Interactive Relighting of Virtual Objects under Environment Lighting

Nick Michiels, Jeroen Put and Philippe Bekaert

Hasselt University - tUL - iMinds, Expertise Centre for Digital Media, Wetenschapspark 2, 3590 Diepenbeek, Belgium

Keywords:

Rendering, Spherical Gaussians, Real-time, Triple Product, Gpu.

Abstract:

Current relighting applications often constrain one or several factors of the rendering equation to keep the ren-

dering speed real-time. For example, visibility is often precalculated and animations are not allowed, changes

in lighting are limited to simple rotation or the lighting is not very detailed. Other techniques compromise on

quality and often coarsely tabulate BRDF functions. In order to solve these problems, some techniques have

started to use spherical radial basis functions. However, solving the triple product integral does not guarantee

interactivity. In order to dynamically change lighting conditions or alter scene geometry and materials, these

three factors need to be converted to the SRBF representation in a fast manner. This paper presents a method to

perform the SRBF data construction and rendering in real-time. To support dynamic high-frequency lighting,

a multiscale residual transformation algorithm is applied. Area lights are detected through a peak detection

algorithm. By using voxel cone tracing and a subsampling scheme, animated geometry casts soft shadows

dynamically. We demonstrate the effectiveness of our method with a real-time application. Users can shine

with multiple light sources onto a camera and the animated virtual scene is relit accordingly.

1 INTRODUCTION

Interaction between the real environment and virtual

scenes is crucial in real-time relighting applications.

Realistic integration of computer generated objects in

real environments is used in movie post-production

and in augmented reality applications. Fully inter-

active applications allow immediate changes of three

important factors. Firstly, they allow changes in the

lighting in the scene. These changes can affect both

distant and near-ﬁeld changes in illumination. Sec-

ond, the geometry of the objects in the scene can

change with animations or with user input. Lastly, the

materials that constitute the objects can change. How-

ever, the evaluation of the required rendering equation

in real-time has so far remained impossible without

constraining at least one of these three factors. Be-

sides, it is also important that the representable con-

tent can contain high-frequency details. There are

several problems to solve before reaching real-time

framerates. Our approach combines the advantages

of previous approaches and allows real-time relight-

ing of dynamic virtual scenes with real-time captured

environment lighting. The data is represented using

spherical radial basis functions (SRBFs). This paper

will explain how to construct such a representation

efﬁciently. Each factor needs to be dynamic and re-

(a) (b)

Figure 1: Interactive rendering where all factors are dy-

namic. (a) Rendering of a virtual object in a real envi-

ronment. (b) Real-time change of material specularity. (c)

Change in geometry requires real-time cone tracing of vis-

ibility. The virtual object can be animated or changed by

user input. (d) Real-time change of lighting. The environ-

ment map is captured real-time.

quires a fast transformation to the SRBF representa-

tion. For environment lighting, we show how a mul-

tiscale residual algorithm can be used for SRBF ﬁt-

ting. The visibility needs to be sampled in real-time

and we show how voxel cone tracing together with

an efﬁcient sampling scheme allow for accurate soft

shadows.

220

Michiels N., Put J. and Bekaert P..

Interactive Relighting of Virtual Objects under Environment Lighting.

DOI: 10.5220/0005360102200228

In Proceedings of the 10th International Conference on Computer Graphics Theory and Applications (GRAPP-2015), pages 220-228

ISBN: 978-989-758-087-1

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

Table 1: Comparison to other techniques that use precomputed radiance transfer for triple product rendering. All compared

techniques use spherical harmonics wavelets or spherical Gaussians to solve the rendering equation. However, they all con-

strain at least one of the factors. Our approach allow for a real-time update for as well lighting, materials and visibility.

all-frequency dynamic lighting dynamic geometry dynamic reﬂectance

Sloan et al., 2003 × × × ×

Ng et al., 2004 X × × ×

Tsai and Shih, 2006 X rotation only × ×

Haber et al., 2009 X × × ×

Wang et al., 2009 X rotation only × X

Lam et al., 2010 X rotation only × ×

Meunier et al., 2010 X limited sources rigid transformations X

Iwasaki et al., 2012 X rotation only low-poly X

our method X X X X

2 RELATED WORK

Our technique is related to Precomputed Radiance

Transfer techniques (PRT) (Sloan et al., 2002; Ng

et al., 2003; Sun et al., 2007; Imber et al., 2014),

in that we factorize rendering and represent the es-

timated data in efﬁcient bases.

Ng et al. (Ng et al., 2004) represent the visibility

term, the environment map and the BRDF slice that

corresponds to the viewing direction ω

in the Haar

wavelet basis Ψ. This basis is deﬁned over the hemi-

sphere using the hemi-octahedral parameterization as

introduced by Praun and Hoppe (Praun and Hoppe,

2003). Later this approach is extended to work with

high-order wavelets (Michiels et al., 2014). Wavelet

representations are good for compression and can be

used efﬁciently in the triple product integration of

PRT rendering. However, the factors themselves can-

not be transformed easily to the wavelet representa-

tion and require ofﬂine processing.

Haber et al. (Haber et al., 2009) use the afore-

mentioned approach to efﬁciently compress and ren-

der with the three factors. However, none of the three

factors are dynamic. For example, all BRDF slices

are ﬁrst sampled in pixel domain and are then trans-

formed to wavelets and the visibility is preprocessed

with ray tracing.

A new basis to represent the three factors of

the rendering are spherical radial basis functions

(SRBFs). The advantage of SRBFs is that they have

an efﬁcient rotation operator. Tsai et al. (Tsai and

Shih, 2006) proposed a method for rendering with all-

frequency lighting using SRBFs. The lighting Gaus-

sians are ﬁtted using an optimization process which

results in high compression ratios, but can take up to

several minutes to ﬁt the full lighting factor. Further-

more, the visibility is precomputed and compressed

using Clustered Tensor Approximation (CTA) and is

therefore limited to static scenes only.

Wang et al. (Wang et al., 2009) also presented ren-

dering with SRBFs for all-frequency lighting. They

lack the possibility to render dynamic scenes since the

visibility is precalculated using a spherical singed dis-

tance function (SSDF). Moreover, SSDFs are not able

to accurately render detailed shadows. To represent

the lighting factor, they use the same elaborate ﬁtting

process as Tsai et al. (Tsai and Shih, 2006).

Lam et al. (Lam et al., 2010) proposed a hierar-

chical method for transforming environment lighting

to a SRBF representation. The positions and band-

width parameters of the SRBF are determined by the

Healpix (Gorski et al., 2005) distribution. The coefﬁ-

cients are obtained by a least-square projection (Sloan

et al., 2003).

Meunier et al. (Meunier et al., 2010) explain how

cosine lobes can be used to represent each term of

the rendering equation. The use of a cosine lobe rep-

resentation for compactly representing a reﬂectance

function is common. The authors also show how di-

rect spherical light sources can be approximated with

cosine lobes as well as show how to off-line simplify

the geometry into a tree of spheres. By splatting these

spheres onto a quad-tree, the visibility is sampled.

Only rigid transformations of the geometry are pos-

sible.

Iwasaki et al. (Iwasaki et al., 2012) developed a

real-time renderer for dynamic scenes which is able

to render under all-frequency lighting using spheri-

cal Gaussians. The lighting can be rotated, but cannot

be updated dynamically. The visibility is dynamically

estimated by projecting bounding volumes onto a grid

of patches of the hemisphere. Occluded patches are

represented with spherical Gaussians. However, up-

dating the bounding volume tree is strongly depen-

dent on the complexity of the scene. Besides, their

tree traversal uses suboptimal branching operation on

InteractiveRelightingofVirtualObjectsunderEnvironmentLighting

221

GPUs.

Our method also uses spherical radial basis func-

tions to represent all three factors. In contrast to pre-

vious techniques, we are able to construct and up-

date all three factors in real-time. We show how a

residual transformation technique can be used to efﬁ-

ciently transform the lighting information to spherical

Gaussians. Cone tracing together with peak-detection

of powerful and high-frequent lights allow for inter-

active rendering of soft shadows. Table 1 gives an

overview of all the discussed techniques. Note that

only our technique allows real-time adjustment of the

lighting. Other techniques support only static lighting

or rotation of the environment map. Furthermore, the

performance of our real-time visibility tracing is not

dependent on the amount of polygons.

3 TRIPLE PRODUCT

INTEGRATION

A key part in our framework is the simulation of light

propagation in a scene based on the reﬂectance equa-

tion over the hemisphere Ω (Kajiya, 1986; Ng et al.,

2004):

B(v, ω

) =

Ω

ρ(v, ω

, ω

)V (v, ω

)

L(v, ω

)dω

(1)

where ρ is the BRDF, incorporating the cosine term

for the incident illumination from ω

, at position v

and the outgoing direction ω

. V is the hemispherical

visibility term evaluated around v and

L is the inci-

dent illumination rotated in the local frame of v. The

components are illustrated in Figure 2, where each of

relighting

BRDF

visibility environment

lighting

Figure 2: Rendering and relighting. The rendering equa-

tion is factorized in material (BRDF), visibility and envi-

ronment map. All the factors are represented over the hemi-

sphere. Rendering is the integration over the hemisphere

of the three factors. Each factor can be changed and will

immediately inﬂuence the rendered result. For example, a

change in environment lighting will result in a relit scene.

the factors affect the appearance of the rendered re-

sult. Now the rendering equation can be evaluated as

a triple-product integral at each point in the scene:

B(v, ω

) =

∑

klm

(2)

where C

klm

Ω

dω

are called the binding

or tripling coefﬁcients of the three bases. The efﬁ-

ciency of this calculation is dependent on the choice

of basis to represent the factors. Calculations in

the pixel domain will be inefﬁcient, as pixels can-

not sparsely represent the information of the factors.

Other techniques using spherical harmonics (Sloan

et al., 2002), Haar wavelets or eigenbases are often

able to more compactly represent the content. These

bases, however, place their own restrictions on the

data or the operations that can be performed on it. For

example, spherical harmonics are not able to sparsely

represent high-frequency signals. On the other hand,

wavelets are very good at compression but lack ﬂexi-

bility. Wavelets are constrained to static scenes, since

the visibility needs to be precomputed. Moreover,

rotation is a complex operation in the wavelet do-

main (Wang et al., 2006). We choose to represent all

three factors in the triple product integral with hierar-

chical spherical Gaussians. A spherical Gaussian G is

deﬁned as

G(v · p, λ, µ) = µe

λ(v·p−1)

(3)

where v · p is the dot product between a vector v on the

sphere and the center of the Gaussian, λ the Gaussian

bandwidth and µ the amplitude. Spherical Gaussians

have several advantages:

• A hierarchy of spherical Gaussians allows the

efﬁcient representation of both low- and high-

frequency information.

• Spherical Gaussians are rotationally symmetric

and therefore allow the efﬁcient rotation of the en-

vironment map to the local vertex coordinate sys-

tem by rotating the center of the Gaussian.

• BRDF functions can be well approximated with

spherical Gaussians, allowing run-time evaluation

of reﬂectance.

• The mixing of Gaussians is additive and allows

for a less complex implementation, compared to

spherical harmonics or wavelet theory.

Additionally, Gaussians have an extra interesting

characteristic. The product and convolution of Gaus-

sians can be solved analytically (Tsai and Shih, 2006):

(v · p

, λ

, µ

(v · p

, λ

, µ

(v · p

, λ

, µ

)dv

4πµ

+λ

sinh(krk)

krk

(4)

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222

where r = kλ

+ λ

k. The binding coef-

ﬁcients out of Equation 4 are now reduced to a simple

formula. However, solving the triple product integral

efﬁciently is not enough for real-time relighting appli-

cations. In order to interactively change lighting con-

ditions or alter scene geometry and materials, these

three factors need to be converted to the SRBF rep-

resentation in a fast manner. In the next sections, we

will demonstrate how we can make the visibility, ma-

terials and lighting factors dynamic by using spherical

radial basis functions.

4 DYNAMIC MATERIALS

There are a few characteristics a good material repre-

sentation must have:

1. The representation should be compact.

2. Easy rotation of the BRDF into the global lighting

and visibility frame.

3. Fast evaluation of double and triple product inte-

grals.

SRBF functions can approximate almost any

BRDF. They are rotationally symmetric and easily ro-

tatable. They also allow for a compact all-frequency

representation, due to their multiscale nature. It is

known that BRDF functions expressed in terms of

a normal distribution function can be approximated

with Gaussian lobes (Ngan et al., 2005; Wang et al.,

2009). These Gaussians are then integrated in the

triple product rendering integral.

Figure 3: Dynamic materials. The lobe of a BRDF is ap-

proximated using one or few Gaussians. This direct map-

ping allows for real-time changes in appearance of the ma-

terial. For example a virtual object can be rendered with

different kinds of materials: Lambertian (top left), dif-

fuse Phong (top right), glossy Phong (bottom left), specular

Phong (bottom right), Cook-Torrance, ...

5 DYNAMIC VISIBILITY

To evaluate the complex visibility term in the render-

ing equation in real-time, a fast and dynamic approxi-

mation is required. Previous techniques have relied on

precomputation, but such a solution is no longer fea-

sible when changes in the geometry occur frequently.

In our framework, we combine PRT techniques with

voxel cone tracing (Crassin et al., 2011), to evaluate

the visibility in real-time entirely on the GPU.

The ﬁrst step in our processing pipeline is to

voxelize the geometry to a 3D texture. This is

done by implementing a one-pass voxelization algo-

rithm (Crassin and Green, 2012). We use a geometry

shader to project all polygon fragments to their domi-

nant axis. Voxelization is a real-time process and only

needs to be partially updated every frame for dynamic

geometry. For this we use a dirty ﬂag mechanism that

leaves the static geometry untouched.

The second step is to perform cone tracing in the

voxel volume. Each visible pixel corresponds to a 3D

position in voxel space. From this position, new cones

can be constructed and traced throughout the voxels.

Current voxel cone tracing is often used to perform

ambient occlusion or low frequency global illumina-

tion effects. However in our application, we shoot

cones to evaluate the visibility factor of the triple

product integral. For this to work, a mapping from

cones to spherical Gaussians is essential. Suppose we

have a Gaussian with size λ. Let us ﬁt a cone that co-

incides with the distance α where the Gaussian eval-

uates 0.5:

λ(cos(α)−1)

= 0.5 (5)

Solving for α:

α = cos

−1

(

log(0.5)

+ 1.0) (6)

where α is used as the solid angle for the cone to trace.

The last step is to select the appropriate cones to

trace. A straightforward method would trace one vis-

ibility cone for each BRDF lobe. However, important

high-frequency detail might be missed. For BRDF

lobes with a large solid angle, all visibility details

are integrated over a large area of the hemisphere.

A better approach is to subsample the BRDF lobe

with smaller visibility cones. The subsampling den-

sity depends on the characteristics of the BRDF. A

circle packing algorithm is used to determine the cen-

ter position and radius. Figure 4 shows our subsam-

pling scheme. For diffuse Lambertian BRDF lobes,

a small number of uniformly traced visibility cones

sufﬁce. For more glossy BRDF lobes, the cones are

scaled and rotated into the lobe. The number of cones

used for subsampling determines the desired level of

InteractiveRelightingofVirtualObjectsunderEnvironmentLighting

223

(a) (b) (c)

Figure 4: Adaptive subsampling of visibility cones. Left: Gaussian of a Lambertian BRDF lobe (orange) approximated with

a number of visibility cones (green). Middle: Gaussian of a glossy BRDF lobe (orange) approximated with the same number

of visibility cones (green), rotated and scaled to enclose the BRDF. Right: for a Gaussian of a specular BRDF lobe (orange)

it sufﬁces to only trace a single visibility cone (green) that coincides the lobe.

Figure 5: Multiscale residual transformation of environment map into SRBF representation from a coarse scale (left) to more

reﬁned scales (right). Each level adds extra detail to the reconstruction.

quality. Because the size of a BRDF lobe dictates

the recoverable frequencies (Ramamoorthi and Han-

rahan, 2001), our subdivision of scaled cones within

the BRDF lobe retains approximately the same level

of quality for all lobe sizes. In our implementation we

obtained good quality renderings using a subdivision

of 7 cones.

6 DYNAMIC LIGHTING

Real-time changes to the lighting environment can

drastically alter the look of three-dimensional models.

To capture the entire distant lighting sphere, we use

HDR omnidirectional video frames extracted from

the Ladybug3 (PointGrey, 2014) camera. To convert

the lighting to an RBF representation, we perform an

RBF ﬁtting algorithm based on Ferrari et al. (Ferrari

et al., 2004). We apply the algorithm on the sphere

using the Healpix (Gorski et al., 2005) distribution,

utilizing a multiscale algorithm. The algorithm starts

from the environment map as input to the ﬁrst scale.

The input of each scale is approximated with a ﬁxed

grid of SRBFs. The difference of the approximated

reconstruction and the input data is the residue and is

passed as input to the next scale. This process contin-

ues until the residual error is below a certain thresh-

old or the maximum level of detail is reached. The

described algorithm is fast and allows for a real-time

transformation. Unlike other methods, no complex

optimization is used (Tsai and Shih, 2006; Lam et al.,

2010). An example of a multiscale approximation is

shown in Figure 5.

The subsampling scheme described in Section 5

performs well for large area light sources and low-

frequency lighting. For these cases, the visibil-

ity cones can stay relatively large. In the case

of very bright area lights, subsampling of visibility

cones would quickly become too ﬁne-grained to be

tractable. We treat these lights as a special case. Their

areas are easily identiﬁed with a peak detection algo-

rithm. First, the incoming environment map lighting

is thresholded, so that only the peaks with the most

inﬂuence remain. Then, the connected component al-

gorithm is used to group pixels into the lights they

constitute. Lastly, a number of Gaussians (1-3) are

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224

Figure 7: Dynamic visibility

. Geometry can be changed using animations or user input. Adaptive cone tracing in the voxel

volume based on the subsampling scheme and peak detection allows for real time rendering of soft shadows.

Figure 6: Peak detection. The input HDR environment map

is thresholded to keep only the high-intensity values. These

peaks are then detected using connected components. Each

connected component can now be represented with a num-

ber of Gaussians. These Gaussians are used to accurately

render soft shadow for high-frequency lighting.

ﬁtted to match the shape of each connected compo-

nent. We trace a visibility cone for every Gaussian.

Figure 6 shows a few examples of our peak detection

algorithm applied on different environment maps.

7 RESULTS

We have designed a custom application to demon-

strate the relighting capabilities of our technique. The

(a) (b)

Figure 8: Peak detection is mandatory for ﬁnding the impor-

tant visibility cones to trace. Left: traced visibility cones

over entire hemisphere using the subsampling scheme of

Section 5. Further subsampling of the hemisphere in more

smaller cones will accurately solve the visibility, but will be

intractable for real-time applications. Right: extra impor-

tance sampling of the hemisphere by using peak detection

of bright light sources. By tracing extra cones in the direc-

tion of the main area light sources, realistic soft shadows

are acquired.

application was tested on an Intel Core i7 3.4 GHz

processor with 8 GB of RAM and a GeForce 770

GTX. The triple product calculation for material, visi-

bility and lighting is done entirely with GLSL shaders

on the GPU. The application can be used to place vir-

tual models under real-world lighting conditions. Our

peak detection process of Section 6 is performed on

the distant illumination environment map in real-time.

Afterwards, the model can be viewed under these

lighting conditions and changes can be made. Unique

to our approach is that all factors can be changed si-

multaneously and in real-time. The lighting can be

Animations are courtesy of Mixamo. https://

www.mixamo.com/motions

InteractiveRelightingofVirtualObjectsunderEnvironmentLighting

225

Figure 9: Dynamic lighting

. The environment lighting is captured using the Ladybug3 (PointGrey, 2014) omnidirectional

camera. Our peak detection algorithm is performed in real-time and passed to the renderer. The virtual object is now rendered

with the lighting conditions from the captured frames. Note how the virtual shadow positions are aligned with the real light

source.

altered, the model can be moved or deformed and the

materials can be edited. If there are spatially-varying

material parameters in the scene, they can be encoded

in textures deﬁned over the virtual model.

Figure 7 shows results with animated geometry.

This geometry causes dynamic changes in the visi-

bility factor. Our algorithm is able to cope with this

in real-time by using voxel cone tracing. The sam-

pling scheme of visibility cones, as explained in Sec-

tion 5, is implemented to quickly get an integrated

visibility value over a certain solid angle, deﬁned by

the BRDF properties. Extra importance sampling of

visibility cones is done by ﬁnding peaks in the light-

ing and is a key feature to efﬁciently render accurate

high-frequency area light sources. Figure 7 clearly

shows that a change in geometry caused different vis-

ibility and that our system is able to render with soft

shadows. Figure 8 illustrates the importance of peak

detection for shadows. The same environment map is

used to render both images, but the right rendering is

done with peak detection and the left with only the

subsampling scheme for visibility.

To demonstrate dynamic visibility, we placed an

omnidirectional camera, such as the Ladybug3 (Point-

Grey, 2014) of Point Grey, near the desired position of

the virtual object in the scene. The residual transfor-

mation algorithm is implemented to extract the spher-

ical Gaussians to render with. Now, a virtual model

can be relit with one or more ﬂashlights, held before

the omnidirectional camera. The results are given in

Figure 9. Note the high-quality soft shadows resulting

from our peak detection algorithm.

To measure the inﬂuence of scene complexity on

performance, the scene was rendered with models of

varying complexity and lighting conditions with a dif-

ferent amount of peaks. An overview of these exper-

iments is given in Table 2. It can be seen that geo-

Table 2: Inﬂuence of scene complexity on performance. All

results are rendered at 1280x720 resolution.

scene peaks triangles FPS

ﬁghter: Fig. 1 6 16k 43

dragon: Fig. 2 top 6 871k 45

dragon: Fig. 2 bottom 1 871k 75

dragon: Fig. 8 11 871k 36

sphere: Fig. 3 6 3k 58

ﬁghter/armadillo: Fig. 7 top 11 708k 34

dancer: Fig. 7 bottom 1 16k 67

dancer: Fig. 9 1 16k 75

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226

metric complexity has only a small inﬂuence on the

framerate. Environmental complexity has a more no-

ticeable inﬂuence, but scales well with the number of

peaks.

8 CONCLUSION

We have presented a unique combination of tech-

niques to allow real-time triple product rendering

where all three factors are dynamic. We use spherical

Gaussians to represent the incoming light, the BRDF

lobes and the visibility over a solid angle. This rep-

resentation enables efﬁcient light integration on the

GPU. Important regions of visibility detail is cone

traced using an adaptive subsampling scheme. Fur-

thermore, peak detection is used to trace complex area

shadows. We have shown in the previous section that

the three factors of material, visibility and lighting are

dynamic and can be updated in real-time. We there-

fore combine all features of previous techniques as

listed in Table 1. We explained how we use cone trac-

ing to support dynamic scenes. Note that our tech-

nique inherits some of the difﬁculties of cone tracing

with respect to the handling of large scenes as well as

well as thin geometry. This is because our current 3D

texture voxelization is not sparse. This limitation will

be overcome by the new partially resident textures on

new GPUs (Sellers, 2013). A second limitation is the

amount of visibility cones. Each new visibility cone

introduces a new triple product calculation. The visi-

bility subsampling scheme together with the peak de-

tection algorithm will limit the amount of visibility

Gaussians. However, environment maps ﬁlled with

different small HDR light sources will inﬂuence the

rendering performance.

ACKNOWLEDGEMENTS

This work has been made possible by the Fund for

Scientiﬁc Research-Flanders (FWO-V Remixing re-

ality) and with the help of a PhD specialization bur-

sary from the IWT. The authors acknowledge ﬁnan-

cial support from the European Commission (FP7 IP

SCENE).

REFERENCES

Crassin, C. and Green, S. (2012). Octree-based sparse vox-

elization using the gpu hardware rasterizer. In Cozzi,

P. and Riccio, C., editors, OpenGL Insights, pages

303–318. CRC Press.

Crassin, C., Neyret, F., Sainz, M., Green, S., and Eise-

mann, E. (2011). Interactive indirect illumination us-

ing voxel-based cone tracing: An insight. In ACM

SIGGRAPH 2011 Talks, SIGGRAPH ’11, pages 20:1–

20:1, New York, NY, USA. ACM.

Ferrari, S., Maggioni, M., and Borghese, N. A. (2004).

Multiscale approximation with hierarchical radial ba-

sis functions networks. IEEE Transactions on Neural

Networks, 15(1):178–188.

Gorski, K., Hivon, E., Banday, A., Wandelt, B., Hansen,

F., et al. (2005). HEALPix - A Framework for high

resolution discretization, and fast analysis of data dis-

tributed on the sphere. Astrophys.J., 622:759–771.

Haber, T., Fuchs, C., Bekaer, P., Seidel, H.-P., Goesele, M.,

and Lensch, H. (2009). Relighting objects from image

collections. In Computer Vision and Pattern Recogni-

tion, 2009. CVPR 2009. IEEE Conference on, pages

627–634.

Imber, J., Guillemaut, J.-Y., and Hilton, A. (2014). Intrinsic

textures for relightable free-viewpoint video. In Fleet,

D., Pajdla, T., Schiele, B., and Tuytelaars, T., edi-

tors, Computer Vision ECCV 2014, volume 8690 of

Lecture Notes in Computer Science, pages 392–407.

Springer International Publishing.

Iwasaki, K., Furuya, W., Dobashi, Y., and Nishita, T.

(2012). Real-time rendering of dynamic scenes under

all-frequency lighting using integral spherical gaus-

sian. Comp. Graph. Forum, 31(2pt4):727–734.

Kajiya, J. T. (1986). The rendering equation. In Pro-

ceedings of the 13th annual conference on Computer

graphics and interactive techniques, SIGGRAPH ’86,

pages 143–150, New York, NY, USA. ACM.

Lam, P.-M., Ho, T.-Y., Leung, C.-S., and Wong, T.-T.

(2010). All-frequency lighting with multiscale spheri-

cal radial basis functions. Visualization and Computer

Graphics, IEEE Transactions on, 16(1):43–56.

Meunier, S., Perrot, R., Aveneau, L., Meneveaux, D., and

Ghazanfarpour, D. (2010). Cosine lobes for interac-

tive direct lighting in dynamic scenes. Computers &

Graphics, 34(6):767–778.

Michiels, N., Put, J., and Bekaert, P. (2014). Product

integral binding coefﬁcients for high-order wavelets.

In Proceedings of the 11th International Conference

on Signal Processing and Multimedia Applications

(SIGMAP 2014). INSTICC.

Ng, R., Ramamoorthi, R., and Hanrahan, P. (2003). All-

frequency shadows using non-linear wavelet lighting

approximation. In ACM SIGGRAPH 2003 Papers,

SIGGRAPH ’03, pages 376–381, New York, NY,

USA. ACM.

Ng, R., Ramamoorthi, R., and Hanrahan, P. (2004). Triple

product wavelet integrals for all-frequency relighting.

ACM Trans. Graph., 23(3):477–487.

Ngan, A., Durand, F., and Matusik, W. (2005). Experi-

mental analysis of brdf models. In Proceedings of

the Sixteenth Eurographics conference on Rendering

Techniques, EGSR’05, pages 117–126, Aire-la-Ville,

Switzerland, Switzerland. Eurographics Association.

PointGrey (2014). Ladybug3. Web page. http://

www.ptgrey.com/. Accessed October 13 , 2014.

InteractiveRelightingofVirtualObjectsunderEnvironmentLighting

227

Praun, E. and Hoppe, H. (2003). Spherical parametrization

and remeshing. ACM Trans. Graph., 22(3):340–349.

Ramamoorthi, R. and Hanrahan, P. (2001). A signal-

processing framework for inverse rendering. In Pro-

ceedings of the 28th annual conference on Computer

graphics and interactive techniques, SIGGRAPH ’01,

pages 117–128, New York, NY, USA. ACM.

Sellers, G. (2013). Opengl extension speciﬁca-

tion: Arb sparse texture. Web page. https://

www.opengl.org/registry/specs/ARB/sparse texture.txt.

Accessed October 11, 2014.

Sloan, P.-P., Hall, J., Hart, J., and Snyder, J. (2003). Clus-

tered principal components for precomputed radiance

transfer. In ACM SIGGRAPH 2003 Papers, SIG-

GRAPH ’03, pages 382–391, New York, NY, USA.

ACM.

Sloan, P.-P., Kautz, J., and Snyder, J. (2002). Precomputed

radiance transfer for real-time rendering in dynamic,

low-frequency lighting environments. In Proceedings

of the 29th annual conference on Computer graph-

ics and interactive techniques, SIGGRAPH ’02, pages

527–536, New York, NY, USA. ACM.

Sun, X., Zhou, K., Chen, Y., Lin, S., Shi, J., and Guo, B.

(2007). Interactive relighting with dynamic brdfs. In

ACM SIGGRAPH 2007 papers, SIGGRAPH ’07, New

York, NY, USA. ACM.

Tsai, Y.-T. and Shih, Z.-C. (2006). All-frequency precom-

puted radiance transfer using spherical radial basis

functions and clustered tensor approximation. In ACM

SIGGRAPH 2006 Papers, SIGGRAPH ’06, pages

967–976, New York, NY, USA. ACM.

Wang, J., Ren, P., Gong, M., Snyder, J., and Guo, B. (2009).

All-frequency rendering of dynamic, spatially-varying

reﬂectance. In ACM SIGGRAPH Asia 2009 Papers,

SIGGRAPH Asia ’09, pages 133:1–133:10, New

York, NY, USA. ACM.

Wang, R., Ng, R., Luebke, D., and Humphreys, G. (2006).

Efﬁcient wavelet rotation for environment map ren-

dering. In Proceedings of the 17th Eurographics Con-

ference on Rendering Techniques, EGSR ’06, pages

173–182, Aire-la-Ville, Switzerland, Switzerland. Eu-

rographics Association.

GRAPP2015-InternationalConferenceonComputerGraphicsTheoryandApplications

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