Copyright c© 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR).

Tone Reproduction: A Perspective from Luminance-Driven Perceptual Grouping

Hwann-Tzong Chen Tyng-Luh Liu Tien-Lung ChangInstitute of Information Science, Academia Sinica

Nankang, Taipei 115, Taiwan{pras, liutyng, tino}@iis.sinica.edu.tw

Abstract

We address the tone reproduction problem by integratinglocal adaptation with global-contrast consistency. Manyprevious works have tried to compress high-dynamic-range(HDR) luminances into a displayable range in imitation ofthe local adaptation mechanism of human eyes. Neverthe-less, while the realization of local adaptation is not theo-retically defined, exaggerating such effects often causes un-natural global contrasts. We propose a luminance-drivenperceptual grouping process to derive a sparse representa-tion of HDR luminances, and use the grouped regions toapproximate local properties of luminances. The advantageof incorporating a sparse representation is twofold: We cansimulate local adaptation based on region information, andsubsequently apply piecewise tone mappings to monotonizethe relative brightness over only a few perceptually signif-icant regions. Our experimental results show that the pro-posed framework gives a good balance in preserving localdetails and maintaining global contrasts of HDR scenes.

1. IntroductionThe attempt to reproduce the visual perception of the realworld is at the heart of painting and photography. Artistshave long been endeavoring to develop skills in simulatingactual reflected light within the limitation of the medium,since our world generally delivers a much wider range ofluminances than pigments can reflect. Apart from artisticconcern, recreating real-scene impressions on limited mediais also inevitable in many vision and graphics applications.For example, the highest contrast of today’s LCD monitorsis around1, 000 to 1; however, we may still need to displaya sunset scene whose contrast exceeds10, 000 to 1.

By a tone reproduction problem, we focus on establish-ing an efficient method to faithfully reconstruct the high-dynamic-range (HDR) radiance on a low-dynamic-range(LDR) image. Thedynamic rangeof a digital image is sim-ply the contrast ratio in intensity between its brightest anddarkest parts. In [20], Ward introduces a floating-point pic-ture format to record HDR radiance in 32 bits per pixel, anddesigns a graphics rendering system that outputs images in

that format. Debevec and Malik have shown that HDR ra-diance ofreal scenes may be captured using regular SLRor digital cameras [5]. They propose a method to combinea series of pictures with different exposure settings into asingle HDR image, which is called aradiance map, withcontrast of about250, 000 to 1. In this context, the aim ofour research can be stated as solving the tone reproductionproblem of radiance maps, that is, generating a displayablestandard RGB image that preserves perceptual properties ofthe original HDR radiance map.

1.1. Related Work

Several works have been devoted to producing HDR imagesof real scenes [2], [5], [11], [12], including those that aredesigned to capture HDR luminances simultaneously undermultiple exposures [2], [11]. Inherently, panoramic imagingcan also be extended to carry HDR luminances by addingspatially varying optical filters to a camera [1], [16]. Dif-ferent from static HDR imaging, Kang et al. [9] proposeto generate HDR videos by changing the exposure of eachframe and then by stitching consecutive frames.

On displaying HDR images, tone reproduction addressesvisibility and impressionthrough finding an appropriatemapping to compress high contrasts into a visible (dis-playable) range, accounting for perceptual fidelity. With aglobal mapping, pixels are mappeduniformlyregardless oftheir spatial or local properties, and hence details are oftensmeared. The main advantage of using a global mappingis its efficiency. Ward et al. [21] describe a more sophis-ticated method to adjust contrast globally based on lumi-nance histograms. Nevertheless, the approach still smoothsout the details in areas of flat histograms. To improve visualfidelity, a number of tone reproduction methods have ex-plorednonuniform(local) mappings, as human visual sys-tem operates more likely this way [3], [6], [7], [8], [14],[19]. In particular, visual cells are organized in a center-surround manner so that we can see a wide range of lumi-nances by discriminating locally. In simulating the center-surround organization, Reinhard et al. [14] calculate, foreach pixel, the average intensity of apropercircular region,and then use the information to adjust a mapping function.

Decomposing a radiance map into layers is another pop-ular choice for preserving image details. Methods of thiskind often separate an image into anillumination layeranda reflectance layer. The illumination layer carries the lu-minance information of the original image and thus hasa wider dynamic range, while the reflectance layer keepsthe textures and is of low dynamic range. Consequently,the dynamic range of an HDR image can be reduced bycompressing its illumination layer. For images of naturalscenes, Land’s retinex theory [10] can be used to estimateillumination and reflectance. Indeed center-surround basedand layer-decomposition based methods are closely related.Both aim to preserve details and exploit local adaptation tomatch human perception. However, overemphasizing localcontrasts may produce halos, which are defects of reversalcontrasts. A number of new methods have been introducedto resolve halos by incorporating more appropriate local av-eraging schemes, e.g.,bilateral filtering [18] used in [6],[7], multi-scale Gaussians [3], and dodging-and-burning[14], or, by directly working on the gradient domain accord-ing to derived PDE formulations, e.g.anisotropic diffusion[19] and the Poisson equation [8].

From a segmentation viewpoint, Schlick [17] has pro-posed to divide an image into zones of similar values, andthen compute the average intensity of each zone. The av-erage intensity map can be used to constitute the spatiallynonuniform tone mapping function. Yee and Pattanaik [22]develop a multi-layer partitioning and grouping algorithmto compute the local adaptation luminance. In each layer,pixels are partitioned based on a given intensity resolution(bin-width), and pixels that are partitioned into the same binform a group. Each pixel’s local adaptation luminance valueis thus computed by averaging over all pixels of the groups(in different layers) to which the pixel belongs.

1.2. Our Approach

We describe an HDR tone reproduction method based onperceptual grouping in luminance. Since most tone repro-duction techniques are intended to construct appropriate av-erage luminances for local adaptation, we believe that it isworth investigating the perceptual grouping for approximat-ing the local characteristics of luminance. In our approach,the grouping process gives rise to a sparse representation foran HDR image so that it is possible to estimatelocal adap-tation luminances[3] based on perception-based region in-formation. As a result, we are able to consider the tonereproduction problem by taking account of local details andglobal perceptual impression. In the following sections, wedescribe first how to construct the local adaptation lumi-nances by perceptual grouping, and then explain how to usethe region information to modulate the mapping functionsfor tone reproduction.

2. A Sparse Representation for HDRImages

The luminance values of an HDR image can be com-puted from itsR, G, and B channels byL(x, y) =0.2126R(x, y) + 0.7152G(x, y) + 0.0722B(x, y). To re-duceL(x, y) into a low dynamic one, we propose asparserepresentationthat decomposes an HDR image into regionsthrough a perceptual grouping process. The dynamic-rangecompression is then carried outregion-wise, where the ad-vantages of using the perceptually significant region infor-mation will be explained in the next section. Suffice it to saynow that working on an adequate number of regions, we canperform the HDR compression without incurring excessiveoverheads in patching together the results across differentregions. On deriving such a decomposition, it takes twosteps:adaptive block partitionandperceptual grouping, de-tailed in what follows.

2.1. Adaptive Block PartitionPrevious experience on exploring perception has suggestedthat the human visual system senses the contrast of lightbased onintensity ratiorather thanintensity difference(e.g.,see the Weber’s law discussed in [13], p.672). Followingthis observation, we consider the decomposition of an HDRimage by examining its luminance property in the logarith-mic domain. More precisely, the luminanceL is trans-formed into log-luminance byL(x, y) = logL(x, y).

Understandably, the outcome of grouping depends on thechoice of thebasic elementof an image partition. Whileworking on pixel level is both time-consuming and sensi-tive to noise, we also find partitioning with blocks of uni-form size often leads to unsatisfactory segmentation results.Though the situation could be improved by using small-sizeblocks, such a tactic again has the drawback of inefficiency.We thus design an adaptive scheme to partition the imagewith blocks of two different sizes. The smaller blocks areplaced in the areas of strong log-luminance gradients; thelarger ones are in the areas of less log-luminance variation.

To partition the log-luminanceL adaptively, we useCanny edge detector [4] to obtain the edge information, andthen divideL into blocks of larger sizebℓ × bℓ. For thoseblocks containing Canny edges, they are further split intoblocks of smaller sizebs × bs. An example to illustratethese steps is given in Figure 1, where block sizesbℓ = 8andbs = 2 are used in all our experiments too.

2.2. Perceptual GroupingAmong the many possible ways to group the blocks, weare interested in finding a sparseness one, driven by thelog-luminance factor. For that, we look at two importantmatters: 1) how to define an appropriate distance function

Figure 1:Garage.From left to right, the corresponding log-luminanceL; the adaptive block partition ofL, where blocksof the smaller size are located in those shaded areas on top ofthe Canny edges; a sparse representation of8 regions forL;and the displayablegarageimage derived by our method.

to measure the degree of similarity between two regions,and 2) how to proceed with a reasonable grouping processto derive a sparse representation. These two issues canbe properly addressed through integrating aperceptual dis-tancewith a luminance-driven grouping process.

2.2.1 Perceptual Distance

We use theearth mover’s distance(EMD) to evaluate theperceptual similarity between two image regions [15]. Ap-plied mostly in image retrieval, EMD has been proven tobe a useful measurement to perceptually correlate two im-ages. In fact, finding the EMD between two distributions isequivalent to solving aminimum cost flowproblem.

The objects involved in the calculation of EMD are oftenrepresented in the form ofsignature. A signature is a setof clusters of which each cluster comprises a pair of featureand weight. In our formulation, the signature of a region(could be just a block or a region of many blocks) is com-puted as follows. We equally divide the dynamic range ofthe region into three bins. The meansi and the numberhi of the pixels in each bin are then calculated. It also di-rectly implies the weight of each bin iswi = hi/

∑

j hj.Thus, the signaturep of each region contains three clusters{(s1, w1), (s2, w2), (s3, w3)} that accordingly represent thebright, the middle-gray, and thedark part of that region.Written explicitly, the perceptual distance between two re-gionsR1 andR2 is defined by

D(R1,R2) = EMD(p1,p2), (1)

wherepi is the signature of regionRi.

2.2.2 Luminance-Driven Grouping

How to optimally decompose an image is a cognitive prob-lem. While analytic arguments are difficult to establish, weprefer a compact/sparse representation to decompose an im-age intofew regions (see Figure 1). Specifically, we adopta greedy approach to grow a new regionas large as pos-sible, starting each time from the location of thebrightest

log-luminance value in the unvisited areas. That is, the al-gorithm follows abrightest-block-firstrule to determine theseeds and to merge image blocks. Since each block’s signa-ture includes three clusters, i.e., the bright, the middle-gray,and the dark parts, the brightest block can be simply identi-fied as the one with the largests1.

All image blocks are initially marked asunvisited. Lateron as the grouping process iterates, the number of unvisitedblocks decreases. At iterationk, we pick the unvisited andbrightest block, say, blockBi∗ , and start to grow the regionRk from it. These steps of region grouping are summarizedin Algorithm 1. Upon termination, the process will yielda decomposition that each derived region consists of con-nected blocks of similar luminance distributions. Indeed,our algorithm works by balancing the local and global simi-larity in a region. Similar blocks are pulled into the same re-gion if the EMD between two neighboring blocks is smallerthanδ. On the other hand, a region will stop growing whenall blocks right beside the region boundary are not closeenough to the whole region withinθ. (See Algorithm 1 forfurther details.) The typical values of EMD thresholdθ arefrom 1.5 to 2.0, and those ofδ are between0.5 and1.0.

3. Region-Based Tone MappingOur method to compress the high dynamic range relies onregion-wise constructing suitable tone mapping functions,based on the estimations oflocal adaptation luminances.It is also critical that the resultingpiecewise tone map-pingscould be smoothly pieced together to produce a good-quality and displayable image without violating the overallimpression of the original HDR radiance map. In this sec-tion, we will show that all these issues can be satisfactorilyaddressed by considering the region information encoded ina luminance-driven sparse representation.

3.1. Local Adaptation LuminancesHuman visual system attains the HDR perception by lo-cally adapting to different levels of luminance to ensure aproper dynamic range can be recreated by the responses of

Figure 2:Stanford memorial.From left to right, the respective results derived bybilateral filtering [7], photographic tonereproduction[14], our method, andgradient domain[8]. Our method not only reveals fine details but maintains a globalimpression similar to that of the photographic [14].

visual cells. For tone reproduction, the local adaptation ef-fect is often simulated by computing the local adaptationluminance. Thus it is important to have a reliable way forpixel-wise estimating the local adaptation luminance of anHDR image. And that in turn can be done by investigat-ing the average log-luminance of asuitable neighborhoodabout each pixel.

Let V (x, y) be the local adaptation log-luminance atpixel (x, y). To computeV , we consider a generalizedversion ofbilateral filtering [18] by constructing a region-dependent scheme such that the computation ofV (x, y)takes account of bilateral effects from different regions.Par-ticularly, for each pixel(x, y) in regionRk, we have

V (x, y) =1

Zx,y

{

∑

(i,j)∈Rk

L(i, j)Gx,y(i, j)Kx,y(i, j)

+∑

(i,j)/∈Rk

L(i, j)Gx,y(i, j)K′

x,y(i, j)

}

,

(2)

where

Gx,y(i, j) = exp{

−(

(i− x)2 + (j − y)2)

/2σ2s

}

Kx,y(i, j) = exp{

−(

L(i, j)− L(x, y))2/2σ2

r

}

K′

x,y(i, j) = exp{

−(

L(i, j)− L(x, y))2/2σ2

r′

}

Zx,y =∑

(i,j)∈Rk

Gx,y(i, j)Kx,y(i, j)

+∑

(i,j)/∈Rk

Gx,y(i, j)K′

x,y(i, j) .

Eq. (2) includes two parts of bilateral filtering. The firstpart calculates the averaging in the same region, and the

second evaluates the contributions from other regions. Notethat we have used the same spatial-domain filterGx,y toregulate the effects to pixel(x, y) from all regions. Sucha choice makes it possible to apply the fast bilateral filter-ing implementation described in [7]. On the other hand, wehaveσr ≥ σr′ to ensure a flatter and more expanded range-domain filterKx,y for pixels in the same region of(x, y),and to lessen the influences from pixels of different regionswith K ′

x,y. If σr = σr′ , the proposed scheme in (2) is re-duced to the one used in [7]. With the region-based filtering,the effects of local adaptation inside perceptually related re-gions can be enhanced by using a largerσr . A suitable valuefor σs can be set to4% of the image size, andσr = 0.4 andσr′ = 0.5 × σr. So far, we have worked in log-luminancedomain. The local adaptation luminance, denoted asV , canbe recovered byV = exp(V ).

3.2. Piecewise Tone MappingsA handy choice of simple functions for compressing thehigh luminances into the displayable range[0, 1] is the non-linear mappingϕ(x) = x/(1 + x). If ϕ is applied to thewhole luminance map, i.e.,L′ = ϕ(L) = L/(1 + L), wewill actually obtain a displayable but smoother image. Thistype of compression scheme is calledglobal mappingorspatially uniform mapping. Another tone mapping methodis to extract fromL the detail layerH byH = L/V . Then,only the local adaptation luminance is compressed byV ′ =ϕ(V ). Recombining the detail layerH with the compressedV ′, we haveL′ = H × V ′ = (L/V ) × (V/(1 + V )) =L/(1 + V ), a local mappingfor preserving details.

Even though a global mapping likeϕ often has the draw-back of losing the details in brighter areas, its monotoneproperty (dϕ/dx > 0) is desirable for preventing halos

Algorithm 1: Luminance-Driven Grouping with EMD.

Input : The adaptive block partitionB of L.Output: A sparse representation ofL.

Initialization: Create an empty priority queueQ onDas in (1); Compute the signatures of all blocks; Labelall blocksunvisited; Let k← 1; Chooseθ, δ > 0.while ∃ unvisited blockdo

Create a new regionRk ← ∅, and letQ ← ∅;Select the brightest blockBi∗ and add it intoQ;LetD(Bi∗ ,Rk)← 0;while Q 6= ∅ do

RetrieveBi fromQ with the smallestD(Bi,Rk);if D(Bi,Rk) < θ then

AddBi intoRk and labelBi visited;UpdateQ by recomputing theDs;FindBi’s unvisitedneighbors{Bj};foreach Bj satisfiesD(Bj,Bi) < δ do

InsertBj intoQ;Update the signature of regionRk.

elseGoto 1.

k ← k + 1.1

Output allRks.

and other artifacts. It would be favorable if the monotonic-ity can be incorporated into a local tone mapping method.Nonetheless, one still needs to figure out a reasonable wayto monotonizea local mapping and determine an appropri-ate “neighborhood” for each such a monotonization.

We argue here that the sparse representation does pro-vide useful hints for solving the foregoing problems. Per-ceptually, the derived region decomposition correlates withan overall visual impression about the scene. Maintainingthis impression after compressing the dynamic range shouldbe a good criterion. We thus consider apiecewise tone map-pingscheme that region-wise performs the monotonization,and globally retains the relative brightness among differentregions, i.e., thoseRks derived in Algorithm 1. The wholeidea of such tone mappings is realized by the following foursteps:

1. Design a local mappingψ. As pointed out in Sec. 3.1,the local adaptation luminanceV plays an importantrole in compressing the luminanceL. We define a localmappingψ of the following form.

ψ(L, V ; ρ, γ) =(L

V

)ρϕγ(V ) =

(L

V

)ρ( V

1 + V

)γ,

(3)

where0 < ρ < 2 and0 < γ ≤ 1 are spatial-dependent

100 150 250

200

150

100

50

0

250 300 350200

0.8

0.40.3

1.4

1.8

0.6

1.2

1.0

1.6

21.5

1

00.5

0 50

ρ surface

ρ value

Figure 3: Theρ values after kernel smoothing. Examplesof correspondences to the log-luminance and to the regiondecomposition are illustrated.

parameters to adjust the image quality resulting fromthe HDR compression. More precisely, whenγ < 1,dark areas in an HDR radiance map will be compressedinto larger brightness levels, compared with the caseγ = 1. On the other hand, sinceL/V is the detaillayer, theρ values would have direct impacts on pre-serving the image details after the dynamic-range re-duction. (In all our experiments,γ = 0.3.)

2. Globally reshapeϕγ by ϕγ = αϕγ +β. LetLmax andLmin be the maximum and the minimum luminancevalues of a given radiance map, respectively. To makesureϕγ will take up the complete displayable range[0, 1], we solve the following linear system to obtainthe proper scaling and shifting parametersα andβ:

[

ϕγ(Lmax) 1ϕγ(Lmin) 1

] [

αβ

]

=

[

10

]

. (4)

The values ofα andβ will be needed in monotonizingthe local mapping of each regionRk.

3. Estimateρ by kernel smoothing.For eachRk, we con-struct a gridDk within Rk such that it is the largestgrid of resolutionǫ × ǫ with all its grid points at leastǫ-pixel away from the region boundary∂Rk. Wethen assign some preliminaryρn value to each pixeln ∈ Dk by

ρn =

γ , if log(Ln/Vn) ≤ −1,

(γ + ρmax)/2 , if log(Ln/Vn) ≥ 1,

ρmax , otherwise.

(5)

LDR

PerceptualGrouping

RegionwiseEMD

Bilateral

Local AdaptationLuminance

Piecewise

ToneFiltering Mapping

LDR LuminanceLog−LuminanceImageHDR

RadianceMap

Log−LuminanceSparse Regions

L = logL Rks V = exp(V ) L′ = αk( LV

)ρ( V1+V

)γ + βk

Figure 4: The steps of our tone reproduction method.

The above rules simply reflect that ifLn is already“very different” from its local adaptation luminanceVn, using a largerρn may only cause an inconsistentoveremphasis that further amplifies the difference. Inaddition, for all pixels on∂Rk, theirρn values are alsoset toγ, and those of the pixels betweenDk and∂Rk

can be computed by interpolation. It will later becomeclear that putting such constraints near∂Rk will be vi-tal in constructing an overall smoothρ surface acrossregions. With all theseρn values pre-defined, we cannow applykernel smoothingto adjust and to derive theρ values for all pixels inRk. Notice that, throughoutthis work, we haveρmax = 1.8 andǫ = 4.

4. Monotonize local tone mappings.A monotonization,say forRk, is to estimateαk andβk so that a localmappingψ in (3) can be elevated toψ = αkψ + βk,and to account for both local and global factors in com-pressing the luminances. We begin by samplingN pix-els from∂Rk according to the sorted| log(Ln/Vn)|values in ascending order. In our experiments, usingthe first 5% of boundary pixels will be sufficient togive good results. The values ofαk andβk can nowbe obtained by calculating the least square solution of[

ψ1 · · · ψN

1 · · · 1

]T [

αk

βk

]

=[

ϕγ1 · · · ϕγ

N

]T.

Finally, we applyψ(L, V ; ρ, γ) = αkψ(L, V ; ρ, γ) +βk to each pixel(x, y) ∈ Rk to compute its dis-playable luminance valueL′(x, y).

The least square fitting to reshapeψk into ψk can bejustified by the facts that the monotonization uses onlypixels on region boundary and theirρ values after kernelsmoothing are still close toγ. Furthermore, with this prop-erty, we can efficiently derive a globally smoothρ surface(see Fig. 3). We conclude this section with a remark thatthe main characteristic of our method is to perform thedynamic-range compression by emphasizing the local de-tails of each region without breaking the global visual con-sistency.

4. Experiments and DiscussionsHaving detailed our approach (summarized in Fig. 4), wenow describe some of our experimental results and compar-isons with other related works. In all our experiments, the

HDR images are downloaded from the Web and stored inradiance map format. A typical radiance map with multipleexposure values is shown in Fig. 5. (In this example, thedynamic range ofStanford memorialis 250, 000 : 1.)

Figure 5: Radiance map. By setting a fixed displayablerange and cutting off out-of-range intensities, the radiancemap can only be viewed like these images.

The bottlenecks of our method lie in the steps of EMDperceptual grouping and region-wise bilateral filtering. Forthememorialimage of size 512 by 768 in Fig. 5, the elapsedtime of perceptual grouping and of bilateral filtering on a2.4GHz PC is about 3.6s and 5.3s, respectively. Clearly, thecomplexity of region-wise bilateral filtering depends on thenumber of regions. By extending fast bilateral filtering [7]to incorporate region support, we can implement a region-wise bilateral filter in a way that slowdowns are not propor-tional to the number of regions. For instance, ten regionsare constructed for thememorial, but region-wise bilateralfiltering (≈ 5.3s) just doubles the time needed for a typicalbilateral filtering (≈ 2.4s).

After luminance reduction, the LDR image can be dis-played by multiplying the compression ratioL′/L to eachof the high dynamic rangeRGB channels. In Fig. 6, weshow several LDR images derived by our method. Ourresults have two aspects of visually pleasing effects: 1)Overall impressions of luminance are maintained; 2) De-tails and local high contrasts are preserved. Some recentmethods [7], [8], [14] on displaying HDR images also caneliminate halos and preserve details. The gradient-domaincompression [8] performs well in preserving local contrastsand details. However, a noticeable difference between theircompression outcomes and ours is that in their results thebrighter areas may not be bright enough as they should be.A good example is the circular window of thememorialinFig. 2. Note that, in the original radiance map, the area ofthe circular window is at least 200 times brighter than thetop-right corner.

Figure 6: HDR tone-reproduction results. From left to rightand top to bottom (with the number of derived regions):Tahoe(5), office(68),Belgium(32),clock(34),designCenter(13),Tintern(14),chairs(14), andgroveC(17).

While our approach relates to photographic tone repro-duction [14] and bilateral filtering [7] in computing the localadaptation luminance, our method generally produces bettercontrasts within the displayable range, and preserves moredetails due toγ parameter and flexibleρ values. Again, theexamples in Fig. 2 well demonstrate these common phe-nomena. In addition, we highlight another two distinctionsin Fig. 7. The first one is that although the photographicmethod [14] basically maintains overall impressions, some-times the approximate local adaptation luminance decreasesthe brightness of a large bright area, e.g., the sun in Fig. 7a.Owing to piecewise tone-mapping, our results do not havethis anomaly, e.g., Fig. 7b. The second distinction is that thebilateral filtering method [7] still generates some halos nearthe boundaries between bright and dark regions. The differ-ences can be observed near the skyline and near the shadowsin Fig. 7c and 7d. Via a smoothρ-surface adjustment, ourmethod produces a bit lower contrasts along boundaries.

In passing it is worth mentioning that, like [8], our tone-reproduction method can also be used to enhance the imagequality of an LDR image. We experiment on this effect byapplying the same process listed in Fig. 4 to LDR images.We obtain fairly good results, compared with those by [8]and histogram equalization functions in MATLAB toolbox.One example of the results is provided in Fig. 7e, 7f.

5. ConclusionWe have thoroughly investigated the tone reproductionproblem in two aspects: 1) deriving local adaptation lumi-nances for preserving details, and 2) region-wise compress-ing the dynamic range without breaking the overall impres-sion. For a visual model, thecorrectnessof the local adap-tation mainly depends on the definition oflocality. We thusintroduce a luminance-driven perceptual grouping to derivea sparse representation for HDR luminances, based on theEMD perceptual distance. With the sparse image decom-position, we are able to improve both the local adaptationluminances and the tone mapping functions. Consequently,a region-wise bilateral weighting scheme can be formulatedto enhance the local adaptation effect inside a region. Asfor piecewise tone mappings, we apply monotonizations toincorporate the global property into local tone mappings sothat the brightness impression of a scene is maintained.

Acknowledgments. This work was supported in partby an NSC grant 93-2213-E-001-010.

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