Bull. Soc. Photogr. Imag. Japan. (2024) Vol. 34 No. 1: 1–8

Original Paper

Reversible Data Hiding for OpenEXR Images in Compressible Encrypted Domain
Noa KIKUCHIa, Shoko IMAIZUMIb

Abstract:In this paper, we propose a novel method for reversible data hiding (RDH) for OpenEXR images in the compressible encrypted domain.
There exist three main advantages in the proposed method. First, it introduces an encryption-then-compression system, which provides
block-by-block encryption, to the encryption process. This leads to a high compression efficiency for marked encrypted images. In the encrypted domain, we embed a payload using an RDH method based on prediction error expansion. This makes the hiding capacity of our
method high. The method further allows for flexible restoration patterns; we can decrypt a marked encrypted image without data extraction.
In this case, a marked image will be obtained. In addition, both the encryption and data hiding processes are carried out while preserving the
dynamic range of an original image. This also contributes both to compression efficiency and marked-image quality. In an experiment, weevaluate the hiding capacity, marked-image quality, and compression efficiency by using JPEG XT so as to clarify the effectiveness of our
proposed method. Additionally, the security of the method is also discussed.

Key words:

HDR image, reversible data hiding, encryption-then-compression system, JPEG XT

1. Introduction
Data hiding is one technique used for copyright protection. It
embeds copyright information into the body data of an image without increasing the file size. Data hiding is classified into reversible
and irreversible methods. Methods that can perfectly recover an
original image by extracting a payload are called reversible data hiding (RDH) 1) – 3), while methods that can never retrieve the original
image even after data extraction are called irreversible data hiding.
Additionally, in the context of privacy protection, RDH in encrypted images (RDH-EI) has been widely studied 4) - 7). In RDH-EI, anowner first encrypts an image and then sends the encrypted image
to a third party, such as a service provider. The third party is thensupposed to embed information such as management data or fingerprints into the encrypted image.
Motomura et al. proposed an RDH-EI method that achieved
both a high hiding capacity and compression efficiency 7). This method introduced an encryption-then-compression (EtC) system 8),
which performs block-by-block encryption, for image encryption sothat a marked encrypted image can be effectively compressed. They
attained a high hiding capacity of up to 7.35 bpp in three color components. Additionally, their method offers flexibility in the recovery
process; it can decrypt a marked encrypted image without data extraction. We focus on their method and call it the RDH-CEI method hereafter.
High dynamic range (HDR) images can represent a wider rangeabof luminance compared with legacy standard dynamic range (SDR)
images 9). HDR images have a large bit depth for capturing real-world luminance. Various file formats for HDR images have beendeveloped, such as OpenEXR 10), Radiance RGBE 11), and LogLUVTIFF 12). In recent years, RDH-EI methods for HDR images havebeen increasingly explored 13) 14). Chia et al. proposed an RDH-EI
method for OpenEXR images that achieved a high hiding capacityof up to 9.14 bpp 13). A marked encrypted image derived by thismethod, however, cannot be compressed efficiently. Further, amarked encrypted image can never be decrypted without extracting
a payload. Thus, this method has a limitation that makes it not possible to provide users with flexible privileges for access control.
In this paper, we propose a novel RDH-EI method for OpenEXR
images. Our method first encrypts a target image using the EtC
system, which allows for image compression even after encryption.
In the data hiding process, a prediction error expansion with a histogram shifting (PEE-HS) method 15) is carried out in each block.
Owing to the PEE-HS method, we can attain a high hiding capacity. This method also has flexibility in the restoration process; we candecrypt a marked encrypted image without data extraction. At thistime, we can obtain a marked image in which the payload still remains. In addition, our method conducts each encryption and datahiding process while maintaining the dynamic range of the original
image, thereby improving both the compression efficiency andmarked-image quality. Additionally, we can further enhance bothadvantages by excluding negative-positive inversion in the encryp-

Received 5th February, 2024; Accepted 26th February, 2024 Published 7th March, 2024
Graduate School of Science and Engineering, Chiba University
1-33 Yayoicho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan
Graduate School of Engineering, Chiba University
1-33 Yayoicho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan

2

Bull. Soc. Photogr. Imag. Japan. Vol. 34 No. 1 (2024)

tion process. We evaluated the effectiveness of our method fromfour aspects: hiding capacity, marked-image quality, compression
efficiency, and key space for security. Here, this paper is an extended
article from our domestic conference paper 16) in terms of further
discussions on both attack resistance and experimental analysis.

This leads to deriving marked images that still contain a payload.
This method achieved the highest hiding capacity among existing
RDH-EI methods that can carry out a decryption process without
data extraction. In the following, we will explain the encryption anddata hiding procedures.

2. Preliminaries

2.2.1 Image Encryption
In the encryption process, as shown in Fig. 3, the RGB components of an original image I are spatially combined to derive an 8-bit
grayscale image IG. Note that this figure shows horizontal combination, but an arbitrary direction can be chosen for combination. In
this example, if the size of I is defined as W × H pixels, IG will have
3W × H pixels. IG is then divided into blocks with B × B pixels andencrypted by using the EtC system so that an encrypted image IGE
can be obtained. The EtC system involves three processes: block-position scrambling, block rotation/inversion, and negative-positive
inversion of pixel values within each block.

In this section, we first explain the structure of OpenEXR image
and then elaborate the RDH-CEI method 7) introduced into our
method.
2.1 OpenEXR Image
OpenEXR is a format for HDR images that was developed byIndustrial Light & Magic. In this format, each RGB component
consists of 16-bit floating-point numbers. This allows images tohave a broader dynamic range and color gamut compared with traditional SDR images, where each component is represented by 8
bits. Figure 1 shows the structure of 16-bit floating-point numbers.
Each pixel value x is represented as(1)
where S, E, and M are a sign, exponent, and mantissa, respectively.
2.2 RDH-CEI Method
We explain the RDH-CEI method 7) adopted for our proposed
method. Figure 2 shows the flow of this method. First, a grayscale-based EtC system 8) is applied to an RGB image for encryption. After encryption, a payload is embedded using a PEE-HS
method 15). The RDH-CEI method uses the EtC system for encryption so that a marked encrypted image can be effectively compressedby international standards such as JPEG-LS 17). Additionally,marked encrypted images can be decrypted without data extraction.

2.2.2 Data Hiding
After image encryption, arbitrary data called a payload is embedded into IGE. In the RDH-CEI method, the PEE-HS method 15) isused for data hiding, but other methods are also available. It should
be noted that the top-left pixel in each block is excluded from thefollowing processes to ensure reversibility.
Step 1. Define a parameter for hiding-capacity control as L andmodify the histogram so that the frequencies of 0 to L and
255-L to 255 turn out 0.
Step 2.Obtain prediction values p̂i,j (0 ≤ i ≤ B−1, 0 ≤ j ≤ B − 1) for
pixel values pi,j within each block:
,



=

max
, +

,

, ,

, ,

,

,

,

,

,

,

,

,

max
min

.

, ,

, ,

,

,

		(2)
Regarding p0,j and pi,0, their prediction values p̂0,j and p̂i,0 are

Fig. 1. Single channel structure of OpenEXR.

Fig. 2. Block diagram of RDH-CEI method 7).

Fig. 3. Spatial combination of RGB component.

Noa KIKUCHI, Shoko IMAIZUMIprovided by
,

,

=

=

,		

,

, , 		

Reversible Data Hiding for OpenEXR Images in Compressible Encrypted Domain

and then embed a payload with the PEE-HS method 15). In thefollowing, we describe the encryption, data hiding, restoration processes, and the features of the proposed method.

(3)
(4)

respectively.
Step 3.Derive prediction errors ei,j :
(5)
, = ,
, . 		
Step 4.Explore a pair of adjacent bins Es and El (Es < El) with thehighest sum of frequencies from a prediction-error histogram.
Step 5.As shown in Fig. 4, embed a payload ω into each ei,j :

,

=

>
=
, =
, <

+ 1,
+ ,
,
,
1,
,

,

,

,

,

3.1 Image Encryption
In the encryption process, we encrypt a target image I using the
EtC system so that an encrypted image IE is derived. Here, we perform the following steps while preserving the original dynamic
range.
Step 1-1. Divide I into blocks with B×B pixels.
Step 1-2. Scramble the positions of all blocks.
Step 1-3. Rotate and/or invert each block.
Step 1-4. Conduct negative-positive inversion on each block:(6),

where ẽ i,j is the marked prediction errors.
Step 6.Repeat Steps 4 and 5 for L-1 times.
Step 7.Obtain marked pixel values p̃i,j by, = ,, . 		
(7)
Step 8.Integrate all the blocks to derive a marked encrypted image
Ĩ GE.



,

,

( )=1
( ) = 0,(8)

3.2 Data Hiding
After image encryption, we embed a payload into IE using thePEE-HS 15) method. This process is carried out while maintaining
the dynamic range of IE so that the compression efficiency andmarked-image quality can be enhanced. As mentioned in 3.1, thetop-left pixel of each divided block is excluded from the following
steps for reversibility. Here, we define a parameter to control theIn this section, we propose a novel RDH-EI method that is extended for OpenEXR images. Figure 5 illustrates the flow of themethod. The pixel values of an original image are treated as signed
15-bit values. First, we encrypt a target image using the EtC system 8)-5 -4 -3 -2 -1 0 1 2 3 4 5+

Our method can enhance the compression performance of encrypted images by preserving the dynamic range of the original images during negative-positive inversion. Additionally, when this inversion is excluded from the encryption process, both thecompression performance and marked-image quality can be further
improved. We discuss this in detail in 3.4 and evaluate the efficiency
in Section 4.

3. Proposed Method+1=

where mk and m’k are the original and encrypted pixels in thek-th block, and r(k) is a random number generated by an encryption key. Note that mmax and mmin are the maximum andminimum pixel values, respectively.
Step 1-5. Shuffle the R, G, and B components within each block.

The RDH-CEI method has attained a high hiding capacity of up
to a total of 7.35 bpp for three color components and a high compression efficiency even after encryption. Additionally, since the encryption and data hiding processes are independent from each other,
this method allows for flexible control of access privileges. Generally, users can decrypt a marked encrypted image only after extracting
a payload. In this method, however, image decryption can be carriedout without data extraction, allowing users to obtain a marked image
where a payload remains.

-1

3

−

+

-5 -4 -3 -2 -1 0 1 2 3 4 5

Fig. 4. Data hiding.

Fig. 5. Block diagram of proposed method.

-5 -4 -3 -2 -1 0 1 2 3 4 5

4Bull. Soc. Photogr. Imag. Japan. Vol. 34 No. 1 (2024)

hiding capacity as L.
Step 2-1. As shown in Fig. 6, modify the histogram so that thefrequencies in the range of mmin to mmin-L and mmax-L to mmax
turn out 0.
Step 2-2. By using Eq. (2), obtain prediction values p̂i,j (0 ≤ i ≤ B−1,
0 ≤ j ≤ B − 1) for pixel values pi,j within each block. In the caseof p0,j and pi,0 , the prediction values p̂0,j and p̂i,0 are given by Eqs.
(3) and (4) , respectively.
Step 2-3. Derive prediction errors ei,j using Eq. (5).
Step 2-4. Search for the pair of adjacent bins Es and El (Es < El) thathas the highest sum of frequencies, from a prediction-error histogram.
Step 2-5. Embed a payload ω into each ei,j belonging to Es or El. The
modified prediction errors ẽ i,j are given by Eq. (6).
Step 2-6. Obtain marked pixel values p̃i,j using Eq. (7).
Step 2-7. Repeat Steps 2-2 to 2-6 for L-1 times.
Step 2-8. Integrate all the blocks to derive a marked encrypted
image Ĩ E.
For ensuring reversibility, it is necessary to store the value of L andthe value of Es in the final iteration process. These values are stored
by replacing the least significant bits (LSBs) of the top-left pixels of
the divided blocks, which were excluded from the above steps. The

other information required for reversibility consists of a location
map for preprocessing, Es in each iteration process, and the originalbits of the above LSBs. The information should be embedded into
the image together with the payload.
3.3 Restoration Process
Our method provides flexible restoration patterns owing to the
independent implementation of the encryption and data hiding processes. Figure 7 depicts three possible restoration patterns with theproposed method.
First, Fig. 7 (a) shows a pattern where a payload is extracted, andan original image I is fully recovered. In this process, a marked encrypted image Ĩ E is divided into blocks with B × B pixels. The valuesof L and the value of Es in the final iteration process are obtained
from the LSBs of the top-left pixels of the divided blocks. The PEEHS method 15) is then carried out in reverse order to extract a payload and the essential information for reversibility. By using the information, each pixel value is corrected. Finally, we decrypt theimage and integrate all the divided blocks so that the original image
I can be completely recovered.
Figure 7 (b) illustrates another pattern where Ĩ E is decrypted
without data extraction. In this case, a user can obtain a marked
image Ĩ where a payload remains. This pattern assumes a scenario

00Fig. 6. Preprocessing.

(a) Data extraction and image decryption(b) Image decryption only(c) Data extraction only
Fig. 7. Three patterns of restoration process.

Noa KIKUCHI, Shoko IMAIZUMI

Reversible Data Hiding for OpenEXR Images in Compressible Encrypted Domain

where the user has the privilege to access the image content only.
The third pattern is shown in Fig. 7 (c) , where only data extraction is available. A user can extract a payload from Ĩ E, but theuser is not allowed to access the image content.
Most previous RDH-EI methods have their restoration process
in the patterns of Fig. 7 (a) and (c), but they cannot decrypt a marked
encrypted image without data extraction as shown in Fig. 7 (b). In
contrast, the proposed method can carry out image decryption withthe payload remaining; in this case, we provide a marked image toeach user.

payloads in advance. In contrast, as mentioned in 3.3, our method
can decrypt a marked encrypted image without extracting the payload, allowing for more flexible access privileges based on user requirements.
Further, the marked encrypted images derived by our method are
effectively compressed with international standards such as JPEG
XT 18). This is because our encryption method, which is based on the
EtC system, retains the correlation among pixels within a block evenafter encryption. In contrast, related studies encrypt an image on a
pixel basis. This causes loss of correlation among adjacent pixels,
leading to an increment in the overall entropy in an image. Consequently, it is difficult for the related studies to compress encrypted
images.
The proposed method preserves the dynamic range of original
images during the encryption and data hiding processes, considering
the compression efficiency and marked-image quality. Particularly,
in the encryption process, if negative-positive inversion is carriedout without maintaining the original dynamic range, the entropy ofan encrypted image will increase. This significantly reduces compression efficiency. Moreover, if either the encryption or data hiding
process affects the original dynamic range, there is a higher risk of
introducing pixel values in the marked image that were not present
in the original image, leading to color distortion. Our method thus
carefully conducts the encryption and data hiding processes while
maintaining the dynamic range of original images. Additionally, we
can enhance both the compression efficiency and marked-image
quality by excluding negative-positive inversion.

3.4 Advantages of Proposed Methods
Here, we elaborate on the advantages of our method in comparison with two previous RDH-EI methods for HDR images 13) 14).
Table 1 summarizes a feature comparison in terms of the hiding
capacity, flexibility of restoration patterns, and compression performance for marked encrypted images.
Regarding the hiding capacity, although the image formats andtest datasets are not uniform among the three methods, our method
attained the highest capacity. The two previous methods use only
several bits of the pixel value for data hiding, while the proposed
method uses all bits of the pixel value. In addition, since the proposed method counts the compression performance of marked encrypted images, an RDH-CEI method 7), which is highly compatible with the EtC system 8), is adopted for the data hiding process.
These efforts lead to an increase in embedding capacity.
Our method offers high flexibility in restoration patterns, particularly allowing for the decryption of marked encrypted images without data extraction. Chia et al.’s method 13) carries out the encryption
and data hiding processes interdependently. Thus, we can only decrypt an encrypted image for which a payload has already been extracted. Tsai et al.’s method 14) first encrypts a target image and thenreplaces the pixel values of the exponent channel with a payload. In
addition, this method embeds another payload into the other channels. In their method, image decryption requires extracting both

4. Experimental Results
In this section, we evaluate the proposed method in terms ofmarked-image quality, compression efficiency of marked encrypted
images, and key space for security analysis. We assessed these perspectives both with and without negative-positive inversion to explore the impacts of this process. For the experiment, we used 20

Table 1. Feature comparison among RDH-EI methods for HDR images.
Image format
Prop.

OpenEXR

Tsai et al. 14)

OpenEXR

Chia et al. 13)

OpenEXR(a) Original image

5

Hiding capacity[bpp]

Restoration pattern

9.14

1

11.14

3

7.03

2

Compression of marked
encrypted image(b) Marked encrypted image

Fig. 8. Example of marked encrypted image.

Effective

Ineffective
Ineffective

6

Bull. Soc. Photogr. Imag. Japan. Vol. 34 No. 1 (2024)

images in the OpenEXR format from The HDR Photographic Survey 19). In this paper, we define B=16 in the EtC system 8). Figure 8
illustrates an example of a marked encrypted image derived by our
method.
4.1 Hiding Capacity and Marked-Image Quality
Our method allows for decryption without data extraction, generating a marked image where a payload remains within the image.
Here, we evaluate the marked-image quality, which is related to the
payload amount. Figure 9 shows examples of marked images obtained by our method. Figures 9 (b) and (c) are the results when the
payload was 4.73 bpp, and Figs. 9 (d) and (e) are those for 9.82 bpp.

As shown in these figures, the quality of the marked images was visually maintained even at a high hiding capacity. When negative-positive inversion was applied, and a large amount of information was embedded, however, some block-wise distortions could beobserved. We can see these distortions clearly in Fig. 10 (a) , which
is an enlarged view of the background regions in Fig. 9 (d). However,as can be seen from Fig. 10 (b) , such distortions can be suppressedby excluding negative-positive inversion.
For image quality evaluation, we introduce LogPSNR 20) and
HDR-VDP-3 21). LogPSNR is an extension of PSNR for HDR
images, which is given by(a) Original image(b) With negative-positive inversion(4.73 bpp/ 56.85 dB/ 6.97)(d) With negative-positive inversion(9.82 bpp/ 33.00 dB/ 4.47)(c) Without negative-positive inversion(4.73 bpp/ 56.97 dB/ 8.43)(e) Without negative-positive inversion(9.82 bpp/ 24.04 dB/ 5.33)

Fig. 9. Examples of marked images (hiding capacity [bpp]/ LogPSNR [dB]/ HDR-VDP (Q)) .

(a) A part of Fig. 9(d)(b) A part of Fig. 9(e)(with negative-positive inversion)(without negative-positive inversion)

Fig. 10. Enlarged views of background regions in Figs. 9 (d) and (e).

Noa KIKUCHI, Shoko IMAIZUMI(,= 20 log

)=

×

(

,

(log

)

,

(9)
log

7

Reversible Data Hiding for OpenEXR Images in Compressible Encrypted Domain

) ,

(10)
where M and N are image dimensions, and A1 and A2 are pixel valuesof an original and marked images, respectively. In our experiment,
we set MAX=216. Additionally, we use HDR-VDP (Q) from HDRVDP-3 for quality assessment, where the maximum value of 10 indicates that the marked image is identical to the original image, anda lower value indicates a lower image quality. Figure 11 shows themean values of LogPSNR and HDR-VDP (Q) for the marked images with and without negative-positive inversion. As shown in thisfigure, the quality of the marked images with our method was high.
This is attributed to the encryption and data hiding processes which
preserve the dynamic range of original images, as discussed in 3.4.
From Fig. 11 (a) , the differences in LogPSNR with and without
negative-positive inversion are negligible. This metric is based on themean squared error of pixels, so the values of LogPSNR for bothcases are analogous to each other at certain amounts of hiding capacity. In contrast, HDR-VDP (Q) considers human visual perception; Fig. 11 (b) indicates significant differences between the twocases. When negative-positive inversion is excluded, we can visually
suppress block-wise distortions, obtaining a higher HDR-VDP (Q)score.
4.2 Hiding Capacity and Compression Efficiency
We evaluate the compression efficiency of marked encrypted images using lossless compression with JPEG XT 18) Profile C. The
compression efficiency is defined as the rate of reduction of the filesize by compression. Here, the original file size of each image is 48
bpp, and the compression efficiency is calculated by

[

= 1

]

(11)
Figure 12 depicts the compression efficiency relative to theamount of a payload. From this figure, compression using JPEG XT
is effective for marked encrypted images generated by our method.
This is because we perform image encryption with the EtC systemwith the aim of preserving the dynamic range of original images. In
the case without negative-positive inversion, a higher compression
efficiency can be attained than the case with negative-positive inversion. Negative-positive inversion increases the entropy of encrypted
images, leading to an expansion in the data volume of the residual
information in JPEG XT. Here, the residual information is necessary for reconstructing an HDR image. Consequently, the inversion
decreases the compression efficiency of marked encrypted images.
4.3 Security Analysis
We evaluate the key spaces of our method against brute-force attacks. The key space is defined as the total number of possible pat-Fig. 12. Compression efficiency of marked encrypted images.

(a) LogPSNR(b) HDR-VDP(Q)
Fig. 11. Marked-image quality.
Table 2. Key spaces against brute-force attacks.

With negative-positive
inversion

Without negative-positive
inversion

Positionscrambling

Rotation andinversion

Negative-positive
inversion

RGB shuffling

Total

23K

6K

(K!)3×(24,576)K

(K!)3

83K

-

6K

(K!)3×(3,072)K

(K!)3

83K

× 100 [%].

8

Bull. Soc. Photogr. Imag. Japan. Vol. 34 No. 1 (2024)

terns for the encryption key. Table 2 shows key spaces in the casewith and without negative-positive inversion. In this table, the number of divided blocks in the encryption process is K. Even though we
exclude negative-positive inversion, the key space is approximately
given as 5.47×10773,776 for an image with 4,288×2,848 pixels. This
number indicates that the proposed method offers high security
against brute-force attacks in terms of computational costs. However, the exclusion of negative-positive inversion has been reported toreduce the resistance against attacks using the jigsaw puzzle solver
22). In our proposed method, we can thus take into account the exclusion of negative-positive inversion only when we prioritize
marked-image quality and compression efficiency over security.

5. Conclusion
In this paper, we proposed a novel RDH-EI method for
OpenEXR images with three main advantages. First, marked encrypted images can be effectively compressed by JPEG XT owing to
the introduction of an EtC system for image encryption. Since we
carefully reviewed the data hiding process, we also achieved a highhiding capacity of up to 11.14 bpp. Our method further offers highflexibility in restoration patterns, allowing for image decryption
without data extraction. The proposed method additionally improved both compression efficiency and marked-image quality bypreserving the dynamic range of original images during the wholeprocess; this is effective for both compression efficiency andmarked-image quality. Compared with other RDH-EI methods for
HDR images, our method surpassed them in terms of hiding capacity, compression performance, and flexibility of access privileges. The
key space was also discussed for security. We confirmed that the key
space was large enough and that the proposed method is secureagainst brute-force attacks.

References
1)
2)
3)

Y.-Q. Shi, X. Li, X. Zhang, H.-T. Wu, and B. Ma, Reversible data hiding: Advances in the past two decades, IEEE Access, 4 (2016).
Z. Ni, Y.-Q. Shi, N. Ansari, and W. Su, Reversible data hiding, IEEE
Trans. Circuits Syst. Video Technol., 16, 3 (2006).
W. He, G. Xiong, and Y. Wang, Reversible data hiding based on adaptive multiple histogram modification, IEEE. Trans. Inf. Forensics Secur.,16 (2021).

4)

P. Puteaux, S. Ong, K. Wong, and W. Puech, A survey of reversible datahiding in encrypted images-The first 12 years, J. Vis. Commun. Image
Represent., 77 (2021).
5) X. Zhang, Reversible data hiding in encrypted image, IEEE Signal Process. Lett., 18, 4 (2011).
6) E. Arai and S. Imaizumi, High-Capacity Reversible Data Hiding in Encrypted Images with Flexible Restoration, J. Imaging, 8, 176 (2022).
7) R. Motomura, S. Imaizumi, and H. Kiya, Reversible Data Hiding inCompressible Encrypted Images with Capacity Enhancement, APSIPA Trans. Signal Inf. Process., 12, 1 (2023).
8) T. Chuman, W. Sirichotedumrong, and H. Kiya, Encryption-then-compression systems using grayscale-based image encryption for JPEG images, IEEE Trans. Inf. Forensics Secur., 14, 6 (2019).
9) E. Reinhard, G. Ward, S. Pattanaik, P. Debevec, W. Heidrich, and K.
Myszkowski, “High Dynamic Range Imaging: Acquisition, Display, andImage-Based Lighting”, 2nd ed., Morgan Kaufmann, CA, USA, 2010.
10) Technical Introduction to OpenEXR. Available online: https://openexr.
com/en/latest/TechnicalIntroduction.html (accessed on 30 November2023).
11) G. Ward, “Real Pixels”, Graphics Gems II, by J. Arvo, Academic Press,
CA, USA, 1991, p.80-83.
12) G. W. Larson, LogLuv Encoding for Full-Gamut, High-Dynamic
Range Images, Journal of Graphics Tools, 3, 1 (2012).
13) K. Chia, K. Wong, and J.-L. Dugelay, Data Hiding in Perceptually
Masked OpenEXR Image, Proc. IEEE MMSP, 1-6 (2019).
14) Y.-Y. Tsai, H.-L. Liu, P.-L. Kuo, and C.-S. Chan, Extending MultiMSB Prediction and Huffman Coding for Reversible Data Hiding in
Encrypted HDR Images, IEEE Access, 10 (2022).
15) T. Luo, G. Jiang, M. Yu, F. Shao, and Z. Peng, Disparity based stereo
image reversible data hiding, Proc. IEEE ICIP, 5492-5496(2014).
16) M. J. Weinberger, G. Seroussi, and G. Sapiro, The LOCO-I lossless image compression algorithm: Principles and standardization into JPEGLS, IEEE Trans. Image Process., 9, 8 (2000).
17) T. Richter, A. Artusi, and T. Ebrahimi, JPEG XT: A New Family of
JPEG Backward Compatible Standards, IEEE MultiMedia, 23, 3(2016).
18) The HDR Photographic Survey. Available online: http://markfairchild.
org/HDRPS/HDRthumbs.html (accessed on 30 November 2023).
19) R. Mukherjee, K. Debattista, T. Bashford-Rogers, P. Vangorp, R. Mantiuk, M. Bessa, B. Waterfield, and A. Chalmers, Objective and subjective
evaluation of High Dynamic Range video compression, Signal Process.:
Image Commun., 47 (2016).
20) R. K. Mantiuk, D. Hammou, and P. Hanji, HDR-VDP3: A multi-metric for predicting image differences, quality and contrast distortions inhigh dynamic range and regular content, arXiv preprint arXiv:2304.13625 (2023).
21) T. Chuman, K. Kurihara, and H. Kiya, On the Security of Block Scrambling-Based EtC Systems against Jigsaw Puzzle Solver Attacks, IEICE
Trans. Inf. & Syst., E101-D, 1 (2018).
22) N. Kikuchi and S. Imaizumi, A Reversible Data Hiding Method inCompressible Encrypted Domain for OpenEXR Images, IEICE Tech.
Rep., 123, 332 (2024) , in Japanese.