Visual Comput (2008) 24: 565–575DOI 10.1007/s00371-008-0237-9 O R I G I N A L A R T I C L E

Rui WangEwen Cheslack-PostavaRui WangDavid LuebkeQianyong ChenWei HuaQunsheng PengHujun Bao

Real-time editing and relightingof homogeneous translucent materials

Published online: 30 May 2008© Springer-Verlag 2008

Electronic supplementary materialThe online version of this article(doi:10.1007/s00371-008-0237-9) containssupplementary material, which is availableto authorized users.

R. Wang (�) · Q. ChenUMass Amherst,Amherst, MA 01003, USAruiwang@cs.umass.edu

R. Wang · W. Hua · Q. Peng · H. BaoZhejiang University,Hangzhou 310027, P.R. Chinarwang@cad.zju.edu.cn

E. Cheslack-PostavaStanford University,Stanford, CA 94305, USAewencp@cs.stanford.edu

D. LuebkeNVIDIA Corporation, Santa Clara,CA 95050, USAdave@luebke.us

Abstract Existing techniques forfast, high-quality rendering oftranslucent materials often fix BSS-RDF parameters at precomputationtime. We present a novel method foraccurate rendering and relighting oftranslucent materials that also enablesreal-time editing and manipulationof homogeneous diffuse BSSRDFs.We first apply PCA analysis ondiffuse multiple scattering to derivea compact basis set, consistingof only twelve 1D functions. Wediscovered that this small basis setis accurate enough to approximatea general diffuse scattering profile.For each basis, we then precomputelight transport data representingthe translucent transfer from a setof local illumination samples toeach rendered vertex. This localtransfer model allows our system tointegrate a variety of lighting modelsin a single framework, includingenvironment lighting, local area

lights, and point lights. To reducethe PRT data size, we compressboth the illumination and spatialdimensions using efficient nonlinearwavelets. To edit material propertiesin real-time, a user-defined diffuseBSSRDF is dynamically projectedonto our precomputed basis set, andis then multiplied with the translucenttransfer information on the fly. Usingour system, we demonstrate realistic,real-time translucent material editingand relighting effects under a var-iety of complex, dynamic lightingscenarios.

Keywords BSSRDF · Precomputedradiance transfer · PCA · Haarwavelets · Spatial compression

1 Introduction

Fast and accurate simulation of translucent appearance hasbecome an increasingly important topic in many graph-ics applications. At different scale levels, most real-worldmaterials exhibit translucency, caused by subsurface scat-tering of light. Early research in this field focused ondeveloping physically based subsurface scattering modelsusing illumination transport equations for participatingmedia [7, 11]. These models have been widely used intoday’s photorealistic visualization and cinematic render-

ing systems. Unfortunately, the translucent appearance de-sign process has typically been labor intensive and timeconsuming, primarily because the high computational costdemanded by these models prevents artists from receiv-ing interactive simulation feedback, even under simplifiedlighting conditions.

We present a novel technique for accurate renderingand relighting of translucent materials that also enablesreal-time editing and manipulation of material properties.Our system provides users with real-time feedback on howchanges to translucent material parameters would affect

566 R. Wang et al.

Fig. 1. These images demonstrate translucent material editing and are generated by our system in real-time

the appearance of final quality rendering. We assume staticscene models and focus on diffuse multiple scattering ef-fects in homogeneous translucent media using the dipoleapproximation model introduced by Jensen et al. [12].Figure 1 demonstrates our real-time rendering results withseveral different materials.

Our system builds on previous research in precom-puted radiance transfer (PRT) [16, 19]. PRT precomputesillumination data offline, then applies basis projectionmethods such as spherical harmonics or wavelets to reducethe datasets, which can then be used at run-time to permitinteractive rendering. Early PRT work fixes BRDFs at pre-computation time; recently, several real-time BRDF edit-ing systems have been presented [1, 21] that enable inter-active editing of arbitrary BRDFs under complex lighting.While allowing dynamic material changes, they usuallyrequire fixing the lighting and viewpoint, or perform atsubinteractive rates due to the large data size. Further-more, they all focus on opaque materials while translucentmaterial editing has received relatively little attention.

We address the translucent material editing problemby incorporating material samples at precomputation timeusing a data-driven basis set. We focus on diffuse mul-tiple scattering and adopt Jensen et al.’s BSSRDF modeldescribed in [12]. We begin by performing principal com-ponent analysis (PCA) on this scattering model and derivea compact basis set, consisting of only twelve 1D func-tions. We discovered that this small basis set is accurateenough to represent a general diffuse scattering profile.We then use PRT to precompute for each scattering basisthe translucent transfer from a set of surface illuminationsamples to every rendered vertex. To efficiently removedata redundancy, we exploit the large spatial coherencepresent in the precomputed data by using spatial nonlinearwavelet compression. Finally, the precomputation resultsare linearly combined at run-time to simulate realistic ren-dering under dynamic BSSRDFs. Our work makes thefollowing two contributions:

1) PCA analysis of diffuse multiple scattering. We are thefirst to perform a data-driven analysis on the diffusemultiple scattering model [12], and use PCA to derivea compact basis set.

2) Nonlinear wavelet spatial compression. We apply non-linear wavelets to compress the spatial data, achievingsuperior reconstruction performance. Furthermore, weuse the same algorithm on visibility data compression,permitting fast environment lighting with little over-head.

2 Related work

Real-time material editing. Opaque materials are often de-scribed by parametric BRDF functions, and can be easilyedited in real-time using standard GPU rendering assum-ing simple lighting models. A work by [3] developed anintuitive and general BRDF editing system called BRDF-Shop. The real-time BRDF editing systems built by Ben-Artzi et al. [1] allow for interactive editing of arbitraryBRDFs under complex environment lighting. However,their system requires fixed lighting and viewpoint. A re-lated system by Sun et al. [21] achieves the same goalbut performs at subinteractive rates and computes onlya limited range of BRDF samples.

Building a real-time editing system for translucentmaterials presents a greater challenge, as the simulationinvolves integrating illumination contributions from thescene model. Several existing techniques [4, 8, 13, 15, 18,24] render diffuse multiple scattering in real-time, but areeither restricted to simple geometry and lighting, or re-quire fixing BSSRDF parameters. A recent work by [5]applies sums of Gaussians for a multi-layered skin model,but does not yet support real-time editing of BSSRDF par-ameters. Our work is closely related to the work by Xuet al. [25]. However, while they apply a preselected poly-nomial basis to reduce the translucent transfer function,we perform data-driven reduction using a PCA-derivedbasis.

Precomputed radiance transfer. Our system builds on PRTtechniques [16, 19] that precompute light transport ef-fects and compress them using projection onto a basissuch as spherical harmonics (SH) or wavelets. With thecompressed dataset, the rendering computation at run-

Real-time editing and relighting of homogeneous translucent materials 567

time is significantly reduced and performed at real-timerates. Subsequent work extended PRT to handle chang-ing viewpoint [14, 23], local lighting [26], and deformablemodels [20]. Wang et al. [24] simulate all-frequencytranslucency effects including both single and diffuse mul-tiple scattering, but require fixed material parameters.

Our technique is similar in spirit to incorporating sur-face BRDFs in PRT, using a preselected or derived ma-terial basis. However, run-time projection of an arbitraryBRDF onto a basis set is very costly to compute, evenfor low-order approximations [17]. In contrast, we derivea compact BSSRDF basis set that consists of only twelve1D functions, thus the editing and projection of BSSRDFscan both perform at real-time rates.

Spatial compression of PRT. Previous work in spatialcompression schemes for PRT include clustered PCA(CPCA) [14, 18], clustered tensor approximation (CTA)[22], and 4D wavelets [2]. PCA-based approaches areusually very slow to precompute and prone to numericalstability issues. CPCA and CTA reduce the computationalcost by partitioning, but require nontrivial algorithms tomaximize the partition coherence and reduce boundaryartifacts.

Our system uses a simple spatial compression schemethat projects our transport data onto nonlinear wavelets de-fined in a parameterized spatial domain. Due to the speedand efficiency of the wavelet transform, we achieve fastprecomputation at less than 2 h for all test scenes, and3–4× speed up in relighting performance compared withno spatial compression. In addition, our scheme does notrequire data partitioning, thus is not subject to compres-sion boundary artifacts.

3 Algorithms and implementation

Review of BSSRDF. We use the diffuse BSSRDF modelintroduced by Jensen et al. [12], which assumes multiplescattering within a homogeneous medium. The materialproperties of such a medium are described by the absorp-tion coefficient σa, the scattering coefficient σs, and theextinction coefficient σt = σa +σs. Under spatially varyinglighting L(xi, ωi), the scattered radiance is computed by:

B(x, ωo) =∫∫

S(xi, ωi; x, ωo)L(xi, ωi)(ωo ·n)dωi d A

(1)

where ωi and ωo are the incident and viewing directions,B is the scattered radiance at point x in direction ωo, L isthe incident radiance at point xi in direction ωi , n is thesurface normal at point x, and S is the BSSRDF, definedas the sum of a single scattering term S(1) and a diffusemultiple scattering term Sd. The diffuse assumption comes

from the fact that multiple scattering tends to becomeisotropic due to the large number of scattering events. Thisis especially true for highly scattering materials such asmarble. For these materials, the multiple scattering com-ponent also dominates the total scattered radiance [10].Therefore the single scattering part S(1) can be ignored;and the multiple scattering Sd can be further defined as:

Sd(xi, ωi; x, ωo) = 1

πFt(η, ωi)Rd(‖xi − x‖)Ft(η, ωo) (2)

where Ft is the Fresnel transmittance at the interface,η is the relative index of refraction, and Rd is the diffusereflectance function approximated using a dipole sourcemodel as:

Rd(r) = α′4π

[zr

(σtr + 1

dr

)e−σtrdr

d2r

+zv

(σtr + 1

dv

)e−σtrdv

d2v

],

where σ ′s = (1 − g)σs and σ ′

t = σa +σ ′s are the reduced

scattering and extinction coefficients; α′ = σ ′s/σ

′t is the

reduced albedo; g is the mean cosine of the scatter-ing angle; σtr = √

3σaσ′t is the effective extinction co-

efficient; dr = √r2 + z2

r and dv = √r2 + z2

v are the dis-tances from an illumination point xi to the dipole source,with r = ‖x − xi‖ being the distance between xi and x,and zr = 1/σ ′

t and zv = zr(1 + 4A/3) being the dis-tances from x to the dipole source. Here A = (1 + Fdr)/(1− Fdr), and Fdr is a diffuse Fresnel term approximatedby Fdr = −1.440/η2 + 0.710/η+ 0.668 + 0.0636η. Forconvenience, we denote Rd in general as

Rd(r, σ) = Rd(r, σ ′s, σa), (3)

where σ represents the collection of all independent BSS-RDF parameters.

Equation 1 is expensive to compute as it involves in-tegrating the light transport from all illumination samples.To accelerate this computation, Jensen et al. [10] useda two-pass hierarchical integration approach. The key ideais to compute incident irradiance in a separated pass, thusmaking it possible to reuse illumination samples.

3.1 A PCA basis set for Rd

Note that in Eq. 2 the distance r = ‖x − xi‖ is a 1D vari-able and is a purely geometric term that can be pre-computed assuming static scene models; all other param-eters σ are dynamic and cannot be precomputed. Witha naive approach, we could attempt to sample all pos-sible BSSRDF parameters at precomputation time, butthat would lead to an impractical amount of precomputeddata. Instead, our goal is to seek a lower dimensional lin-ear subspace for Rd, and approximate it using a linear sum

568 R. Wang et al.

of basis functions:

Rd(r, σ) ≈K∑

k=1

bk(r)sk(σ). (4)

Here bk(r) is a set of orthogonal basis functions, each oneof which is a 1D function of r, and K is the total num-ber of approximation terms. The basis functions may bepreselected, but they can also be derived from standardfactorization techniques such as PCA. To do so, we sampleand discretize Rd into a matrix Rd, then apply a singu-lar value decomposition (SVD): Rd = USV ′ which resultsin an orthogonal left matrix U , a corresponding right ma-trix V, and a diagonal matrix S that represents the sin-gular values in order of importance. The column vectorsof the left matrix U naturally form an orthogonal basisset bk(r), and the column vectors of the right matrix Vrepresent the projection coefficients of all sampled BSS-RDFs.

The idea of seeking a linear basis for Rd is not new.Several other works have presented the same effortsusing preselected basis functions, such as polynomialsor Gaussian functions [5, 25]. By using a data-driven ap-proach, however, our method adaptively computes theoptimal common basis set for all sampled BSSRDFs ina least squares sense. In Sect. 4, we show that the first 12PCA basis functions suffice to accurately represent a gen-eral diffuse BSSRDF profile. The small size of the basisset allows us to dynamically project any user-specifiedBSSRDF onto the basis in real-time. Therefore it elim-inates the need to store the right matrix V of the SVDresult, as the basis coefficients sk(σ) of the actual BSS-RDF are being evaluated dynamically on the fly.

Implementation notes. To construct the sampled materialmatrix Rd, we discretize both r and σ parameters withinreasonable ranges. For the distance parameter r, we foundthrough experiments that 650 uniform samples within therange [0.0, 65.0] is sufficient to produce high-quality re-sults. Experiments with more samples or a wider range didnot produce significant improvements in our tests. The σparameters are sampled within a range of [0.0, 5.0] asdensely as memory constraints permit. These ranges arerepresentative of values found in measured datasets [12].

3.2 Precomputed multiple scattering transfer

We precompute multiple scattering light transport by in-corporating the BSSRDF basis derived from above. Thisstep is similar to how a BRDF basis is incorporated inPRT [14, 23]. Substituting Eq. 4 into Eqs. 2 and 1, the ren-dering equation becomes:

B(x, ωo) = 1

πFt(ωo)

∑k

sk(σ)

∫

A

E(xi) ·bk(r)d A, (5)

where E(xi) represents the total incident irradiance re-ceived at an illumination point xi :

E(xi) =∫

2π

L(xi, ωi)Ft(ωi)(ni ·ωi)dωi. (6)

This can be computed via any available illuminationmodel, such as GPU-based shadow mapping or PRT-basedenvironment lighting.

For convenience, we express Eq. 5 using matrix form:

B =∑

k

sk(σ)(Tk · E) =∑

k

sk(σ)vk (7)

where Tk is a precomputed transport matrix represent-ing bk(‖x − xi‖), the transfer from xi to x projected ontothe k-th BSSRDF basis, E is the illumination vector, andvk = Tk · E. The factor 1

πFt(ωo) is omitted as it is easily

computed in a shader. The matrix-vector multiplication isexpensive to compute but can be accelerated by projectingboth E and the rows of Tk onto wavelets:

vk = (Tk ·w′) · (w · E) = Twk · Ew (8)

where w is an orthonormal matrix representing waveletprojection, and w′ ·w = I; Tw

k and Ew represent thewavelet-transformed transfer matrix and illumination vec-tor. Efficient nonlinear compression of Tw

k is achieved byculling insignificant coefficients based on their magnitude.Note that the rows of Tw

k represent the illumination trans-fer dimension, while the columns represent the spatialdimension. Therefore this step applies nonlinear waveletcompression to the transfer dimension (transfer compres-sion), but leaves the spatial dimension intact.

We observe that after the transfer compression, ourdata still contain considerable coherence in the spatial do-main (i.e., vertices that are close to each other have similardata). We therefore apply a further wavelet projection inthe spatial domain of Tw

k , resulting in:

vk = w′ · (w · Tk ·w′) · (w · E) = w′ · (wTwk · Ew

). (9)

Using the linearity of wavelets, Eq. 9 can be combinedwith Eq. 7, giving:

B = w′ ·∑

k

sk(σ)(wTw

k · Ew)

(10)

where wTwk represents the precomputed transfer matrix

that has been doubly projected onto wavelets in both thetransfer and spatial dimensions. The leftmost multipli-cation by w′ represents the spatial reconstruction of thecolor, and is computed by a single inverse wavelet trans-form as the last step of rendering.

Transfer compression. We use a set of uniformly dis-tributed surface sample points as illumination points xi . In

Real-time editing and relighting of homogeneous translucent materials 569

order to apply 2D wavelets, we must parameterize xi ontoa square 2D domain. We create this parameterization usingthe tree-based hierarchal construction scheme presentedby Hasan et al. [9]. To do so, we first compute m ×2n ×2n

uniform samples around the scene, where both m and nare integers; we then apply a spatial partition algorithm tosplit these unstructured points into m parts. We build a bal-anced quadtree for each partition using the same methodas Hasan et al. and flatten the tree. This maps each par-tition to a square texture that also maintains good spatialcoherence for efficient wavelet approximation.

Spatial compression. Due to the size of our precomputeddata, a straightforward approach to directly perform thedouble projection, taken by Cheslack-Postava et al. [2], isnot feasible as it requires storage of the full matrix. In-stead, we apply nonlinear approximation on the transferdimension first, then apply the second wavelet projec-tion using compressed row vectors. This two-pass ap-proach has been exploited previously in [24] to signifi-cantly reduce the precomputation time while preservingaccurate all-frequency effects. Note that the spatial do-main wavelet projection requires a parameterized model,such as geometry images [6]. Alternatively, for small tomedium size models (∼ 20 000 vertices), we can also omitthe spatial compression step (thus no parametrization is re-quired) and still maintain interactive relighting and editingspeed.

Implementation notes. To summarize, we perform pre-computation in two passes. The first pass loops overeach vertex, uses each BSSRDF basis to compute the

Fig. 2. Overview of our relighting algorithm

transport matrix Tk, and performs a nonlinear waveletapproximation on Tk. We maintain a relatively large num-ber of wavelet terms in this stage to retain high accu-racy for the second pass of spatial compression. Dur-ing the second pass, we loop over each BSSRDF basis,read in the compressed data from the first pass, andperform a spatial wavelet transform step on each basisslice. As Haar wavelets generate objectionable spatial re-construction artifacts, we instead use the smoother CDF9/7 wavelet. For nonlinear compression, we adaptivelychoose the transformed vectors with the highest energy inL2 norm, until a user-specified energy threshold is met.The chosen transport vectors are then truncated to their fi-nal size according to a targeted data size, and quantizedto 16-bit integers with 16-bit indices. When the numberof illumination points exceeds the index range (216), weinstead use 14 data bits with 18 index bits.

Much of first pass can be trivially parallelized, so weutilize multiple CPU cores. Furthermore this step requiresvery little memory beyond an array to hold the currenttransport vector. The second step could also be paral-lelized, but would be much more challenging as the mem-ory consumption is substantially higher – each transportmatrix Tk (corresponding to the BSSRDF basis) must fitentirely in memory to be further processed.

3.3 Relighting and BSSRDF editing

Relighting from our precomputed data is similar to otherPRT systems, with additional steps for editing BSSRDFparameters. Our relighting algorithm is illustrated in Fig. 2and summarized as follows:

570 R. Wang et al.

Fig. 3. Images synthesized from our system using increased number of Rd basis functions (from left to right). The two rows show meas-ured marble and potato materials, respectively. At the far right are reference images generated without approximation on Rd. Using only12 Rd basis vectors, our system produces images indistinguishable from the reference

1. Calculate the direct lighting E and project it onto theHaar wavelet basis to find Ew.

2. For each BSSRDF basis, calculate the matrix-vectormultiplication wvk = wTw

k · Ew.3. A dynamic BSSRDF is provided by the user by defin-

ing its parameters σ ; it is then sampled and projectedonto the basis set to obtain coefficients sk(σ):

sk(σ) =∫

r

Rd(r, σ)bk(r)dr.

4. Take the linear sum of vectors wvk with sk(σ) asweights, then perform an inverse wavelet transform onthe resulting vector to get a color vector Lo represent-ing the color of each vertex.

To compute direct lighting E in step 1, we permitany direct lighting model that can be evaluated in real-time, such as shadowed point lights, environment lighting,and local area lighting. Note that the steps involving thedynamic BSSRDF occur after computing wvk which isthe major computational bottleneck. Therefore our systemprovides real-time response to BSSRDF editing, whilemaintaining interactive relighting speed, even for fairlylarge models.

Implementation notes. Below we describe three types ofdirect illumination models we support:

1. Shadowed point light. This is handled using standardGPU shadow mapping. To do so, we store illuminationsample points in textures and use a fragment shader tocompute the shadowed irradiance values, which are thenread back to the CPU and projected onto the Haar waveletbasis, resulting in Ew.

2. Environment lighting. We handle environment lightingusing standard wavelet-based PRT. Specifically, we pre-compute a set of visibility vectors for each illuminationsample point, apply a nonlinear wavelet approximation, anduse them to compute the irradiance E at run-time. Thisrequires additional precomputed data; but we discoveredthat the same spatial compression step can be applied againhere to fully exploit the data’s spatial coherence and reducethe storage requirement. This method brings an additionaladvantage that the run-time algorithm can directly obtainwavelet-transformed irradiance Ew and eliminate a wavelettransform step from E to Ew, thus saving time during re-lighting. Because Ew is never visualized directly, it can beheavily compressed with little effect on the resulting qual-ity. This method allows us to include realistic environmentlighting effects with minimal overhead.

3. Local area lights. To include local area lights, weuse the source radiance fields (SBF) technique presentedby [26]. This approach samples the radiance field ofa local area light in its surrounding 3D space, then usessimple interpolation to quickly evaluate the spatially vary-ing illumination field at an arbitrary point xi .

4 Results and discussion

Our timings are recorded on an Intel Core 2 Duo 1.8 GHzPC with NVIDIA 7600 GT graphics card. The first passof precomputation and the relighting algorithms both usethreads to utilize both CPU cores.

Analysis of Rd. Figure 4a plots the square roots of thefirst 15 singular values resulting from the SVD analysis

Real-time editing and relighting of homogeneous translucent materials 571

Fig. 4. a The decay of square roots of the first 15 singular values of Rd. b Plots of the first four PCA basis functions. c Plots of the L2

approximation error using 12 terms, and d plots of log10(relative L∞ error), indicating the digits of accuracy of the Rd approximation.The axes are for BSSRDF parameters σ ′

s (vertical) and σa (horizontal)

of Rd. We can see that the singular values decrease veryquickly, indicating that only a few terms are needed toaccurately approximate Rd. In Fig. 4b we plot the firstfour basis functions derived from our analysis. We onlyplot the range of [0.0, 5.0] as the first four bases rep-resent dominant local transfer effects, thus they decreaseto zero very rapidly as the distance r increases. Fig-ure 3 shows a sequence of renderings with an increas-ing number of basis terms. A reference rendering is pro-vided at the right. As expected from the SVD analysis,a small number of terms is sufficient to represent thesematerials. The material shown in the first row (marble)is dominated by near field transfer effects, thus is verywell represented only using a few terms; on the con-trary, the material shown in the second row (potato) isnot as well represented by as few terms. This BSSRDFhas stronger scattering effects over longer distances, andtherefore cannot be accurately represented with only thefirst few terms.

To analyze the range of representable BSSRDF param-eters using our method, in Fig. 4c we plot of L2 approxi-mation error of Rd resulted from using 12 terms for a rangeof material parameters; in addition, Fig. 4d shows the log-arithm of the relative L∞ error where the color coding in-dicates the number of digits of accuracy resulting from theapproximation. The axes represent parameter σ ′

s along thevertical direction with a range [10−6, 5] and parameter σaalong the horizontal direction with the same range. Theseranges cover the measured parameter values found in [12]with significant slack. The figure shows that our approxima-tion is accurate for almost all parameters. Those for whichit is not are uninteresting cases where multiple scatteringis insignificant, thus it is more appropriate to handle thesematerials using the diffuse BRDF model.

Precomputation: transfer compression. Table 1 summar-izes our precomputation benchmark for five test scenes.The angel and bird models are unparameterized models

572 R. Wang et al.

Table 1. Precomputation benchmark for our test scenes. The values, from left to right represent: the number of mesh vertices, illuminationpoints, the total processing time and storage size for precomputation pass 1, the number of terms per stored transport vector after pass 1,and the corresponding compression ratio, the same statistics for pass 2, and the total preserved energy, indicating the L2 accuracy resultingfrom the spatial compression

Pass 1: Transport Pass 2: SpatialVerts Samples Time Size NLA Ratio Time Size NLA Ratio Energy

Angel 12 k 64 k 3 min 141 MB 256 0.4% – – – – –Bird 30 k 64 k 8 min 359 MB 256 0.4% – – – – –Beethoven 16 k 64 k 5 min 1.5 GB 1024 1.5% 13 min 44 MB 256 1:5 95%Gargoyle 64 k 128 k 40 min 6 GB 1024 0.8% 73 min 125 MB 256 1:6.3 97%David 96 k 256 k 2 h 9 GB 1024 0.4% 3 h 175 MB 256 1:6.6 95%

Fig. 5. Comparison of rendering quality by varying spatial compression ratio. The numbers below each image indicate the percentage ofpreserved energy, the spatial compression ratio, and the relighting speed

and cannot be compressed spatially by our system. Theother three models are all parameterized as geometryimages, so we compress them spatially. Raw datasetsrange from 35 GB to 1.1 TB, but we never have to storethem because the first pass immediately compresses mostof them to less than 1% of their original size while main-taining a very accurate representation of the light trans-port. Even for the largest dataset we produce, the interme-diate storage is reasonable. Further, common datasets takeonly minutes to compute.

Precomputation: spatial compression. The second pass –spatial compression – is more expensive to compute,partly because it is not parallelized. Because spatial com-pression artifacts will be directly visualized, we usesmooth, high-order wavelet filters for this step. We foundthat the CDF 9/7 filter from the JPEG 2000 image com-pression standard is most effective for our data even at

very aggressive compression ratios. Figure 5 comparesrenderings of models computed with progressively higherspatial compression ratios. The figure indicates the per-centage of signal energy maintained, the spatial compres-sion ratio, and the relighting speed. In general we findthat with 95–98% preserved spatial signal energy (equiva-lent to normalized L2 error), we lose very little quality.This corresponds to roughly 1 : 5–1 : 6 spatial compres-sion ratio. Thus after the second pass, our storage neverexceeds 0.2% of the original matrix size, and the matrixcan now fit comfortably in memory.

Our spatial compression scheme is more efficient tocompute compared to previous PCA-based approaches.By using nonlinear wavelets, we achieve excellent com-pression ratios and our approach is not subject to parti-tion boundary artifacts. This provides a significant per-formance speed up in relighting while maintaining highaccuracy. The artifacts caused by further spatial com-

Real-time editing and relighting of homogeneous translucent materials 573

Table 2. Relighting and material editing benchmark for our testscenes

Rendering FPSVerts Samples Relighting Editing

Angel 12 k 64 k 24 220Bird 30 k 64 k 10 200Beethoven 16 k 64 k 68 120Gargoyle 64 k 64 k 20 50David 96 k 128 k 17 33

Fig. 6. Examples of environment lighting captured in real-time

pression take the form of smoother scattering details, ashigh-frequency spatial terms are dropped from the ap-proximation. The size of the object greatly affects spatialcompression since smaller objects are more influencedby short-distance scattering effects and thus contain moredata coherence to exploit.

Relighting and editing. Relighting and editing in our sys-tem are very efficient (see Table 2). Relighting speed isroughly proportional to the stored matrix size since the al-gorithm linearly steps through the entire matrix once perrelighting frame. Interactive rates are always maintainedin all cases. Editing speed is real-time. Editing spatiallycompressed models is slightly more costly because wemust perform an additional inverse wavelet transform atthe last step. Figure 6 shows some results captured underenvironment lighting. Additional demos can be found inthe video attached with this paper.

5 Conclusions and future work

We have presented a novel method for real-time edit-ing and relighting of diffuse translucent BSSRDFs undercomplex lighting. This permits interactive manipulation oftranslucent material properties and provides accurate real-time feedback of final-quality rendering. Our system iscurrently limited in three aspects: first, we are limited tostatic scene models due to the use of PRT. Second, weonly handle diffuse multiple scattering effects and ignoresingle scattering and directional scattering effects, whichare much more challenging to simulate. Third, our spa-tial compression scheme requires a parameterized scenemodel, which is not always feasible for complex geometry.In future work, we plan to extend the current editing sys-tem by addressing the above issues. First, we would like toincorporate other, more complicated translucency models,such as multi-layer model, measured diffuse scatteringmodel, and more generally, heterogeneous translucent ma-terials. Second, we would like to study extensions of thecurrent system to deformable scene models. Finally, weplan to investigate other spatial compression schemes thatdo not rely on a parameterized domain.

Acknowledgement This work is partly supported by National Nat-ural Science Foundation of China (Grant No. 60633070), the 973Program of China (Grant No. 2002CB312102).

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RUI WANG received his Ph.D. degree in appliedmathematics from Zhejiang University in 2007.Now He is an assistant researcher in the StateKey Laboratory of CAD&CG of Zhejiang Uni-versity. His research interests include real-timerendering, virtual reality and geometry approxi-mation.

EWEN CHESLACK-POSTAVA is a Ph.D. studentin the Graphics Laboratory in the Department ofComputer Science at Stanford University. He re-ceived is B.S. degree in Computer Science fromthe University of Virginia. His research interestsinclude interactive photorealistic rendering, ren-dering techniques for large scale virtual worlds,and computer vision.

RUI WANG is an assistant professor in theDepartment of Computer Science at Univ. ofMassachusetts Amherst. He received his Ph.D.in Computer Science from the University of Vir-ginia in 2006, and B.S. from Zhejiang Universityin 2001. His research interests are in the fieldof computer graphics, with focuses on global il-lumination algorithms, interactive photorealisticrendering, GPU rendering, and appearance mod-eling.

DAVID LUEBKE is a research scientist atNVIDIA Research, which he helped found in

2006 after eight years on the faculty of the Uni-versity of Virginia. He received his Ph.D. inComputer Science from the University of NorthCarolina under Dr. Frederick P. Brooks, Jr., andhis Bachelors degree in Chemistry from the Col-orado College. Dr. Luebke and his colleagueshave produced dozens of papers, articles, chap-ters, and patents; a short film in the SIGGRAPH2007 Electronic Theater; the book “Level of De-tail for 3D Graphics”; and the Virtial Monticelloexhibit seen by over 110,000 visitors to the NewOrleans Museum of Art.

QIANYONG CHEN is an Assistant Professor inthe Department of Mathematics and Statistics atthe University of Massachusetts Amherst. He re-ceived his Bachelor degree from the Universityof Science and Technology of China (USTC) in1996, and Ph.D. from Brown university in 2004.His research interests include developing stableand highly efficient numerical methods for solv-ing partial differential equations.

WEI HUA received the Ph.D. degree in appliedmathematics from Zhejiang University in 2002.He is now an associated professor of the StateKey Laboratory of CAD&CG of Zhejiang Uni-versity. His research interests include real-timesimulation and rendering, virtual reality and soft-ware engineering.

QUNSHENG PENG is a Professor of computergraphics at Zhejiang University. His researchinterests include realistic image synthesis, com-puter animation, scientific data visualization, vir-tual reality, bio-molecule modeling. Prof. Penggraduated from Beijing Mechanical College in1970 and received a Ph.D from the Departmentof Computing Studies, University of East An-glia in 1983. He serves currently as a member ofthe editorial boards of several international andChinese journals.

HUJUN BAO received his Bachelor and Ph.D. inapplied mathematics from Zhejiang Universityin 1987 and 1993. His research interests includemodeling and rendering techniques for largescale of virtual environments and their applica-tions. He is currently the director of State KeyLaboratory of CAD&CG of Zhejiang University.He serves currently as a member of the editorialboards of several international and Chinese jour-nals. He is also the principal investigator of thevirtual reality project sponsored by Ministry ofScience and Technology of China.