Temporally Filtered Particle Tracing [77], Section 4.5.1SSVA: Spatiotemporal Sensitivity and Visual Attention

driven Global Illumination [74], Section 4.5.2TPR: Two Pass Radiosity [89], Section 4.6


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