The Trilateral Filter for High Contrast Images and Meshes
Eurographics Symposium on Rendering2003,pp.1–11
Per Christensen and Daniel Cohen-Or(Editors)
The Trilateral Filter for High Contrast Images and Meshes
Prasun Choudhury and Jack Tumblin
Department of Computer Science,Northwestern University,Evanston,IL,USA.
1.Introduction and Related Work
Despite decades of widespread interest in the problem 5681118232425313335,simple and robust edge-preserving smoothing of visual signals has proven elusive,because the terms are ill-de?ned and somewhat contradictory.Edges are perceived discontinuities that are not always matched to a re-liable mathematical discontinuity.In the past six years,sev-eral edge-preserving smoothing methods have addressed the stubborn problem of visual appearance-preserving contrast reduction28102433.The?lter described in this paper was developed for this task,but we will show that it may have broader uses such as de-noising higher dimensional data and 3D meshes.
Contrast reduction,and the closely-related“tone map-ping”problem long known in photography and printing,is increasingly important because the usable contrast abilities of print and electronic displays remains small,typically be-tween about10:1to30:1,but many interesting scenes con-tain far greater contrasts such as11,000:1in Figure1.Scenes depicted in Figures1and18are usually impossible to pho-tograph well conventionally,because no single exposure set-ting for a camera can capture all the visible details in both the brightest and darkest areas.As explained in a general framework for tonemapping by Tumblin and Rushmeier32, a tone-mapped image should express exactly what a human observer would see in the original scene,including glare, afterimages,?oaters,and all other human visual?aws and effects.They offered an early?lm-like solution,and other better methods soon followed;see818for a detailed sum-mary.We will not address perception,but only focus on the task of contrast reduction that preserves as much scene detail as possible without introducing objectionable artifacts. Now that photography of even the most extreme“high dy-namic range”(HDR)or high contrast scenes is now yield-ing to multiple-exposure image capture methods7(used for Figure1)and novel cameras19,the problem is more ur-gent;these new images are not directly displayable without loss of many visually important details.High contrast im-age display is dif?cult because often no one-to-one mapping of scene to display intensities is satisfactory.Photographic scaling and contrast compression(e.g.I out M Iγin forγ1 and0M1)can fail because compressing large contrasts enough to match the display devices will also compress small contrasts to invisibility.Several early tone-mapping-
c The Eurographics Association2003.
Figure2:Trilateral?ltering can restore a noise corrupted mesh in a single pass.Middle image shows additive Gaussian noise withσ15th mean edge
length.
Figure1:Low contrast image(20:1)made with the trilateral?l-
ter from a high contrast image(11,000:1).Small images show the
original scene radiances progressively scaled by factors of
10.
Figure3:Contrast reduction method based on edge-preserving
?lters.
related papers81826reduced contrasts by compressing only
the image components selected by one or more low pass?l-
ters,but this approach can easily cause strong halo-like arti-
facts.However,recent papers by Ashikhmin2and Reinhard
et al.24have largely overcome these drawbacks by selecting
the best?lter diameter for each pixel from an image pyra-
mid.
Many other published detail-preserving contrast reduc-
tion methods use some form of edge-preserving smooth-
ing810182433to separate the input image into compressible
and incompressible contrast components,as shown in Fig-
ure3.We also follow this approach.This frequently recur-
ring contrast reduction scheme in Figure3is homomorphic;
it?lters the logarithm of intensity as Stockham did28,using
a“detail removing?lter”of some sort to smooth away the
small and complex variations presumably due to re?ectance
changes.The large simpli?ed illumination-related?lter out-
put“Base”is compressed,usually by a scale factorγ(and
sometimes offset by a scale factor log M),and then added
back to the complex details that the?lter removed.Conver-
sion from logarithmic back to a linear signal produces the
displayed image result.A few papers such as33extended this
idea by using multiple?lters to re?ne compression amounts.
The success of the approach in Figure3depends entirely
on the design of the“detail-removing?lter.”If the?lter’s
smoothing is incomplete,the“Base”signal may destroy
some important scene details due to severe contrast com-
pression by factorγ.Worse,if the?lter blurs or distorts
its illumination-like output even slightly,then these distor-
tions will escape compression as part of the“Details”sig-
nal.These errors can cause strange halo-like artifacts in the
result,especially near specular highlights or in broad but
strongly shaded regions such as the sky near the tree line
in Figure1.Entirely avoiding both errors continues to elude
most published methods.
With few exceptions,edge-preserving?lters useful for
contrast reduction fall into two broad classes of(a)itera-
tive solvers and(b)nonlinear?lters.Iterative solver meth-
ods gradually and repeatedly modify an initial image I in to-
wards a?nal“in?nite time”image I∞guided by a discretized
partial differential equation(PDE).Research in scale-space
methods using heat-?ow PDEs led to anisotropic diffusion
PDEs23that combine smoothing and edge sharpening into a
single iterative process.It rapidly forms sharp,?xed shocks
at edges,and gradually smoothes between them by diffus-
ing towards a piecewise-constant I∞result.However,this
method forms strong,spurious step-like shocks across any
large high gradient region3533,such as the back-lit cirrus
clouds in Figure1.To avoid this,third order curvature?ow
PDEs such as LCIS33smooth towards piecewise minimum-
curvature solutions,and instead form shocks as discontinu-
ous gradients rather than intensities.Though its results are
appealing,LCIS smoothing is slow and its best published
c The Eurographics Association2003.
results combine multiple LCIS images using as many as ten hand-selected parameters.
Nonlinear?lter approaches are at least as old as Land’s classic Retinex work,continued with Chiu and Shirley’s8 early work,and were recently advanced by an intriguing se-ries of papers by Black et al.56,Tomasi and Manduchi31 and Durand and Dorsey10.Black et al.6showed equivalence or strong parallels between iterative robust statistical meth-ods and anisotropic diffusion23.Soon afterwards,Tomasi and Manduchi introduced the bilateral?lter31.This simple, fast and elegant nonlinear?lter performs good-quality edge-preserving smoothing in a single pass,and produces PDE-like results without an iterative solver or instability risks. Unlike the iterative solvers,nonlinear?lter methods com-pute each output pixel separately,as a position-dependent function of input pixels in a local neighborhood.Derivations by Barash4,Elad11and con?rmed by Durand and Dorsey10 show that bilateral?ltering is equivalent both to a single it-eration of a discrete version of anisotropic diffusion and to several robust estimation methods.Durand and Dorsey10 then demonstrated the value of the bilateral?lter for con-trast reduction,and used Fouri?g:hdrer transform techniques to greatly accelerate it.However,the bilateral?lter shares some of the drawbacks of anisotropic diffusion for contrast reduction.
In a different approach to contrast reduction,Fattal et al.12compressed the magnitude of the large image gradients that are responsible for its high contrasts,then iteratively solved a Poisson equation to?nd an image that best?ts the compressed gradients in the least-squares sense.Their fast solver converges more quickly,requires fewer parameters, and avoids the often excessively‘busy‘or noisy appearance of the LCIS method.All of these methods have guided our new work.
The trilateral?lter is a substantially improved“detail-removing?lter”for Figure3because it:
better approximates scene illumination as a sharply-bounded,piecewise smooth signal with locally constant gradient,
works in one pass,without an iterative PDE solver, forms sharp boundaries and corners much like shock forming PDEs,
self-adjusts to the image,requiring one user-supplied pa-rameter,
extends easily to N-dimensional signals,both discrete and continuous-valued.
Polygonal mesh smoothing methods also apply nonlin-ear?ltering techniques and iterative PDEs and were origi-nally motivated by the problem of smoothing large irregular polygonal meshes of arbitrary topology151727(see30for an excellent survey).Diffusion and curvature?ow PDEs39re-placed initial Laplacian smoothing methods27and overcame its inherent mesh shrinkage problem.Tasdizen et al.29used
a
Figure4:Unilateral,Bilateral and Trilateral?lter windows. variational strategy to?lter the surface normals instead of the point positions on the mesh.Their mesh smoothing method
follows a4-th order gradient-descent-based PDE. Several recent papers used non-iterative nonlinear?lters
for denoising meshes,but their quality depends on how ef-
fectively the non-linear?lter can emulate the behavior of complicated higher-order edge preserving PDEs.Peng et al
.21and Alexa1have used Weiner?lters for smoothing3D
meshes.Jones et al.16presented a two-pass approach that smoothes the face normals with a low-pass?lter and then
bilaterally smoothes the point positions in the mesh model
using corrected normal information.Fleishman et al.14have also used the bilateral?lter for smoothing the vertex loca-
tions of a3D mesh model.We build on these methods to
apply trilateral?lters to meshes.
2.Filter Preliminaries
Linear and nonlinear?lters make an output signal I out by combining together neighboring parts of an input signal I in
in interesting and useful ways.The?lters in this paper make
weighted sums of neighboring values,but the weights and
the neighborhoods may vary.Each?lter described below is valid for N-dimensional inputs,but we will use1-D and2-D
illustrations for clarity.
We begin with the linear“Finite Impulse Response”(FIR)
or“unilateral”?lter of Figure4(a)to de?ne our terms.The value of the?ltered signal I out at position x x y is the integral of neighboring I in values weighted by a?lter
kernel c,or a weighted sum of nearby pixels for discrete input data.The offset vectorζmeasures position in a local neighborhood or“domain”around x,and the domain kernel function c provides a position-dependent scalar weight for each point’s contribution to the output:
I out x
∞
∞
I in xζcζdζ(1) The domain kernel c may be any function,but we use the Gaussian function with varianceσc for simplicity.Only the I in points near x whereζis small will receive a large weight,
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Figure5:Given a noisy piecewise linear signal(a),the bilat-eral?lter blunts sharp corners(1b)and smoothes high gradient re-gions poorly(2b);the trilateral?lter both sharpens corners(1c)and smoothes high gradient regions well(2c).
and all points outside this“?lter window,”marked by a hor-izontal line in Figure4(a),will have little effect on I out x. Gaussian?lter c removes details well,but also smoothes across the edges we wish to preserve.
Tomasi and Manduchi’s bilateral?lter31offers much bet-ter edge-preserving smoothing.As illustrated in Figure4(b), it expands the?lter window of domain c into a sec-ond dimension by multiplying with a“range”?lter s that weights neighborhood values by their intensity difference from I in x.If s is another Gaussian function with variance σs,then neighborhood I in points with values nearly equal to I in x receive the highest s weight,but“outlier”points with greatly different values receive s weights near zero. Only the input points within the rectangular?lter window shown in Figure4(b)can strongly affect the output value I out x:
I out x 1
dζ
(2)
(Note underlined portions of Equations2,3match).To en-sure bilaterally?ltered outputs are the average of similarly-valued nearby pixels,we normalize the neighborhood weights by k x:
k x
∞
∞
cζs I in xζI in x
kθx
∞
∞
?I in xζcζs?I in xζ?I in x
dζ(5)
We use forward differences instead of central differences
to minimize the smoothing effect for approximating gra-
dients in discrete images:?I in m n I in m1n
I in m n I in m n1I in m n.
Tilting the?lter window in Figure4(c)also confuses its
de?nition,because the domain?lter c and range?lter s
are no longer orthogonal.The solution is simple;rather than
computing a range weight s for neighboring I xζby
measuring its closeness to the center point value I x,instead
we measure its closeness to a plane through I x,which acts
as a“centerline”for the?lter window of Figure4c.Formally,
this plane of intensity values P xζde?nes the?lter’s in-
put range as the?rst-order Taylor-Series approximation of
neighborhood point values around I in x.The plane orienta-
tion is set by the smoothed gradient vector Gθinstead of the
ordinary gradient?I in:
P xζI in x Gθζ(6)
Note that x,Gθandζare all N-dimensional vectors.To com-
pute trilateral?lter output values I out x,we subtract scalar
value P from neighborhood I in values to?nd a local de-
tail signal I?xζ.Instead of?ltering the input signal as in
c The Eurographics Association2003.
Figure6:We?nd neighborhood fθfrom a stack of min-max gradient images.Each pixel in level K holds the min and max values in a2K12K1size neighborhood of the level0image.
Eqns.2,3we apply the c and s weighting functions to I?ζand add the result to I in x to form I out x.The neigh-borhood used for each x is further restricted by the binary function fθxζ01explained in next section.
I?xζI in xζP xζ(7)
I out x I in x 1
dζ
(8)
The trilateral?lter also normalizes local weights by k?x (underlined portions of Equations7,8match):
k?x
∞
∞
cζs I?xζfθxζ
Figure 7:Bilateral smoothing can blunt sharp corners and smoothes high gradient regions poorly.Trilateral ?lter,like LCIS,drives the ?nal signal towards a piecewise linear ap-
proximation.
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Figure 8:Small adjacent high gradient image regions near the
lamp-base top,wall corner and bulb cause dif?culties for many pre-vious methods.Image excerpt from a larger bulb scene,courtesy of Peter Shirley,University of Utah.
age gradient G avg in this neighborhood for each x ,and then use the min and max G avg as an estimate of overall gradient variability.This variability de?nes outliers for gradients that will be rejected by σs θ:
σs θ
βmax G avg x
min G avg x
(11)
Large σs θimproves noise reduction,but also reduces outlier rejection,and may blur weaker boundaries of slight intensity changes.Unfortunately,βis a small fraction we set empir-ically to 015;values between 01and 02always worked best.Armed with σc θand σs θ,we then compute the min-max stack of Section 3.2.We set the globally-applied region-?nding threshold by R σs θto ensure region size f θdoes not include gradient outliers excluded from the bilateral ?l-tering.
Finally,we compute the trilateral ?lter output from Equa-tions 7,8,and 9.Domain ?ltering for I in uses the same neigh-borhood size applied earlier for gradient ?ltering:σc σc θ.The range ?ltering variance is more interesting,because the trilateral ?lter smoothes detail I ?measured from the plane P of Equation 6.The amplitude of the detail signal is closely related to the variance of the gradients or the difference between the smoothed gradient G θand the actual gradi-ents.Thus we can re-use our de?nition for gradient outliers:σs σs θ.These simple rules have proven surprisingly robust for a wide variety of signal classes,including images and 3D geometric meshes.
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Figure 9:Despite high contrasts and strongly varying gradients,
the trilateral ?lter preserves details that escape many previous meth-ods.Note the ring-like specular highlight (1)that often escapes con-trast compression.Only the trilateral ?lter and gradient attenua-tion 12methods capture the subtle gold medallions (2)and radial lines near the skylight.Image excerpt from larger Stanford Church scene,courtesy of Paul Debevec,University of Southern California.
4.Results
In this section,we apply the trilateral ?lter to the tasks of dis-playing high contrast images and de-noising 3D mesh mod-els.
4.1.HDR Tone Mapping or Contrast Reduction The trilateral ?lter offers several notable improvements when used for high dynamic range (HDR)tone mapping or contrast reduction.We collected several HDR source images from previous tone-mapping papers and applied the trilateral ?lter of Equations 7,8,9in the “base/detail”method shown in Figure 3.In side-by-side comparisons with ?ve other re-cently published methods 210122433the differences are in-structive.
c The Eurographics Association 2003.
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Figure10:Nonuniform gradient compression12can some-times lead to brightness anomalies.Image courtesy of Shree Nayar, Columbia
University.
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Figure11:Trilateral?lter automatically selects all but one pa-rameter;adjusting for good results is relatively easy.Images cour-tesy of Dani Lischinski,Hebrew University,Israel.
Figure1,8,10and others show that the trilateral?lter is particularly good at edge-preserving smoothing in nar-row ramp-like high gradient regions of an image,such as the shading at the top of the lamp base.Here,as in Fig-ure5(arrow3),the bilateral?lter can span different high gradient regions and cause strange,strip-like bipolar halos. Though Ashikhmin’s method2is more successful,it blurs the lamp slightly and makes the lampshade and wall bound-aries indistinct.Conversely,photographic tone mapping by Reinhard et al.24keeps the image sharp,but surrounds the bare lightbulb with a thin black halo.
Like LCIS33,the trilateral?lter smoothes towards a piece-wise constant gradient or low curvature result,and in most Figures(e.g.9,10,13)trilateral results more closely re-semble LCIS than any other.But LCIS works by iterative smoothing,and require many hand-selected parameters,and poor choices can lead users to washed-out,overly busy re-sults as in Figure11,but the single-parameter trilateral?lter easily provides more pleasing results.
As Figure5(arrow1)shows,tilting and adaptive neigh-borhoods help trilateral?lters preserve large,sharp gradi-ent changes.Smoothing across these changes causes a dark
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Figure12:Halo artifacts from bilateral?ltering10at the top of the sofa and chair from are absent in the other methods.Image courtesy of Simon Crone,Perth,Australia.
halo at the chair top in the bilateral results in Figure12. Adaptive neighborhoods help the trilateral?lter smooth well even near very high-contrast features,enabling preservation of very subtle medallions and radial lines in the decorative rings nearest the skylight border in Figure9at area2.Even the gradient attenuation method12results loses some de-tails here.As in Figure5,bilateral?ltering10blunts the sharp specular highlights in an outer ring,permitting uncom-pressed brilliance in the result(“1”in Figure9).LCIS33 over-emphasizes some details near the skylight and some-how lost to the subtle golden medallions revealed by trilat-eral?lter(at“2”in Figure9).
The trilateral?lter also avoids blooming effects that en-large,blur or brighten high gradient neighborhoods,such as the inner ring of the skylight for Figure9.Figure10seems to show some blooming-like brightness anomalies due to nonuniform compression of image gradients12that are not reproduced by the trilateral?lter.Figure13demonstrates that blooming(at arrow)for extremely high contrast spec-ular re?ections can be dif?cult to avoid in the bilateral?l-ter10,but both the trilateral?lter and gradient attenuation method12nearly match the blooming suppression of the other three methods.
Table4.1shows the computation time and the half of the
c The Eurographics Association2003.
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Figure 13:Compared to bilateral ?lter 10,trilateral ?ltering lim-its blooming of sharp specular highlights and its performance is similar to the gradient attenuation 12method.
Figure#:Size
Bilateral Trilateral f θTime(s)f θTime(s)8:4003001013.13 6.6721.213:113075010110.1 5.4179.39:5127681057.2 4.9589.111:102476810100.5 5.9160.112:750
485
10
51.4
6.6
90.2
Table 1:Running time and average size of adaptive neigh-borhood (kernel radius f θin pixels)for trilateral ?lter.
adaptive ?lter kernel f θfor the bilateral and the trilateral ?lter.Theoretically,the trilateral ?lter should take roughly twice the time of bilateral ?lter as it is a two-step bilateral ?ltering procedure.In practice,the running time for the tri-lateral ?lter is a little less,due to variable neighborhood size f θ.In Table 4.1,the ?lter window half-width f θis constant for the bilateral ?lter for all the images.For the trilateral ?l-ter f θvaries with the scene details and the average ?lter win-dow half-width is often smaller than the bilateral ?lter value.All running times measure non-optimized code for both the bilateral and the trilateral ?lter.The Fourier transform and sub-sampling based acceleration techniques devised by Du-rand and Dorsey 10should greatly reduce the running times for both ?lters.
4.2.Mesh Smoothing
The trilateral ?lter can also perform 3D mesh smoothing.Though several mesh smoothing approaches are possible,we chose a two-step process:?rst,trilateral normal ?ltering (Section 4.2.1)computes the new vertex normals N Vout and de?nes a “?lter plane”P V X V ζfor each.Then trilateral vertex ?ltering (Section 4.2.2)smoothes together distances from the ?lter plane to mesh faces in its neighborhood,and we use this distance to ?nd a new vertex position X Vout along the new mesh normal direction.
Note that our method for smoothing each mesh vertex V requires both its position X V X Y Z and surface nor-mal vector N V .If normals are unknown,then N V is typically computed as the area weighted average of normals for inci-dent faces of V 14.
4.2.1.Trilateral Normal Filtering
To ?nd new vertex normals,begin by bilaterally ?ltering the given vertex normals N V with Equations 4and 5.Sim-ply substitute normal vectors N V for gradient vectors ?I in ,use the domain ?lter c to weight the contribution of each nearby vertex’s normal according to its 3D distance from vertex V ,and let the range ?lter s assign weights that will reject outlier directions for normals.The resulting bilaterally smoothed normals N θV allow us to ?nd a connected neigh-borhood of nearby mesh faces with similar normals.
For trilateral normal ?ltering,we refer to each mesh face near vertex V by the name ζF ,and its face normal and face center point is X ζF and N ζF respectively.As before,func-tion f θde?nes the adaptive neighborhood around vertex V ,and its limited extent ensures that the trilateral ?lter win-dow will not cross sharp corners of the mesh during ?lter-ing.Function f θV ζF is 1for all connected neighborhood faces around V that share normal vectors similar to N θV ,and is otherwise zero.Breadth-?rst search implemented as a re-gion growing algorithm ?nds this connected neighborhood.The traversal starts at vertex V and terminates when all sur-rounding face normals N ζF differ signi?cantly from the ver-tex normal N θV :
f θV ζF
1if N θV N ζF R
0otherwise
(12)
The bilateral ?ltered normal N θV also sets the ?lter plane for each vertex V .Analogous to the ‘centerline’in Section 3.1,planeeq:trilat2P V X V ζpasses through vertex V and is per-pendicular to the bilaterally smoothed normal N θV .Unlike the plane P in Equation 6which provides a range value for a given location x ,the plane P V X V ζis de?ned only in the 3D domain,and the detail signal is set only by the distance to that plane.
P V X V ζsatis f ies ζ
X V
N θV
0(13)
We compute the trilaterally ?ltered normal N Vout for vertex V from the ?lter plane P V and the normals of neighboring
c The Eurographics Association 2003.
Figure 14:The bilaterally ?ltered normal N θV de?nes a center plane P V X V ζthrough each vertex V.The adaptive region f θselects nearby
faces with
similar normals.Dis-tance from each face center X ζF to the plane de?nes the detailed distance signal X ?ζF .
Original Model Noisy Model Smoothed Model
Figure 15:In a single pass,a trilateral ?lter can remove most visible corruptions caused by additive Gaussian noise in both vertex positions and normals.Some small high cur-vature creases were lost due to smoothing in the hair,eyelids and lips.
faces selected by F θ.The ?lter smoothes a “normal detail signal”N ?ζF made from differences with neighborhood face normals N ζF around the vertex V :
N ?ζF
N θV
N ζF
(14)
The domain ?lter c N ζF is a Gaussian weighting function that falls towards zero as the 3D distance X V X ζF from vertex to face center increases.The range ?lter s N N ?ζF gives low weights to outlier face normal directions N ζF that are drastically different from N θV .Echoing Equation 8,the trilaterally ?ltered normal N Vout is then:
N Vout
N θV
(15)
1
where the weighting coef?cients of the trilateral ?lter are normalized by k N ζF :
k N ζF
∑
F ζF
c N ζF s N N ?ζF
f θV ζF
k V ζF
∑
F ζF
X ?ζF c V p ζF s V X ?ζF
f θV ζF
(19)
4.2.3.Mesh Smoothing Results
Figure 2shows an arti?cially corrupted dragon face model before and after trilateral smoothing.Trilateral ?lter retains most of the sharp curvatures in the face of the dragon.Fig-ure 15shows the effect of trilateral smoothing on the noisy David input model.Leaving aside a little blurring in the eye-lid and hair of the input David model,our ?lter preserves sharp features throughout the model.Figure 16compares the results for mesh denoising using trilateral ?lter with two re-cent mesh smoothing algorithms 1614.All the three methods ef?ciently smoothes the noisy input mesh,though the result of Fleishman et al.’s algorithm 14is comparable in quality to the trilateral ?lter perhaps because both the algorithms ?l-ter the tangent plane distance for neighborhood points.Fig-ure 17shows the results of smoothing a different input model for the trilateral ?lter and the modi?ed bilateral ?lter pro-posed by Jones et al.16.The performance of both the algo-rithms are roughly similar,but some minute differences are visible around the ear and mouth outlines.
c The Eurographics Association 2003.
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Figure16:All the three algorithms are effective for denois-
ing the noisy Fandisk model,but the trilateral?lter result is
closely matched to Fleishman et al.’s14
result.
Figure17:Jones et al.’s16smoothing algorithm and trilat-
eral?lter produce similar results except for small differences
at the edges of the dog’s ears and lips.
5.Conclusions and Future Work
The trilateral?lter offers new edge-preserving detail-
remover that smoothes input towards a piecewise constant
gradient approximation.The?lter requires only one user-
speci?ed parameter and is applicable to N-dimensional data.
We demonstrated its usefulness for different applications
like high contrast image display and mesh smoothing.The
?lter is also“embarrassingly parallel”and may prove suit-
able for fast hardware implementation.
Trilateral?lter’s ability to separate details from the noisy
original image and to predict gradient discontinuities in spa-
tial domain with sub-pixel accuracy might prove useful in
image and photo-editing operations2022.The?lter might
also bene?t from a more pricipled justi?cation for the con-
stantβin Eqn.11.The trilateral?lter extended to the spatio-
temporal domain can also predict occlusions in temporal do-
main and this feature has potential for various video-based-
rendering applications1334.
Acknowledgments:
The authors thank Michael Ashikhmin,Simon Crone,Fredo
Durand,Paul Debevec,Rannan Fattal,Dani Lischinski,Erik
Reinhard and Greg Ward for providing original high dy-
namic range images,results,and permission to use them.
We are also grateful to Mathieu Desbrun,Shachar Fleish-
man and Ray Jones for providing mesh and results data
for comparison with their current mesh smoothing algo-
rithms.
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Figure18:Examples of high dynamic range radiance map compression and mesh smoothing using trilateral?lter.(Top Row, from left):Stanford Memorial Church,courtesy of Paul Debevec,Univ.Southern California.Tree on a Foggy Night,Washington DC Cathedral,courtesy of Max Lyons.(Middle Row):Synagogue,courtesy of Dani Lischinski,Hebrew University,Israel, Burswood Hotel Suite Refurbishment,c1995Simon Crone.(Bottom Row):Noisy Venus model and its smoothed version using trilateral?lter.c The Eurographics Association2003.