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IEICE TRANS. FUNDAMENTALS, VOL.Exx–??, NO.xx XXXX 200x 1 PAPER A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem Yuma KINOSHITA , Student Member, Kouki SEO , Artit VISAVAKITCHAROEN , Nonmembers, and Hitoshi KIYA a) , Fellow SUMMARY We propose a novel hue-preserving tone map- ping scheme. Various tone mapping operations have been studied so far, but there are very few works on color distortion caused in image tone mapping. First, LDR images produced from HDR ones by using conventional tone mapping operators (TMOs) are pointed out to have some distortion in hue values due to clipping and rounding quantization processing. Next,we propose a novel method which allows LDR images to have the same maximally saturated color values as those of HDR ones. Generated LDR images by the proposed method have smaller hue degradation than LDR ones generated by conventional TMOs. Moreover, the proposed method is applicable to any TMOs. In an experiment, the proposed method is demonstrated not only to produce images with small hue degradation but also to maintain well-mapped lu- minance, in terms of three objective metrics: TMQI, hue value in CIEDE2000, and the maximally saturated color on the constant- hue plane in the RGB color space. key words: Tone Mapping, Color Correction, Maximally Satu- rated Color, Hue Preservation 1. Introduction The interest of high dynamic range (HDR) imaging has recently been increasing in various area: photog- raphy, medical imaging, computer graphics, on vehi- cle cameras, astronautics. HDR images have the in- formation of the wide dynamic range of real scenes. However, commonly used display devices having low dynamic range (LDR) cannot express the information that HDR images have. In contrast, display devices which can directly represent HDR images are not pop- ular yet. Therefore, the importance of tone mapping (TM) operations has been growing in order to display HDR images on conventional LDR devices. Tone mapping (TM) operation generates LDR im- ages from HDR ones to display HDR ones on conven- tional LDR devices. Various research works on TM have so far been reported [1–13]. Most conventional studies have focused on compressing the luminance range of HDR images. In these methods, the range of the luminance of an HDR image is compressed by us- ing a TM operator (TMO), and then an LDR image is Manuscript received January 1, 2019. Manuscript revised January 1, 2019. The authors are with Department of Information and Commu nication Systems, Tokyo Metropolitan University, Hino-shi, 191-0065 Japan. a) E-mail: [email protected] DOI: 10.1587/transfun.E0.A.1 produced by combining the compressed luminance and the color information of the original HDR image. How- ever, TM operations only focusing on the luminance cause image colors to be distorted as pointed out in [14]. Mantiuk et al. [14] showed that the color distortion in tone-mapped LDR images occur due a tone curve, and they proposed a color correction formula on the basis of experimental results illustrating a relationship between the contrast-compression ratio and the saturation of the image. However, they only focused on tone curves as the cause of the color distortion, and other causes have never been considered. In this paper, we first point out that color distor- tion in tone-mapped images is primarily caused by clip- ping and quantizing pixel values of tone-mapped LDR images. Then, we propose a novel hue-preserving tone mapping scheme based on constant-hue plane in the RGB color space. The proposed method consists of two steps: tone mapping with an conventional method and compensating hue distorted by the tone mapping. The proposed compensation method utilizes the hue information based on the maximally saturated colors [15, 16], for suppressing color distortions due to the tone mapping. The compensation is done by replac- ing the hue information of a tone-mapped LDR image with that of the original HDR image. Hue-preserving image-processing methods have already been developed in various research areas such as image enhancement and noise reduction [15, 17–22]. These methods per- form some operations under the conditions that the hue is fixed. In contrast, there are very few hue-preserving TM operations [14], and the proposed hue compensa- tion method is independently performed from TM. This approach enables us not only to reduce color distortion, but also to maintain advantage of conventional TMOs. To evaluate the effectiveness of the proposed method, we performed a number of simulations. In the simulations, the proposed method was compared with conventional TM operations in terms of the hue difference used in CIEDE 2000 [23] and the maximally saturated color difference. Experimental results showed that the hue difference between tone-mapped LDR im- ages and the original HDR images can be reduced by applying the proposed method. Moreover, results of ob- jective quality evaluation with the tone mapped image quality index (TMQI) [24] illustrated that the proposed Copyright c 200x The Institute of Electronics, Information and Communication Engineers arXiv:1908.06557v1 [eess.IV] 19 Aug 2019
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Page 1: A hue-preserving tone mapping scheme based on constant …

IEICE TRANS. FUNDAMENTALS, VOL.Exx–??, NO.xx XXXX 200x1

PAPER

A hue-preserving tone mapping scheme

based on constant-hue plane without gamut problem

Yuma KINOSHITA†, Student Member, Kouki SEO†,Artit VISAVAKITCHAROEN†, Nonmembers, and Hitoshi KIYA†a), Fellow

SUMMARY We propose a novel hue-preserving tone map-ping scheme. Various tone mapping operations have been studiedso far, but there are very few works on color distortion causedin image tone mapping. First, LDR images produced from HDRones by using conventional tone mapping operators (TMOs) arepointed out to have some distortion in hue values due to clippingand rounding quantization processing. Next,we propose a novelmethod which allows LDR images to have the same maximallysaturated color values as those of HDR ones. Generated LDRimages by the proposed method have smaller hue degradationthan LDR ones generated by conventional TMOs. Moreover, theproposed method is applicable to any TMOs. In an experiment,the proposed method is demonstrated not only to produce imageswith small hue degradation but also to maintain well-mapped lu-minance, in terms of three objective metrics: TMQI, hue value inCIEDE2000, and the maximally saturated color on the constant-hue plane in the RGB color space.key words: Tone Mapping, Color Correction, Maximally Satu-rated Color, Hue Preservation

1. Introduction

The interest of high dynamic range (HDR) imaginghas recently been increasing in various area: photog-raphy, medical imaging, computer graphics, on vehi-cle cameras, astronautics. HDR images have the in-formation of the wide dynamic range of real scenes.However, commonly used display devices having lowdynamic range (LDR) cannot express the informationthat HDR images have. In contrast, display deviceswhich can directly represent HDR images are not pop-ular yet. Therefore, the importance of tone mapping(TM) operations has been growing in order to displayHDR images on conventional LDR devices.

Tone mapping (TM) operation generates LDR im-ages from HDR ones to display HDR ones on conven-tional LDR devices. Various research works on TMhave so far been reported [1–13]. Most conventionalstudies have focused on compressing the luminancerange of HDR images. In these methods, the range ofthe luminance of an HDR image is compressed by us-ing a TM operator (TMO), and then an LDR image is

Manuscript received January 1, 2019.Manuscript revised January 1, 2019.

†The authors are with Department of Information andCommu nication Systems, Tokyo Metropolitan University,Hino-shi, 191-0065 Japan.a) E-mail: [email protected]

DOI: 10.1587/transfun.E0.A.1

produced by combining the compressed luminance andthe color information of the original HDR image. How-ever, TM operations only focusing on the luminancecause image colors to be distorted as pointed out in [14].Mantiuk et al. [14] showed that the color distortion intone-mapped LDR images occur due a tone curve, andthey proposed a color correction formula on the basis ofexperimental results illustrating a relationship betweenthe contrast-compression ratio and the saturation of theimage. However, they only focused on tone curves asthe cause of the color distortion, and other causes havenever been considered.

In this paper, we first point out that color distor-tion in tone-mapped images is primarily caused by clip-ping and quantizing pixel values of tone-mapped LDRimages. Then, we propose a novel hue-preserving tonemapping scheme based on constant-hue plane in theRGB color space. The proposed method consists oftwo steps: tone mapping with an conventional methodand compensating hue distorted by the tone mapping.The proposed compensation method utilizes the hueinformation based on the maximally saturated colors[15, 16], for suppressing color distortions due to thetone mapping. The compensation is done by replac-ing the hue information of a tone-mapped LDR imagewith that of the original HDR image. Hue-preservingimage-processing methods have already been developedin various research areas such as image enhancementand noise reduction [15, 17–22]. These methods per-form some operations under the conditions that the hueis fixed. In contrast, there are very few hue-preservingTM operations [14], and the proposed hue compensa-tion method is independently performed from TM. Thisapproach enables us not only to reduce color distortion,but also to maintain advantage of conventional TMOs.

To evaluate the effectiveness of the proposedmethod, we performed a number of simulations. Inthe simulations, the proposed method was comparedwith conventional TM operations in terms of the huedifference used in CIEDE 2000 [23] and the maximallysaturated color difference. Experimental results showedthat the hue difference between tone-mapped LDR im-ages and the original HDR images can be reduced byapplying the proposed method. Moreover, results of ob-jective quality evaluation with the tone mapped imagequality index (TMQI) [24] illustrated that the proposed

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method can maintain the performance of conventionalTMOs.

2. PREPARATION

A general TM operation and the constant-hue plane inthe RGB color space are summarized, here.

2.1 Tone mapping

A general TM operation is summarized, here. A TMoperation consists of the following four steps.

(a) The world luminance Lw(p) of an HDR image IHis calculated from RGB pixel values of the HDRimage as,

Lw(p) = 0.27R(p) + 0.67G(p) + 0.06B(p) (1)

where R(p), G(p) and B(p) are RGB pixel values of theHDR image with a pixel p, respectively.

(b) The display luminance Ld(p) is calculated by usinga TMO.

(c) The floating-point pixel values Cf (p) of the LDRimage is calculated as follows:

Cf (p) =Ld(p)

Lw(p)C(p) (2)

where C(p) ∈ {R(p), G(p), B(p)} is the floating-pointRGB value of the input HDR image IH , and Cf (p) ∈{Rf (p), Gf (p), Bf (p)}. Besides, the gamma correctionis performed for Cf (p) as needed.

(d) The 8-bit color RGB values Ci(p) of the LDR im-age IL is derived from

Ci(p) = round(Cf · 255) (3)

where round(A) rounds A to its nearest integer value,and Ci(p) ∈ {Ri(p), Gi(p), Bi(p)}. Further, the valueof Ci(p) is redefined as follows:

Ci(p) =

0 (Ci(p) < 0)Ci(p) (0 ≤ Ci(p) ≤ 255)255 (255 < Ci(p))

(4)

where if Ci(p) takes a value over 255, it is clipped at255. Also, if Ci(p) takes a negative value, it is clippedat 0. The rounding quantization in Eq.(3) and clippingin Eq.(4) generate some error.

In the case of ”Photographic Tone Reproduction”[1] which is a typical TMO, the display luminance Ld(p)in step(b) is calculated in accordance with the follow-ing procedure. The geometric mean Lw of the worldluminance Lw(p) is calculated as follows:

Lw = exp(1

N

N∑p=1

logLw(p)) (5)

where N is the total number of pixels in the input HDRimage IH . The scaled luminance L(p) is calculated as

L(p) =α

Lw

Lw(p) (6)

Fig. 1 A conceptual diagram of the RGB color space

where α ∈ [0, 1] is the parameter called key value, whichindicates subjectively if the scene is light, normal, ordark. The display luminance Ld(p) is calculated byusing the TMO as follows:

Ld(p) =L(p)

1 + L(p)(7)

2.2 Constant hue plane in the RGB color space

We focus on the constant hue plane in the RGB colorspace [15] to discuss color distortion. An input imageis a 24-bit full color image and each pixel of the imageis represented as x ∈ [0, 1]3. xr, xg and xb are the R,G, and B components of the pixel x, respectively, asshown in Fig.1. In the RGB color space, a set of pix-els which has the same hue forms a plane, called con-stant hue plane. The shape of the constant hue plane isthe triangle whose vertices correspond to white, blackand the maximally saturated color, where w = (1, 1, 1),k = (0, 0, 0) and c are white, black and the maximallysaturated color with the same hue as x, respectively.The maximally saturated color c = (cr, cg, cb) is calcu-lated by

cr =xr −min (x)

max (x)−min (x),

cg =xg −min (x)

max (x)−min (x), (8)

cb =xb −min (x)

max (x)−min (x)

where max (·) and min (·) are functions that return themaximum and minimum elements of the pixel x, re-spectively. Therefore, from Eq.(8), the elements of ccorresponding to the maximum and minimum elementsof the pixel x become 1 and 0, respectively.

On the constant hue plane, a pixel x can be rep-resented as a linear combination as

x = aww + akk + acc (9)

whereaw = min(x),

ac = max(x)−min(x), (10)

ak = 1−max(x).

Since w,k, c and x exist on the plane and x is an inte-rior point of w,k and c, the following equations hold.

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Fig. 2 The framework of the proposed method

aw + ak + ac = 1, (11)

0 ≤ aw, ak, ac ≤ 1. (12)

3. PROPOSED HUE COMPENSATION

We propose a method for compensating hue values oftone-mapped images.

3.1 Hue distortion

Hue distortion occurs due to the influence of the fol-lowing three operations.

a) Tone curve in step (b)b) Rounding quantization in Eq.(3)c) Clipping in Eq.(4)

Mantiuk et al. pointed out that a) tone curve generatescolor distortion on the CIECAM02 color appearancemodel, and proposed a correction formula [14]. How-ever, they have never pointed out the influence of theoperations b) and c).

The framework of the proposed method is shownin Fig.2. As illustrated in Fig.2, the proposed methodcan be applied to any TMO and moreover the influenceof the above three operations can be considered.

Figure 3 shows an example of the difference of themaximally saturated colors between an original HDRimage and the tone-mapped LDR image including theinfluence of clipping and rounding quantization process-ing. Figure 4 shows an example of the maximally sat-urated color of an original HDR image and the tone-mapped LDR image. In these figures, the influence ofrounding quantization and clipping is demonstrated tocause color distortion.

3.2 HDR images on the constant hue plane

We consider giving HDR images the same pixel repre-sentation on the constant hue plane as LDR ones de-scribed in 3.1.

Each pixel of an HDR image is represented asxH = (xr, xg, xb) where xr, xg and xb are generallyreal numbers. As well as LDR images, we define white,black and maximally saturated color as w = (1, 1, 1),k = (0, 0, 0) and cH . Maximally saturated color cH ofthe HDR image is calculated by replacing x with xH

in Eq.(8), and then the pixel value xH is representedas a linear combination as

xH = aww + akk + accH (13)

where aw, ak and ac are coefficients which are calculatedin accordance with Eq.(10). For HDR images, w,k, cHand xH exist on the same plane in the RGB color space,but xH is not always an interior point of w,k and cH .That is, aw, ak and ac do not meet Eq.(12), althoughthey satisfy Eq.(11).

The proposed method aims to suppress some huedistortion included in LDR images mapped from HDRones. Now, let x′ be a pixel value of a tone-mappedLDR image that includes the influence of roundingquantization and clipping processing. In accordancewith Eq.(9), the pixel value x′ is expressed as follows

x′ = a′ww + a′kk + a′cc′ (14)

where c′ is a maximally saturated color calculated fromthe pixel value x′ by Eq.(8). a′w, a

′k and a′c are coeffi-

cients calculated by Eq.(10). Here, in general, c′ = cHis not met due to the above reasons. Therefore, to cor-rect the hue of x′, we replace x′ with x′′ as,

x′′ = a′ww + a′kk + a′ccH . (15)

Note that xH and x′′ are on the same constant hueplane.

3.3 Proposed procedure

The procedure of the proposed tone mapping scheme issummarized as follows.

(1) Generate an LDR image from an HDR image byusing a conventional TMO.

(2) Calculate the coefficients a′w, a′k, a

′c of the gener-

ated LDR image for each pixel value x′ in accor-dance with Eq.(10).

(3) Calculate the maximally saturated color cH of theoriginal HDR image by using Eq.(8).

(4) Calculate the pixel value x′′ = (x′′r , x′′g , x

′′b ) of

the compensated LDR image in accordance withEq.(15).

The R, G and B components of cH are in the range [0, 1]from Eq.(8). Therefore, the R, G and B components ofx′′ are also in the range [0, 1] even after compensation.This allows us to prevent clipping error.

The proposed scheme is applicable to any conven-tional TMO. In addition, it can consider all influencescaused in three operations described in 3.1.

4. Simulation

In an experiment, the proposed scheme was comparedwith conventional TMOs without any compensationand Mantiuk’s hue correction formula.

4.1 Simulation condition

We used 10 HDR images selected from an HDR imagedatabase [25] for the evaluation. The following is theprocedure of the evaluation.

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(a) (b) (c) (d)

Fig. 3 Difference of maximally saturated colors in ”Tree” where the ref-erence is the maximally saturated color of the original HDR image. (a)Tone-mapped image, (b) Difference (performed clipping & rounding), (c)Difference (performed only clipping), (d) Difference (performed only round-ing)

(a) (b)

Fig. 4 Maximally saturated color in ”Tree”. (a) Original HDR image, (b)Tone-mapped LDR image with clipping and rounding quantization

(1) Generate LDR images I ′L from prepared HDRimages IH by using four TMOs: Reinhard’sGlobal Operator [1], Reinhard’s Local Operator[1], Drago’s TMO [2], Fattal’s TMO [3], Shan’sTMO [4] and Gu’s TMO [5].

(2) Apply the proposed method to I ′L, and obtain com-pensated LDR images I ′′L.

(3) Compare I ′′L with I ′L and images corrected by Man-tiuk’s method.

4.2 Simulation results

A Hue distortion

We used two objective metrics to evaluate hue distor-tion caused in TM operations. One is the difference inthe maximally saturated colors between image I1 withM×N pixels and I2 with M×N pixels. it is calculatedby the following three steps.

(1) Calculate the maximally saturated colors c1(i), c2(i)from a pixel value x1(i) in I1 and x2(i) in I2, fromEq.(8), where xj(i) indicates the i-th pixel of im-ages Ij , j ∈ {1, 2}, and cj(i) is its the maximallysaturated color.

(2) The difference ∆c(i) between c1(i) and c2(i) for

each pixel is given by

∆c(i) = ‖c1(i)− c2(i)‖

where ‖ · ‖ is euclidean norm.(3) Calculate the average value ∆c of ∆c(i) over all

pixels.

The other is the hue differences in CIEDE2000,which was published by the CIE [23]. The difference ofhue values between two images was calculated as ∆H(i)for each pixel, and as the average value of all pixels ∆H.

Tables 1 and 2 show the evaluation results in termsof the objective metrics, where I1 is an HDR image andI2 is a tone-mapped image. ”Conventional” indicatesthat images were generated by a conventional TMOwithout any hue compensation. In the tables, the pro-posed method outperformed the conventional approachfor all TMOs. Therefore, the proposed method is ef-fective for improving hue distortion included in fusedimages in terms of not only ∆c but also ∆H. Notethat ∆c for the proposed method does not become zerovalue. This is because the rounding quantization hasto be carried out again to generate integer pixel values,although clipping does not be done. Figures 5, 6 and 7show some examples of the simulation results.

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Table 1 Simulation result (∆c)

Reinhard(global) Reinhard(local) Drago Fattal Shan GuImages Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop.

Apartment float 0.0766 0.0672 0.1405 0.1318 0.0198 0.0133 0.0136 0.0099 0.0472 0.0400 0.0132 0.0089dani belgium 0.0130 0.0104 0.0388 0.0315 0.0150 0.0036 0.0103 0.0036 0.0274 0.0217 0.0131 0.0053Desk 0.0227 0.0136 0.0655 0.0450 0.0276 0.0028 0.0166 0.0030 0.0439 0.0320 0.0238 0.0057Display1000 float 0.0222 0.0184 0.0830 0.0737 0.0137 0.0050 0.0127 0.0076 0.0269 0.0208 0.0170 0.0107memorial 0.0605 0.0429 0.1116 0.0973 0.0345 0.0054 0.0308 0.0016 0.0321 0.0028 0.0362 0.0032MtTamWest 0.0053 0.0024 0.0449 0.0121 0.0468 0.0009 0.0175 0.0081 0.0406 0.0300 0.0205 0.0065rend06 0.0159 0.0037 0.0463 0.0322 0.0204 0.0016 0.0396 0.0016 0.0411 0.0025 0.0518 0.0030rosette 0.0056 0.0035 0.0558 0.0062 0.0640 0.0008 0.0106 0.0023 0.0127 0.0044 0.0127 0.0025StillLife 0.0221 0.0029 0.0507 0.0190 0.0355 0.0007 0.0247 0.0009 0.0258 0.0020 0.0316 0.0022Tree 0.0434 0.0152 0.0844 0.0622 0.0435 0.0029 0.0213 0.0045 0.0216 0.0066 0.0223 0.0022

Table 2 Simulation result (∆H)

Reinhard(global) Reinhard(local) Drago Fattal Shan GuImages Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop.

Apartment float 0.8193 0.2674 0.4721 0.3147 0.4177 0.1720 0.2542 0.1514 0.4268 0.2959 0.2780 0.1281dani belgium 0.5589 0.3940 0.9748 0.7122 0.9940 0.4174 0.6488 0.3175 0.9644 0.6987 0.6961 0.3003Desk 2.6314 0.6395 3.3420 1.3861 3.9240 0.9566 2.0510 0.7582 2.1173 1.2641 2.9466 0.7737Display1000 float 0.4630 0.2664 0.9950 0.7335 0.6737 0.2687 0.4691 0.2634 0.6964 0.4213 0.5600 0.2615memorial 3.2015 0.4858 1.8574 0.7741 3.5305 0.2863 3.8368 1.5534 4.5643 1.3001 4.8098 1.6655MtTamWest 1.0522 0.5513 4.0217 1.8243 6.9016 1.9800 1.1497 0.2810 1.4351 0.5257 1.8670 0.2307rend06 1.9946 0.5657 2.0995 1.4428 1.7591 1.1248 8.4673 3.7136 9.3332 2.8647 13.5360 3.5505rosette 0.7701 0.4208 10.3067 4.9597 18.1123 2.9129 0.8894 0.9286 0.8983 0.9128 1.1258 0.9651StillLife 7.9052 2.5178 6.8135 2.8522 11.3119 4.9404 6.8368 3.8103 6.6331 3.5000 9.9990 4.8098Tree 6.4565 0.5583 3.2179 1.0439 5.6125 0.9509 2.1995 0.7863 1.9026 0.7583 2.7228 0.8890

Table 3 Simulation result (TMQI)

Reinhard(global) Reinhard(local) Drago Fattal Shan GuImages Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop. Conv. Prop.

Apartment float 0.8024 0.8029 0.8235 0.8241 0.7935 0.7941 0.7887 0.7887 0.7309 0.7310 0.8892 0.8894dani belgium 0.9219 0.9214 0.9011 0.9009 0.9072 0.9072 0.8542 0.8542 0.7368 0.7369 0.9489 0.9508Desk 0.9609 0.9535 0.9495 0.9407 0.9604 0.9443 0.8921 0.8815 0.7521 0.7510 0.8272 0.8335Display1000 float 0.9551 0.9537 0.8609 0.8596 0.9370 0.9363 0.7882 0.7873 0.7316 0.7311 0.8795 0.8782memorial 0.8271 0.8475 0.8563 0.8601 0.8325 0.8590 0.7978 0.7909 0.7894 0.7828 0.8553 0.8701MtTamWest 0.9673 0.9643 0.8936 0.8797 0.9518 0.9185 0.8052 0.8039 0.7798 0.7795 0.9267 0.9347rend06 0.9491 0.9441 0.8149 0.8108 0.9385 0.9277 0.7873 0.7758 0.7840 0.7644 0.9218 0.8241rosette 0.8265 0.8231 0.8469 0.8304 0.8136 0.7566 0.7968 0.7936 0.7632 0.7605 0.8741 0.8704StillLife 0.8825 0.8436 0.8211 0.7996 0.8611 0.8117 0.7272 0.7284 0.7423 0.7384 0.8230 0.8011Tree 0.9609 0.9430 0.9212 0.9117 0.9641 0.9473 0.8499 0.8407 0.7748 0.7701 0.8340 0.8381

Table 4 Comparison with Mantiuk’s method∆c ∆H

Images Conventional Mantiuk [14] Proposed Conventional Mantiuk [14] Proposeddani belgium 0.0505 0.0548 0.0467 1.8327 1.8655 1.6308memorial 0.0490 0.0548 0.0184 5.3609 5.5372 3.0708Tree 0.1123 0.1151 0.0894 6.7300 6.0663 3.3379

B Influence on tone mapping

Next, we evaluated the quality of tone-mapped LDRimages in terms of Tone Mapped image Quality Index(TMQI) [24], which is a well-known objective qualityassessment algorithm for tone-mapped images by com-bining a multi-scale signal fidelity measure based ona modified structural similarity (SSIM) [26] index anda naturalness measure based on intensity statistics ofnatural images. A higher TMQI score indicates higherquality.

From Table 3, the proposed scheme is shown tooffer almost the same TMQI scores as those of the con-ventional approach, but many of the scores slightly de-creased, due to the change of luminance caused by us-ing the proposed method. In contrast, the change ofluminance is easily corrected by adjusting the mean lu-minance of an image by multiplying all luminance val-ues by a constant. Figure 8 shows the image of ”Still-Life” in which TMQI is remarkably low compared withthe conventional method. By comparing Fig.8(b) withFig.8(c), it is confirmed that the slight change of lu-

minance caused by applying the proposed method waseasily corrected by the simple post-processing, so theTMQI score was improved, while maintaining ∆c and∆H.

4.3 Comparison with Mantiuk’s method

Finally, our method was compared with Mantiuk’s huecorrection formula [14]. We generated three LDR im-ages by using Durand’s TMO [6] as in [14], and bothour method and Mantiuk’s method were applied to theimages respectively. Table 4 shows the comparison re-sult. From the table, the our method is confirmed tooutperform Mantiuk’s method in terms of both ∆c and∆H. This is because Mantiuk’s method does not con-sider the influence of clipping and rounding quantiza-tion processing as described in 3.1. In contrast, the ourmethod can compensate hue distortion caused by threeoperations.

5. Conclusion

In this paper, we proposed a novel TM scheme that uti-lize maximally saturated colors calculated from original

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(a) Conventional (b) Proposed

Fig. 5 Simulation results with Reinhard’s global op-erator (Tree)

(a) Conventional (b) Proposed

Fig. 6 Simulation results with Reinhard’s local oper-ator (Desk)

(a) Conventional (b) Proposed

Fig. 7 Simulation results with Gu’s TMO (Desk)

HDR image on the basis of the constant hue plane in theRGB color space. The proposed method enables us tocompensate the hue distortion of the tone-mapped LDRimage caused by a conventional TMO, while maintain-ing TM performances that conventional TMOs have.Simulation results showed the effectiveness of the pro-posed method in terms of three objective metrics: ∆c,∆H and TMQI. Moreover, our method was comparedwith Mantiuk’s method to show the effectiveness.

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(a) Conventional(TMQI=0.8825, ∆c=0.0221,∆H=7.9052)

(b) Proposed(TMQI=0.8436, ∆c=0.0029,∆H=2.5178)

(c) Proposed with mean lu-minance adjustment(TMQI=0.8827, ∆c=0.0029,∆H=2.9721)

Fig. 8 Effects of mean luminance adjustment. (a)Tone-mapped image by Reinhard’s global operator, (b)Tone-mapped image by using the proposed method, (c)Imageadjusted from (b)

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Yuma Kinoshita received hisB.Eng. and M.Eng. degrees from TokyoMetropolitan University, Japan, in 2016and 2018, respectively. From 2018, he hasbeen a Ph.D. student at Tokyo Metropoli-tan University. He received IEEE ISPACSBest Paper Award in 2016, IEEE SignalProcessing Society Japan Student Confer-ence Paper Award in 2018, and IEEE Sig-nal Processing Society Tokyo Joint Chap-ter Student Award in 2018, respectively.

His research interests are in the area of image processing. He isa student member of IEEE and IEICE.

Kouki Seo has been a Beginer coursestudent at Tokyo Metropolitan Universityfrom 2015. His research interests includeimage processing.

Artit Visavakitcharoen receivedhis B.Eng. and M.Eng. degree fromKing Mongkut’s University of TechnologyThonburi, Thailand in 2013 and 2015, re-spectively. He currently studies in Ph.D.course at Tokyo Metropolitan University,Japan. His research interests include im-age processing.

Hitoshi Kiya received his B.E andM.E. degrees from Nagaoka University ofTechnology, in 1980 and 1982 respectively,and his Dr. Eng. degree from TokyoMetropolitan University in 1987. In 1982,he joined Tokyo Metropolitan University,where he became Full Professor in 2000.From 1995 to 1996, he attended the Uni-versity of Sydney, Australia as a VisitingFellow. He is a Fellow of IEEE, IEICEand ITE. He currently serves as President

of APSIPA, and he served as Inaugural Vice President (TechnicalActivities) of APSIPA in 2009-2013, and as Regional Director-at-Large for Region 10 of IEEE Signal Processing Society in 2016-2017. He was also President of IEICE Engineering Sciences So-ciety in 2011-2012, and he served there as Vice President andEditor-in-Chief for IEICE Society Magazine and Society Publi-cations. He was Editorial Board Member of eight journals, in-cluding IEEE Trans. on Signal Processing, Image Processing,and Information Forensics and Security, Chair of two technicalcommittees and Member of nine technical committees includingAPSIPA Image, Video, and Multimedia Technical Committee(TC), and IEEE Information Forensics and Security TC. He hasorganized a lot of international conferences, in such roles as TPCChair of IEEE ICASSP 2012 and as General Co-Chair of IEEEISCAS 2019. Dr. Kiya is a recipient of numerous awards, includ-ing six best paper awards.