Tone Mapping for HDR Images with Dimidiate
Luminance and Spatial Distributions of Bright and Dark Regions
Masaki Kitaura, Fumio Okura, Masayuki Kanbara and Naokazu Yokoya
Graduate School of Information Science, Nara Institute of Science and Technology,
Takayama 8916-5, Ikoma, Nara, 630-0192, Japan
ABSTRACTThis paper proposes a novel tone mapping method in consideration of characteristics of human visual perception for ahigh dynamic range (HDR) image with dimidiated luminance and spatial distributions of bright and dark regions. In
order to represent an HDR image with a low dynamic range (LDR) display, it is necessary to appropriately compress adynamic range of HDR image by a tone mapping. There are some HDR images which cannot be re-represented with an
LDR display precisely by applying a conventional tone mapping method. In this study, we focus on an HDR image withdimidiated luminance and spatial distributions of bright and dark regions as a target image. We assume that human visual
perception does not feel a sense of discomfort even if a magnitude relationship between luminance values of pixels near
the boundary between bright and dark regions is reversed when these regions are definitely divided according to dimidiatedluminance and spatial distributions. Under this assumption, we divide an HDR image into bright and dark regions andapply a different tone mapping function to each region independently. In experiments, we show that the proposed tone
mapping method produces the image represented by using a dynamic range effectively. In addition, we confirm that the
proposed tone mapping method is useful through subjective evaluation and discuss the features of the HDR images suitable
for the proposed method.
Keywords: tone mapping, high dynamic range, HDR, segmentation

1. INTRODUCTION
High dynamic range (HDR) image has attracted much attention to capture and represent the real scenes precisely. In
general, an HDR image is produced by the method1, 2 which combines multiple images captured with different exposure
settings into a single HDR image. Each pixel of an HDR image has gradation value more than 8-bit like a normal low
dynamic range (LDR) image. In order to display an HDR image on a standard LDR display which can represent gradation
value of 8-bit, it is necessary to appropriately compress a dynamic range of the HDR image by using tone mapping.
A lot of related works of tone mapping have been proposed. Reinhard et al.3 have proposed a tone mapping method
which applies the traditional techniques of photographic practice, such as the Zone System and dodging-and-burning. Fattal
et al.4 have focused on the change of gradients and have developed the tone mapping method which can represent detailed
textures of the HDR image by compressing the higher contrast parts more than the lower contrast parts. However, thesemethods implicitly have the restriction to keep a magnitude relationship between luminance values of pixels in the image,and thus a dynamic range is limited in a generated LDR image. It is difficult for the method of Reinhard3 to represent theenough textures of bright and dark regions in an HDR image, and the method of Fattal4 has the problem that the resulting
image looks like a painting containing a gradation which does not exist in original image.
In order to overcome these problems, Yee et al.,5 Chen et al.6 and Krawczyk et al.7 have proposed tone mapping
methods based on local adaptation mechanism in human visual perception. They divide an HDR image into regions basedon luminance distributions and then apply tone mapping according to the computed local adaptation luminance. Since amagnitude relationship between luminance values of non-adjacent pixels is allowed to be reversed, a dynamic range can beused more effectively than other conventional methods. However, in order to avoid uncomfortable feelings to the resulting
image, it is necessary to keep a magnitude relationship between luminance values of adjacent pixels. In other words, since
the amount of change of luminance values between adjacent pixels is limited successively over the whole image so that a
Further author information:
M.K,F.O,M.K,N.Y: E-mail: {masaki-ki, fumio-o, kanbara, yokoya}@is.naist.jp

Figure 1. An example of image with dimidiate luminance and spatial distributions of bright and dark regions.

Figure 2. Tone mapping curves.

dynamic range of each region used for representation is limited, there are some HDR images which cannot represent thereal scene precisely.
In this paper, we propose a tone mapping method for HDR images with dimidiate luminance and spatial distributionsof bright and dark regions; for example, images captured in a scene where both outdoor and indoor regions are included.
Figure 1 is such an example of HDR images with dimidiate luminance and spatial distributions of bright and dark regions.
Under the condition like the scene of Figure 1, we assume that human visual perception does not feel a sense of discomfort
even if the magnitude relationship between luminance values of pixels near the boundary of bright and dark regions isreversed. Under this assumption, the proposed method divides an HDR image into bright and dark regions and applies
a different tone mapping method to each region independently. Figure 2 illustrates tone mapping curves which represent
the relationships between luminance value of HDR image and that of LDR image. In this study, by restricting the target
images, the magnitude relationship between luminance values of pixels is allowed to be reversed so that a dynamic rangeof each region is able to be utilized effectively.

2. TONE MAPPING APPLIED TO DIMIDIATE BRIGHT AND DARK REGIONS INDEPENDENTLY
2.1 Outline of proposed tone mapping method
Our method focuses on an HDR image with dimidiate luminance and spatial distributions of bright and dark regions andaims to produce an image which uses a dynamic range of each region effectively by applying a different tone mapping toeach region independently. The proposed method consists of the following two processes.

1. Segmentation of HDR image into bright and dark regions.
2. Conversion of luminance values in bright and dark regions.

2.2 Segmentation of HDR image into bright and dark regions
In the first step, it is necessary to apply the method which divides an image into regions interactively and in consideration of
the boundaries of regions, because the HDR image should be segmented based on the spatial regions which human visual
perception recognizes. According to this requirement, GrabCut algorithm,8 which is one of the interactive and robust
segmentation methods in manipulation of boundaries, is employed in this study. In the first step of GrabCut,8 segmentation
using iterative graph cut is performed. This is followed by border matting in which alpha values are computed in a narrow
part around the segmentation boundary. Full transparency, other than at the border, is not dealt with by GrabCut.8 Thismethod requires the user simple interactions and the user can indicate target regions easily. In addition, computation ofalpha values used for border matting reduces visible artifacts. Figure 3 shows an example of segmentation with GrabCut8
for the input image as shown in Figure 1.

2.3 Conversion of luminance values in bright and dark regions
In the next step, tone mapping is applied to divided bright and dark regions in the HDR image independently. Our method
does not limit the tone mapping method applied to each region. In addition, if either bright or dark region consists ofsome small regions, the region is divided into small regions additionally and tone mapping is applied to further segmented
regions independently. As a tone mapping method applied to each region in our implementation, we have employed themethod of Reinhard,3 which is one of the representative tone mapping methods and designed for wide variety of images.
Figure 4 shows a resulting image by the proposed method employing the tone mapping method of Reinhard.3
2.3.1 Tone mapping method of Reinhard
This section briefly reviews the tone mapping method of Reinhard,3 which scales luminance values of input HDR images
according to the criterion value which is computed from a dynamic range of HDR image to be luminance value of middle
part of the dynamic range in the resulting image. In addition, it works to decrease luminance values of bright regions andto increase luminance values of dark regions locally. We first show how to compute the criterion value to be the luminancevalue of middle part of the dynamic range in the resulting image. Like a lot of related works of tone reproduction,9–11
we view the log-average luminance value as a useful approximation to the criterion value in the scene. This log-averageluminance value L̄w is computed by
)
(
∑
1
L̄w =
exp
log (δ + Lw (x, y)) ,
N
x,y

(1)

where Lw (x, y) is the input luminance value for pixel (x, y), N is the total number of pixels in the image and δ is a smallvalue to avoid the singularity that occurs if black pixels exist in the image. The whole image is scaled by L̄w as follows:
L(x, y) =a
Lw (x, y),
L̄w

(2)

where L(x, y) is a scaled luminance value and a is a parameter. Parameter a has influence to the image after applying
the above scaling. Besides, according to the fact that modern photography prefers applying transfer curves which mainlycompress the high luminance values, the effect that high luminance values are compressed strongly is added to the Equation(2):
Ld (x, y) =L(x, y),1 + L(x, y)(3)

where Ld (x, y) is the luminance value after scaling. In Equation (3), high luminance values are scaled by approximately
1/L, while low luminance values are scaled by 1. The denominator causes a graceful blend between these two scalings.
This formulation is guaranteed to bring all luminance values within displayable range. However, Equation (3) is not always

Figure 3. An example of segmenting Figure 1 by GrabCut.8

Figure 4. Tone-mapped image generated from Figure 1 by the proposed method.

desirable in compressing high luminance values. Equation (3) can be extended to allow high luminance values to burn out
in a controllable fashion by using the following equation.

Ld (x, y) =L(x, y)(1 + LL(x,y)
)
2
white

1 + L(x, y),(4)

where Lwhite represents the smallest luminance value that is mapped to pure white. This function is a blend between
Equation (3) and a standard linear mapping. If Lwhite value is set to the maximum luminance value in the scene or higher,
no burn-out occurs. If it is set to infinity, then the function reverts to Equation (3). By default, we set Lwhite to the
maximum luminance value in the scene.
Reinhard’s3 tone mapping method described here is originally applied to the whole image. It should be noted that inthis study the log-average luminance value L̄w and parameter a of each region are computed and set respectively.

3. EXPERIMENTS
3.1 Acquisition of HDR images
In experiments, we have used two kinds of HDR images as input images. One is the HDR image produced by combining
multiple images captured with different exposure settings. The other is the set of benchmark HDR images.12, 13 The former
is generated by combining multiple images using a high dynamic range image editing software14 after a series of pictureswith different exposure settings were taken by using the auto bracket function of the digital single-lens reflex camera(K-7,
PENTAX). The latter is selected from HDR images shown in the work12 and the website.13

3.2 Results of the proposed tone mapping method
In this section, we show the results of applying the proposed method to a number of HDR images and compare themwith those by Reinhard’s3 and Fattal’s4 methods. Figure 5 shows the tone mapping results of three methods for HDR
images generated by combining multiple images captured with different exposure settings. Figures 6 and 7 are the tone
mapping results for benchmark HDR images. Generally, images generated by the method of Reinhard3 contain regions
where highlights and shadows appear since a dynamic range to represent each region run short. For example, in Figure5(a), the indoor region has a high percentage of pixels of low luminance values. In Figure 6(a), the outdoor region mainly
consists of pixels of high luminance values, so that it is difficult to recognize textures of each region.
The images generated by the method of Fattal4 clearly represent bright and dark regions by using dynamic ranges
effectively and the textures can be recognized. However, due to the nature of this method that maintains the magnituderelationship between luminance values of adjacent pixels, luminance values drastically change near the boundary of brightand dark regions. It can be observed that artifacts like gradation, which does not exist in the original image, appears near
the window frame parts of Figures 5(b) and 6(b).
Compared with these two conventional methods, the images generated by the proposed method, as shown in Figures5(c) and 6(c), are represented by effectively utilizing dynamic ranges of bright and dark regions. This is due to the tone
mapping applied to each of bright and dark regions independently. The artifacts of gradation caused by the method of
Fattal4 are not generated by applying the tone mapping to each region independently. In additon, the stained grass partsin Figure 7(c) generated by the proposed method have precisely represented textures in contrast with the results of otherconventional methods. From these results, we can confirm that human visual perception does not feel a sense of discomfort
even if the magnitude relationship between luminance values in different regions is reversed. In the next section, we firstshow the results of subjective evaluation, in which we compare the proposed method with the methods of Reinhard3 andFattal.4 We then discuss the features of images suitable for the proposed method.

3.3 Subjective evaluation
3.3.1 Preparation
In order to confirm the usefulness of the proposed method and investigate the features of HDR images which are suitable
for the proposed method, we have conducted an experiment of subjective evaluation for tone mapped images generated bythree tone mapping methods from 25 HDR images. These images consist of HDR images generated by combining a seriesof pictures with different exposure settings and benchmark HDR images, and we have used the resulting images generated
by the methods of Reinhard,3 Fattal4 and the proposed method. Taking the task of tone mapping into account, such as
how textures can be recognized and the presence or absence of uncomfortable feelings caused by artifacts, we have viewed
overall degrees of satisfaction of 11 examinees in 5 levels; 5 is the best and 1 is the worst.
3.3.2 Results
The results of subjective evaluation are given in Figures 8, 9 and 10 in descending order of satisfaction of the proposed
method. We can qualitatively summarize the results as follows. In Figures 8, 9 and 10, the average degrees of satisfaction
for resulting images generated by the proposed method are totally higher than Reinhard.3 In Figures 9(c) and 10(d), resultsof the proposed method are equivalent to, or lower than results of Reinhard.3 The average degrees of satisfaction for
Figures 8(a) to (d) and 9(c) generated by the proposed method are totally higher than Fattal.4 In Figures 9(a), (b) and (d),results of the proposed method are almost equivalent to the results of Fattal.4 Scores of the proposed method in Figures
10(a) to (d) are lower than Fattal.4
3.3.3 Discussion
From the observation that the average degrees of satisfaction for resulting images generated by the proposed method aretotally higher than the results by the method of Reinhard3 in Figures 8, 9 and 10, we can confirm that the frameworkof applying the tone mapping to each segmented region independently is effective. As the reason why there are images
whose degrees of satisfaction are equivalent to or lower than the results of Reinhard,3 we can conclude that distribution of
luminance values in bright and dark region is not one-sided so that utilized dynamic ranges are not expanded enough even
if applying the tone mapping to each region. Besides, reversing the magnitude relationship of luminance values near theboundary of regions as appeared in Figure 10(d) possibly makes human visual perception feel a sense of discomfort.

In comparison with the results of Fattal,4 the reason why the degrees of satisfaction of the proposed method are equal toor lower in Figures 9(a), (b), (d) and 10(b) is because more textures of bright and dark regions can be visually recognizedin the resulting images generated by Fattal.4 The reason why the degrees of satisfaction for the results of the proposed
method are higher in Figures 8(a) to (d) is due to artifacts which make human visual perception feel a sense of discomfort
significantly. This implies that when HDR image, which is divided into bright and dark regions based on luminance andspatial distributions clearly, is applied the tone mapping, the method of Fattal4 causes artifacts to make human visual
perception feel a sense of discomfort in the resulting image, while the proposed method can produce a more appropriate
image.
According to the results and discussion on the subjective evaluation, we can categorize images in Figures 8 as theimages suitable for the proposed method, while the images in Figures 9 as the images whose results by the proposed
method are equivalent to the results of Fattal,4 and the images in Figures 10 as the images unsuitable for the proposed
method. The degrees of satisfaction for images which we supposed to be suitable or unsuitable for the proposed method
before conducting subjective evaluation are almost the same as we expected. However, the degrees of satisfaction of the
proposed method for Figures 9(b) and (d), which were supposed to be suitable in advance, are found to be comparatively
lower and that for Figures 8(c) and (d), which were supposed to be unsuitable, are actually higher than we supposed. As
mentioned above, this is possibly due to the effects of highlights and shadows and sense of discomfort which may bedifferent person by person. Therefore, it is necessary to improve the usefulness of the proposed method by examining thefeatures of images classified through this experiment of subjective evaluation and defining the criteria for deciding whatkinds of images are suitable for the proposed method.

4. CONCLUSION
In this paper, we have proposed a tone mapping method for HDR images with dimidiate luminance and spatial distributionsof bright and dark regions. In this study, when bright and dark regions are definitely divided according to dimidiate
luminance and spatial distributions, we have assumed that human visual perception does not feel a sense of discomfort
even if the magnitude relationship between luminance values of pixels between bright and dark regions is reversed. Basedon the assumption, we have applied a tone mapping method to each segmented region independently and we also haveshown the experimental results which are appropriately represented by utilizing dynamic range effectively. In subjective
evaluation, from the observation that the degrees of satisfaction for the resulting images generated by the proposed method
are totally higher than those by Reinhard,3 we have confirmed that the idea of applying the tone mapping to bright anddark regions independently is useful to most of HDR images. In addition, since there are some images whose degree ofsatisfaction are higher than Fattal,4 the proposed method is able to produce better images than other related work for some
type of HDR images that are suitable for the proposed method. For images which was supposed to be suitable for the
proposed tone mapping method, the results are almost the same as we expected before experiments, but there are foundsome exceptions. In future work, we will investigate the criteria for deciding whether a given image is suitable for the
proposed method and develop a way to classify images by examining the features of images classified in our experiments.

ACKNOWLEDGMENTS
This research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology(MEXT),
Grant-in-Aid for Scientific Research (A), No. 23240024, and also by the ”Ambient Intelligence” project granted by MEXT.

(a) Reinhard3(b) Fattal4(c) Proposed Method
Figure 5. Results of tone mapping with the image supposed to be suitable for the proposed method : lab.

(a) Reinhard3(b) Fattal4(c) Proposed Method
Figure 6. Results of tone mapping with the image supposed to be suitable for the proposed method: room.12(a) Reinhard3(b) Fattal4(c) Proposed Method
Figure 7. Results of tone mapping with the image supposed to be suitable for the proposed method: memorial.12

(a) No.1(b) No.2(c) No.3(d) No.4
Figure 8. The degrees of satisfaction in subjective evaluation with HDR images suitable for the proposed method.

(a) No.5(b) No.6(c) No.7(d) No.8
Figure 9. The degrees of satisfaction in subjective evaluation with HDR images suitable or unsuitable for the proposed method.

(a) No.9(b) No.10(c) No.11(d) No.12
Figure 10. The degrees of satisfaction in subjective evaluation with HDR images unsuitable for the proposed method.

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