A comparative study of steganography using watermarking and modifications pixels versus least significant bit

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 13, No. 6, December 2023, pp. 6335~6350
ISSN: 2088-8708, DOI: 10.11591/ijece.v13i6.pp6335-6350  6335
Journal homepage: http://ijece.iaescore.com
A comparative study of steganography using watermarking and
modifications pixels versus least significant bit
Hector Caballero, Vianney Muñoz, Marco A. Ramos-Corchado
Department of Computer Science, Faculty of Engineering, State of Mexico University, Toluca, Mexico
Article Info ABSTRACT
Article history:
Received Feb 9, 2023
Revised May 24, 2023
Accepted Jun 4, 2023
This article presents a steganography proposal based on embedding data
expressed in base 10 by directly replacing the pixel values from images red,
green blue (RGB) with a novel compression technique based on watermarks.
The method considers a manipulation of the object to be embedded through
a data compression triple process via LZ77 and base 64, watermark from
low-quality images, embedded via discrete wavelet transformation-singular
value decomposition (DWT-SVD), message embedded by watermark is
recovered with data loss calculated, the watermark image and lost data is
compressed again using LZ77 and base 64 to generate the final message.
The final message is embedded in portable network graphic (PNG) images
taken from the Microsoft common objects in context (COCO), ImageNet
and uncompressed color image database (UCID) datasets, through a filtering
process pixel of the images, where the selected pixels expressed in base 10,
and the final message data is embedded by replacing units’ position of each
pixel. In experimentation results an average of 40 dB in peak signal noise to
ratio (PSNR) and 0.98 in the similarity structural index metric (SSIM)
evaluation were obtained, and evasion steganalysis rates of up to 93% for
stego-images, the data embedded average is 3.2 bpp.
Keywords:
Compression
Security
Singular value decomposition
Steganography
Watermarking
Wavelets
This is an open access article under the CC BY-SA license.
Corresponding Author:
Hector Caballero
Department of Computer Science, Faculty of Engineering, State of Mexico University
Toluca de Lerdo 50000, Mexico
Email: hcaballeroh045@alumno.uaemex.mx
1. INTRODUCTION
Nowadays are different branches of computer science in charge of protecting information so that it
remains preserved from malicious attacks, such branches include cryptography [1], watermarking and
steganography [2]. Cryptography is widely used to protect information that requires high privacy but has the
particularity that encrypted data is recognized as sensitive information by attackers, which means an effort by
attackers to obtain the original message [3]. There are other areas such as watermarking and steganography to
protect information.
Steganography is the science and art of information concealment, it is generally used to transport
hidden information in digital objects such as video, image, audio, and other objects that are used by
computers, although the objects have the greatest use are digital images because authors allow embedding
high rates of information [4]. In steganography, there are spatial methods such as least significant bit (LSB)
[5], pixel value differentiation (PVD) [6], tri-way pixel value differentiation (TPVD) [7], bit plane caps
segmentation (BPCS) [8], which represents spatial information manipulation, and the methods that use
discrete wavelet transformation (DWT), discrete cosine transformation (DCT) and discrete Fourier
transformation (DFT) are responsible for embedding information through frequency-based transformations
[9]. Generally, spatial methods in steganography are optimal for embedding large amounts of information

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Int J Elec & Comp Eng, Vol. 13, No. 6, December 2023: 6335-6350
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without loss, while methods based on the frequency domain are suitable for securing information against
attacks such as clipping and compression or noise applications such as Gaussian or Brownian, although the
information may suffer data loss, and on some occasions the embedding rates are lower than what was
achieved in the spatial [10].
One of the main characteristics is in the case of stego-images must look as like the cover images, in
addition to the fact that stego-images must be considered to approve steganalysis techniques such as
chi-square, RS and PVo, among others [11]–[14]. A steganography system is a quintuple 𝛿 = 𝐶, 𝑀, 𝐾, 𝐷𝑘, 𝐸𝑘,
where 𝐶 is the set of all cover images, 𝑀 is the messages to hide, 𝐾 is the set of secret keys,
𝐸𝑘 ∶ 𝐶 × 𝑀 × 𝐾 → 𝐶, and 𝐷𝑘: 𝐶 × 𝐾 → 𝑀 [15] are two functions, the first is the embedding and the second is
the extraction function, such that 𝐷𝑘(𝐸𝑘(𝑐, 𝑚, 𝑘) 𝑘 = 𝑚 [16]. On the other hand, watermark is a digital
signature used to identify the data integrity of the cover object, as well as confirm the authenticity of the
object [17]. Objects that contain a watermark, when are video or images, it is possible to visually verify if
contain a distinctive element of this type of method, on the other hand, watermarks do not necessarily require
that be visible, said characteristic it can be shared with that of steganography, although the purpose is not the
same [18]. Watermarks must be designed to withstand attacks such as rotation, scaling, joint photographic
experts group (JPEG) compression, Gaussian noise, brightness shifting, cropping, or deletion [19].
There are many mathematical techniques to implement watermarks, one of the most used is singular
value decomposition (SVD), which is a factorization of a real or complex matrix. An image can be
represented in the form of a matrix of scalar values [20]. SVD decomposes an image represented by a matrix
𝐴 of size 𝑀 𝑁 into a product of three matrices 𝐴 = 𝑈𝑆𝑉 T where 𝑈 and 𝑉 𝑇 are orthogonal matrices 𝑀 𝑁 and
𝑁 𝑁, respectively. 𝑆 is a diagonal matrix 𝑁. . . 𝑁. The elements of 𝑆 are only nonzero on the diagonal and are
called singular values of 𝐴. Equation (1) represents the general form of SVD.
𝐼 = 𝑈𝑆𝑉𝑡
(1)
𝐼 is an image and this indicates that 𝐼 belongs to 𝑅𝑀 × 𝑁 where 𝑅 represents a real number. Where 𝑈 ∈
𝑅𝑁 × 𝑀 and 𝑉 ∈ 𝑅𝑁 × 𝑁 are unitary matrices and 𝑆 ∈ 𝑅𝑁 × 𝑁 is a diagonal matrix with diagonal integers if
it satisfies 𝑠1 ≥ 𝑠2 ≥ 𝑠3 ≥ 𝑠𝑁 ≥ 0 and the superscript denotes the transpose matrix. 𝑈 and 𝑉 are left and
right singular vectors and 𝑆 is a singular value of the transpose matrix.
Vector 𝑈 and vector 𝑉 are right and left, and 𝑆 is a singular value of the matrix. The main property
of SVD in image processing is that the singular value of the image has a high stability and is known with a
small perturbation, this means that the image of the singular value does not present significant changes [21].
The singular vectors of an image specify the geometry of the image, while the singular values specify the
luminance (energy) of the image. Slight variations in singular values do not affect the visual perception of
image quality. The psychovisual effect-based property allows embedding of the watermark bits into the
original image by minor modification to singular values of the original image [22].
DWT can be applied in watermarking and steganography; this represents the small waves of
variable frequency and limited duration are wavelets. It is widely used due to its ability to compact space and
frequency energy compaction. At each level, DWT decomposes an image into four sub bands, a lower
resolution approximation (LL) component and three other spatial direction components corresponding to the
horizontal (HL), vertical (LH) and diagonal (HH) components. High-resolution sub bands help locate edge
and texture patterns in any image [23]. In the next subsection, a detailed mention will be made about the
interesting proposals of existing steganography and watermarking.
Different research has been carried out aimed at hiding information aimed at replacing information
by means of secret digits, as in the research by Nagaraj et al. [24] using the pixel value modification (PVM)
by module function, Shashikiran et al. [25] used a data encryption process to hide information in digital
images, using knight movements with 5×5 blocks. A proposal for the combination of parity bit pixel value
difference (PBPVD) and improved rightmost digit replacement (IRMDR) is in [26], the method divides the
cover image into two non-overlapping blocks of pixels, the value of the difference between the pixels in each
block is used to determine the selection of PBPVD and IRMDR for RS analysis evasion. Other investigations
that use combination with steganography and cryptography is the work of Al-Mamun et al. [27], proposes
that the image pixels are randomly selected using the Stern-Brocot sequence, while the keying is achieved
with multiple LSBs of color components (RGB). On the other hand, Hossen et al. [28] applies a cryptosystem
with advanced encryption standard (AES) and Rivest cipher 5 (RC5). Kordov and Zhelezov [29] propose an
approach to hide secret text messages in color images, combining steganography and cryptography. The
location and order of the image pixels chosen for embedding are randomly selected by a chaotic
pseudorandom generator.
Some studies that use a combination of steganography with watermarking can be seen in Gutub and
Al-Shaarani [30], by combining LSB and DWT to hide digital images in cover images. An application of

Int J Elec & Comp Eng ISSN: 2088-8708 
A comparative study of steganography using watermarking and modifications pixels … (Hector Caballero)
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LSB sees the work of Zakaria et al. [31], use data mapping to reduce the amount of bit modification per
pixel, in such a way that four secret data bits are mapped to the four most significant bits of a coverage pixel,
the only two bits of a pixel are modified to indicate the mapping strategy for evasion of analysis by histogram
and RS. Sahu and Swain [32] propose replacement of n right-oriented bits to hide the secret data in an image,
where 1 is less than n and less than 4, to avoid the fall of boundary problem (FOBP), as well as resist attacks
by noise of salt, pepper, and RS.
Fractal images allow embedding large amounts of data as Durafe and Patidar [33] use SVD and
DWT to hide the information content within the cover image. The method proposed by the authors employs a
cover image using fractals, to reconstruct when have exact parameters in the fractal imaging equations. These
parameter values become part of the secret key. The authors also apply the hybrid IWT-SVD technique to
monitor the differences in performance with respect to the DWT-SVD scheme.
Abdallah et al. [34] propose an embedding that relies on the use of SVD orthogonal matrices as a
container for embedding information rather than embedding in the singular values of the images. Subhedar
and Mankar [35] developed an image steganography scheme based on the framelet transformation that hides
a secret image in the cover image, using bidiagonal singular value decomposition, because the secret
information is embedded in singular values of framelet coefficients. Rodriguez-Mendez et al. [36] present a
steganographic model that hides a digital voice signal in a color image, shows embedding capabilities,
robustness, and imperceptibility of the secret message, as well as superior visual quality of the stego-image
and audio quality of the signal of recovered voice compared to the state-of-the-art (SoTA) schemes. The
model proposed by the authors obtained average values of 32 dB and 0.92 in peak signal to noise ratio
(PSNR) and similarity structural index metric (SSIM).
Transforms such as the sharp frequency localized contourlet transform (SFLCT) are combined with
SVD to build a secure watermarking pseudocode, as observed by Najafi and Loukhaoukha [37]. A formal
generic model for digital image watermarking is seen in research [38] for the initial construction of a basic
watermark model was developed to incorporate the use of keys. Rupa [39] uses several levels of security with
steganography and watermarks, first level is with Gyration encryption pseudocode, in the second level it uses
PLSB to hide encrypted information and in the third level the watermark image is embedded in the original
image. Rahman et al. [40] has authored the novel least significant bit technique (NLSBT) using the magic
matrix and multi-level encryption algorithm (MLEA) and expels the repetition of the most normal letters. In
this procedure by inserting a secret message into a file, one can then prove ownership and/or guarantee the
reliability of the item. Vu et al. [41] propose the multi-bit marking layer (MBML) method, which consists of
reusing results from the previous embedding time (layer) as input data to continue embedding them in audio
signals, the method demonstrates adequate performance in the error and signal to noise ratio (SNR)
embedding rate surpassing methods such as LSB, large sample embedding (ELS), bit marking (BM) and
BM/SW method (sliding window) which consist of a single layer.
In the reviewed information is possible observed that the regular ways of applying steganography
and watermarks allow us to manipulate information contained in the images that underwent the watermarking
process, although the loss of data is contemplated, which is not highly important, because the survival of the
signature that identifies the authenticity of the carrier object is widely considered. Loss handling Information
that may exist in a watermarking process can be leveraged to represent information without data loss. The
following section presents a steganography method that takes advantage of watermarks for information
compression, in addition to providing an encapsulation of information which cannot be retrieved directly.
2. METHOD
The proposal of this work is focused on combining watermarks to achieve information
compression through an ingenious method that encompasses the DWT-SVD process with lossless
compression techniques based on run length encoding (RLE) and base 64, to later embed this information
in digital images with RGB color model without data loss due to compression, portable network graphic
(PNG) format. The data embedding process is carried out by replacing the units with the lowest weight of
each pixel when these are represented in base 10. Figure 1 shows the methodology to follow for the
steganography process with watermarking as a compression mechanism of data, also named steganography
method based in watermarking and replacing pixels (SMWRP). As can be seen in Figure 1 are three
essential stages in SMWRP, the first stage being the conversion of a message into an RGB image, stage
two is the application conversion process where 𝐼𝑏10 is embedded in 𝐼𝑙𝑞 (image of low quality), to obtain
𝑀𝑓, which is the sum of 𝐼𝑤 and 𝑀𝑅𝐸, finally there is stage 3 that represents the embedding of 𝑀𝑓 in the
cover image, called 𝐼𝑝 by replacing the base 10 units of each pixel of cover image. Below is a more
detailed description of each stage.

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Conversion of the message into an image. The input message is called 𝑀𝑖, this message is
compressed by LZ77, then the number of symbols generated by LZ77 is reduced by base 64 encoding, in
such a way that all symbols are represented by 8 bits, finally, each symbol it is represented by its position in
the base 64 alphabet (represented in base 10), and the message 𝑀𝑏10 is generated. 𝑀𝑏10 is inserted into a new
RGB image, whose initial values in all its pixels is 0, this image is 𝐼0, the data embedding process must be
carried out through a cycle, prioritizing the data input to the R channel. In this stage are the following phases
to complete the transformation of the message.
− Watermarking process. A low quality RGB image is generated, where the smallest possible image size is
obtained, to later start the engraving process with SVD and DWT. The SVD process consists of
multiplying the channels of the cover image with a constant, in the same way with DWT the
multiplication process. By forming the stego-image by the watermarking process, to initialize the message
recovery. This stage presents the following phases.
− Recovery of the watermarking message. A recovered message is subjected to verification to calculate the
loss and recover it based on the recovered message and the original message expressed as an image, in
which a third image is formed to respect positions that have been lost.
− Sum of messages. The stego-image formed with watermarking and the image that represents the loss are
compressed by RLE and encoded in base 64, to be later concatenated. The message that is obtained from
the concatenation is a final message to be embedded in a cover image.
− Concatenated message conversion. The message that represents an image with the watermarking process
and the image that recovered data represented are converted to base 10, from this phase the 𝑀𝑓 message is
formed (the 𝐼𝑏10 image).
Figure 1. General diagram of the steganography process

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Data replacement 𝑀𝑓 message is sliced to form a digit-based data stream to replace the cover image
pixel data. The process begins with filtering the image. The data replacement is applied to the cover image 𝐼𝑝,
where a filter is applied to determine pixels in which the unit replacement process will be applied for each
modified pixel, giving rise to the stego-image 𝐸𝑓. On the other hand, data recovery is focused on
reconstructing the message in its entirety, without affecting the message that was originally embedded. The
following steps are the process of recovering the embedded message.
Step 1: In 𝐸𝑓, the range of pixels where the values close to color 255 are represented is chosen. Later, the
chain of digits that represents the 𝑀𝑓 is converted into a vector to replace the units of the pixels with
that of the data.
Step 2: The digits are concatenated to generate a series of pairs that are going to make up the base
64 symbols in the vector 𝑀′𝑓. The message that has been base 64 encoded is again encoded to separate
the image corresponding to the image representing 𝐼𝑤 and the image representing 𝑀𝑅𝐸.
Step 3: 𝐼𝑤 is generated again, as well as 𝑀𝑅𝐸. Once 𝐼𝑤 has been extracted, the reverse watermarking process
is applied to obtain 𝑀𝐼𝑅 and compare with 𝑀𝑀𝑅.
Step 4: Both 𝑀𝑅𝐸 and 𝑀𝐼𝑅 are compared in its positions to verify missing data sections, all data representing
changes are stored in its corresponding coordinate in 𝑀𝑅𝐸, to recover 𝐼𝑏10.
Step 5: The 𝐼𝑏10 pixels are read from the R channel to the B channel, stop being decoded in base 64,
decompressed with LZ77 and finally 𝑀𝑖 is recovered.
Algorithm 1 presents the general mechanism for embedding 𝐼𝑏10 in an 𝐼𝑙𝑞 image. Algorithm 2
represents recovery of loss data, because the watermarking process generates data loss. The purpose of these
two algorithms is to preserve the integrity of the message to be embedded.
Algorithm 1. Process to embed 𝑀𝑖 in 𝐼𝑙𝑞
1: Start
2: 𝑀𝑖 //Message
3: 𝑀𝑏10=𝐵10(𝐵64(𝐿𝑍77(𝑀𝑖))) //Codification to 𝑀𝑖
4: Read(𝐼𝑏10) //𝑀𝑖converted in image
5: Read(𝐼𝑙𝑞) //Image to degraded in quality
6: 𝐼𝑙𝑞=Low-quality(:𝐼𝑙𝑞) //Low quality image
7: 𝑀𝐼𝑅 //image to recover
8: Iw=DWT(𝐼𝑙𝑞)*SVD(𝐼𝑏10)*𝑐𝑖 //Merging process to 𝐼𝑤
9: 𝑀𝐼𝑅 = 𝐼𝑤 ∗ 𝐼𝐷𝑊𝑇 ∗ 𝐼𝑆𝑉𝐷 //Embedded inverse
10: End
Algorithm 2. Recovery loss data
1: Start
2: Read(𝑀𝐼𝑅)//Image that represented loss data from 𝐼𝑤
3: Read(𝐼𝑏10)//Image with ASCII code in base 10
4: 𝑀𝑅𝐸=Generated_imageRGB()//Imagen RGB empty
5: 𝑖=0, 𝑒=0, 𝑐ℎ𝑎𝑛𝑛𝑒𝑙=0, 𝑇𝑦𝑝𝑒𝐷=“Segment data”
6: while 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 ≤ 3 do
7: [𝑀, 𝑁]=: 𝐼𝑏10//dimensions
8: for 𝑖≤𝑀 do
9: for 𝑒≤𝑁 do
10: if 𝐼𝑏10[𝑖][𝑒]! = 𝑀𝐼𝑅[𝑖][𝑒] then
11: 𝑀𝑅𝐸[𝑖][𝑒] = 𝐼𝑏10[𝑖][𝑒]
12: end if
13: end for
14: end for
15: channel ++//Increase channel
16: end while
17: Write(𝑀𝑅𝐸)//Data recovery converted in image
18: 𝑀𝑓=𝑩𝟔𝟒(𝐿𝑍77(: 𝑀𝑅𝐸 + “𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑜𝑟′′ + 𝑩𝟔𝟒(𝐿𝑍77(: 𝐼𝑤))))//Message to embedded into final cover image
19: End
When 𝑀𝑅𝐸 has been generated, this image is converted to a string by using the functions LZ77 and
B64, after this, 𝐼𝑤 is converted to a string and both results are concatenated, in such a way that the result is
added to a new chain named as 𝑀𝑓. This can be visualized in a general way in (2). The data embedding
process consists of filtering the 𝐼𝑝 cover image, selecting which pixels are candidates to be modified in its
unit position by 𝑀𝑓 values that are expressed in base 10, going through all the 𝐼𝑝 channels, at the end the
stego-image 𝐸𝑓 is generated. Algorithm 3 shows the data embedding process.

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𝑀𝑓 = 𝐵64(𝐿𝑍𝑊(𝑀𝑅𝐸 + 𝐵64(𝐿𝑍𝑊(𝐼𝑤)))) (2)
Algorithm 3. Data embedded process
1: Start
2: Read (𝐼𝑝)//Cover image
3: 𝐸𝑓=: 𝐼𝑝//Read stego-image
4: 𝐶𝑜𝑢𝑛𝑡𝑒𝑟=0, 𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝐶
5: 𝑐ℎ𝑎𝑛=𝑪𝒉𝒂𝒏𝒏𝒆𝒍(𝐼𝑝) //Image channels
6: 𝑀𝑡 = 𝐵64(𝐿𝑍𝑊(𝑀𝑓))
7: for 3≤channel do
8: for 𝑥≤𝑡𝑒𝑟𝑚 do
9: for 𝑦≤𝑡𝑒𝑟𝑚 do
10: if 𝐼[][]≤filter and 𝐶𝑜𝑢𝑛𝑡𝑒𝑟<𝐿𝑒𝑛𝑔𝑡ℎ(𝑀𝑡) then
11: 𝐸𝑓[𝑥][𝑦]. 𝑓𝑖𝑟𝑠𝑡_𝑑𝑖𝑔𝑖𝑡 = 𝑀𝑡[𝐶𝑜𝑢𝑛𝑡𝑒𝑟]
12: end if
13: end for
14: end for
15: 𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝐶 + +
16: end for
17: Display(𝐸𝑓)
18: End
To recover the information, several algorithms are used for the reverse process. The data recovery
algorithm 4 indicates that the stego-image is read, a filter indicates the pixels that make up a range of values
where it is possible to find the substituted data in its numerical value of the first digit of the selected pixels of
the stego-image. The digits are concatenated in the concatenate variable.
The concatenate variable contains a message that encompasses 𝐼𝑤 and 𝑀𝑅𝐸. The digits stored in the
concatenate variable are converted into numbers corresponding to base 64 to later be decompressed, as can
be seen in algorithm 4. In algorithm 5, the process of generating the image to which the code was applied
begins. The watermarking process, represented by 𝐼𝑤, and the 𝑀𝑅𝐸 image which contains the information that
represents data loss by the DWT-SVD application process.
Algorithm 4. Counted chain deployment
1: Start
2: Read(𝐸𝑓)
3: Filter_pixels(𝐸𝑓)
4: 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 = 𝑪𝒉𝒂𝒏𝒏𝒆𝒍(𝐸𝑓)//Extraction channels
5: for 3≤channel do
6: for 𝑖≤𝑒𝑛𝑑 do
7: for 𝑒≤𝑒𝑛𝑑 do
8: if 𝐸[][] ≤filter then
9: 𝑐𝑜𝑛𝑐𝑎𝑡𝑒𝑛𝑎𝑡𝑒+= 𝐸[𝑥][𝑦]. 𝑓𝑖𝑠𝑡𝑠_𝑑𝑖𝑔𝑖𝑡
10: end if
11: end for
12: end for
13: end for
14: Display(concatenate)
15: End
Algorithm 5. Main image extraction
1: Start
2: Read(𝑁𝑐𝑎𝑑64)
3: breaker=“x”
4: for 𝑖≤𝑐𝑎𝑑64 do
5: 𝐼𝑐𝑤 //Representation of values from Iw
6: if 𝑁𝑐𝑎𝑑64 (𝑖)! = "𝑏𝑟𝑒𝑎𝑘𝑒𝑟" then
7: 𝐼𝑐𝑤 += 𝑁𝑐𝑎𝑑64 (i)
8: Else
9: Print(’First image’)
10: 𝑓𝑙𝑎𝑔=1
11: end if
12: if 𝑁𝑐𝑎𝑑64 (i) !=breaker and 𝑓𝑙𝑎𝑔==1 then
13: 𝑀𝑐𝑅𝐸+=𝑁𝑐𝑎𝑑64(i)
14: end if
15: end for
16: End

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Algorithm 6 expresses the conversion of the 𝑀𝑐𝑅𝐸 and 𝐼𝑐𝑤 chain to give way to the generation of the
𝐼𝑤 and 𝑀𝑅𝐸 images again, reconstructing its R, G, and B channels, through the conversion of the converted data
in base 64, to recover values in base 10. When recovering the image that received the treatment by
watermarking using DWT-SVD, the process of breaking it down using DWT to obtain the R, G, and B
channels, then SVD process is applied to recover in 𝑒𝑤 the image that presents the stored message and contains
the original message. In algorithm 7, when the 𝑀𝐼𝑅 image is recovered, a comparison is made with the 𝑀𝐼𝑅
image that represents the loss of data when applying DWT-SVD, in such a way that it is compared with the 𝑀𝑅𝐸
image, in a series of cycles where the values that are the same in 𝑀𝑅𝐸 are replaced in 𝐼𝑏10 by the values of 𝑀𝐼𝑅,
because these represent the values that were not lost in the watermark generation process, whereas, if the values
do not match, these are passes the 𝑀𝑅𝐸 values to 𝐼𝑏10. At the end of the 𝐼𝑏10 values, these are decoded from
ASCII to B64 and later decompressed to give rise to the originally embedded message.
Algorithm 6. Image transformation process
1: Start
2: 𝑟𝑒𝑠𝑜𝑙 = 𝑥, 𝑟𝑒𝑠𝑜𝑙 = 𝑦 image resolution
3: for 𝑥 ≤ 𝑟𝑒𝑠𝑜𝑙 = 𝑥 do
4: for 𝑥 ≤ 𝑟𝑒𝑠𝑜𝑙 = 𝑦 do
5: 𝑀𝑅𝐸. 𝑅 = 𝑀𝑐𝑅𝐸(𝑖). 𝐷𝑒𝑐𝑏64//Numerical conversion from pixels
6: 𝐼𝑤. 𝑅 = 𝐼𝑐𝑤(𝑖). 𝐷𝑒𝑐𝑏64
7: end for
8: end for
9: for 𝑥 ≤ 𝑟𝑒𝑠𝑜𝑙 = 𝑥 do
10: for 𝑥 ≤ 𝑟𝑒𝑠𝑜𝑙 = 𝑦 do
11: 𝑀𝑅𝐸. 𝐺 = 𝑀𝑐𝑅𝐸(𝑖). 𝐷𝑒𝑐𝑏64
12: 𝐼𝑤. 𝐺 = 𝐼𝑐𝑤(𝑖). 𝐷𝑒𝑐𝑏64
13: end for
14: end for
15: for x≤resol=x do
16: for x≤resol=y do
17: MRE.B=McRE(i).Decb64
18: Iw.B=Icw(i).Decb64
19: end for
20: end for
21: End
Algorithm 7. Message extraction with DWT-SVD
1: Start
2: 𝑹𝒆𝒂𝒅( 𝐼𝑤)
3: Read( 𝐼𝑏10)//Message in base 10
5: 𝑤𝑚𝐿𝐿, 𝑤𝑚𝐿𝐻, 𝑤𝑚𝐻𝐿, 𝑤𝑚𝐻𝐻=DWT Iw, haar
6: 𝐼𝑚𝑤 = 𝑤𝑚𝐿𝐿//Im represent the image
7: 𝑅 = 𝑤, 𝐵 = 𝑤, 𝐺 = 𝑤
8: 𝑈𝑖𝑚𝑟, 𝑆𝑖𝑚𝑟, 𝑉𝑖𝑚𝑟 = 𝒔𝒗𝒅(𝑟𝑒𝑑)
9: 𝑈𝑖𝑚𝑔, 𝑆𝑖𝑚𝑔, 𝑉𝑖𝑚𝑔 = 𝒔𝒗𝒅(𝑔𝑟𝑒𝑒𝑛)
10: 𝑈𝑖𝑚𝑏, 𝑆𝑖𝑚𝑏, 𝑉𝑖𝑚𝑏 = 𝒔𝒗𝒅(𝑏𝑙𝑢𝑒)
11: 𝑆𝑒𝑤𝑟 = (𝑆𝑖𝑚𝑟 − 𝑆𝑖𝑚𝑔𝑟1)/0.10//ew process watermarking
12: 𝑆𝑒𝑤𝑔 = (𝑆𝑖𝑚𝑔 − 𝑆𝑖𝑚𝑔1)/0.10
13: 𝑆𝑒𝑤𝑏 = (𝑆𝑖𝑚𝑏 − 𝑆𝑖𝑚𝑏1)/0.10
14: 𝑒𝑤𝑟 = 𝑈𝑖𝑚𝑟2 ∗ 𝑆𝑒𝑤 ∗ 𝑉𝑖𝑚𝑟´2
15: 𝑒𝑤𝑔 = 𝑈𝑖𝑚𝑔2 ∗ 𝑆𝑒𝑤 ∗ 𝑉𝑖𝑚𝑔´2
16: 𝑒𝑤𝑏 = 𝑈𝑖𝑚𝑏2 ∗ 𝑆𝑒𝑤 ∗ 𝑉𝑖𝑚𝑏´2
17: MIR=Concatenate_matrix(3, ewr,ewg,ewb);
18: while channel≤3 do
19: [𝑀, 𝑁] = 𝐼𝑏10//dimension extracted
20: for 𝑖 ≤ 𝑀 do
21: for 𝑒 ≤ 𝑁 do
22: if 𝑀𝐼𝑅[𝑖][𝑒]! = 𝑀𝑅𝐸[𝑖][𝑒] then
23: 𝐼𝑏10[𝑖][𝑒] = 𝑀𝑅𝐸[𝑖][𝑒]
24: end if
25: if 𝑀𝐼𝑅[𝑖][𝑒] == ’𝑒𝑞𝑢𝑎𝑙’ then
26: 𝐼𝑏10[𝑖][𝑒] = 𝑀𝐼𝑅[𝑖][𝑒]
27: end if
28: end for
29: end for
30: channel ++//increase channel
31: end while
32: 𝑀𝑏10 = 𝑫𝒆𝒄𝒐𝒅𝒆𝒃𝟏𝟎(𝑀𝑅𝐸)//𝑀𝑅𝐸 transformed in base 10
33: Print(𝒅𝑳𝑾𝒁(𝒅𝟔𝟒(𝑀𝑏10)))//Decodification 𝑀𝑏10
34: End

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When carrying out the analysis of the big O [42], [43] for the previous pseudocodes, the following
complexities have been observed: in algorithm 1 it is observed that the variables present an assignment of
values, but from this assignment process functions that demand great computational power are used, because
it corresponds to algorithms 3 to 7, which will be discussed later. In algorithms 2 to 4 a nesting of 3 cycles is
observed, this complexity would correspond to O(n3
). In algorithm 5 a complexity O(n) is observed,
algorithm 6 has a complexity of O(n2
) because the code segments with the greatest weight are those that have
two nested cycles. While in algorithm 7 the highest complexity observed is O(n3
), on the other hand, the
message decoding functions, as well as the watermarking process present levels of O(n2
) for the process
matrix multiplication. The stages with the highest computational cost occur in the watermarking process, the
embedding of the final message and the recovery of the message process.
3. RESULTS AND DISCUSSION
This section presents the evaluation of SMWRP. Cover images have been randomly selected from
uncompressed color image database (UCID) [44], Microsoft common objects in context (COCO) [45] and
ImageNet [46], three sets of images named A, B and C was conformed from these datasets, each set contains
500 digital images with RGB color model and in PNG, with a resolution of 512×512 pixels. For each cover
image a 320,000 bytes message was embedded, both image sets A, B, C, and the message was used to
perform a comparison with LSB. In Figure 2 shows the evaluation process to SMWRP.
Figure 2. Experimental process for SMWRP
The stego-images generated in the evaluation process will be subjected to an analysis to calculate
the relationship of modifications are present against the cover images, the metrics CC, MSE, PSNR, SNR and
SSIM have been considered, for the steganalysis it has been used the StegExpose tool [47]. The
implementation of SMWRP has been developed in MATLAB 2015b development environment, on a Mac
Book Pro computer with a 2.3 GHz Core i5 processor and 8 GB of RAM. One of the metrics developed to
check the structural integrity of an image is the mean squared error (MSE), which is defined as a mean square
error, where f(x,y) is a carrier signal (cover image), 𝑓
̂(𝑥, 𝑦) is a processed signal (stego-image), M×N is the
size of the signal in 2D [48], equation (3) represents the calculation of the MSE.
𝑀𝑆𝐸 =
1
𝑀× N
∑ ∑ [𝑓(𝑥, 𝑦) − 𝑓
̂(𝑥, 𝑦)]
2
𝑁−1
𝑦=0
𝑀−1
𝑥=0 (3)
The existing relationship between the signal and the noise known as SNR is established between the
proportion that exists between the signal of the power that is transmitted and the power of the noise signal
that breaks it down by [49]. This ratio is measured in decibels and is defined by (4). The PSNR is defined as
a limit, where the relationship with the error receptor is approximated through the human vision system. The
PSNR is dimensionless since the units of both the numerator and denominator are pixel values [50] in (5).
𝑆𝑁𝑅 =
∑ ∑ 𝑓
̂(𝑥,𝑦)2
𝑁−1
𝑦=0
𝑀−1
𝑥=0
𝑀𝑆𝐸
(4)
𝑃𝑆𝑁𝑅(𝑑𝐵) = 10𝑙𝑜𝑔10𝐿2
/𝑀𝑆E (5)
The SSIM is a method used to determine the similarity between two images, this metric allows to
measure or predict the quality of the image, based on an initial image that is not compressed or without
distortion (cover image) [51]. Generally, the mean SSIM (MSSIM) index is used to assess the overall quality
of an image, 𝑓(𝑥, 𝑦) represents the ported image and 𝑓
̂(𝑥, 𝑦) represents the distorted image, 𝑓𝑗 and 𝑓𝑗
̂ are the
content of the jth local window, and 𝑊 is the number of local windows in the image, equation (6) represents
MSSIM [52]. Correlation coefficient (CC) of two random variables is a quantity of linear dependence [53]. If
each variable has 𝑛 scalar observations, the Pearson correlation coefficient is defined as in (7). Where 𝐴

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represents the first variable and 𝐵 the second variable, being 𝑚 and 𝑛 the sections to be evaluated between
the random variables.
𝑀𝑆𝑆𝐼𝑀(𝑓(𝑥, 𝑦), 𝑓
̂(𝑥, 𝑦)) =
1
𝑊
∑ (𝑓𝑗, 𝑓𝑗
̂)
𝑊
𝑗=1 (6)
𝑟 =
∑ ∑ ((𝐴𝑚𝑛−𝐴̅)(𝐵𝑚𝑛−𝐵
̅))
𝑛
𝑚
√(∑ ∑ (𝐴𝑚𝑛−𝐴̅)2
𝑛
𝑚 )(∑ ∑ (𝐵𝑚𝑛−𝐵
̅)2
𝑛
𝑚 )
(7)
3.1. Results and discussion
In Table 1 important aspects can be observed during experimentation process, first, it can be noted
that the quality of the stego-images with SMWRP demonstrated when analysis was applied present a PSNR
with greater than 42 dB for sets A, B and C, which indicates that visually there are no great differences with
respect to cover images, the SNR registers 36 dB, although a striking increase is observed in the MSE of
more than 4 points, it is important to clarify that the SSIM registers for the three sets a score higher than
0.980, which validates that visually there are no significant deformations that are appreciable by the human
vision system, while the CC is entered at 0.999 points. When analyzing the results of the stego-images with
the LSB implementation, it can be observed that the results presented by the quality metrics in PSNR and in
SNR show less 9 dB than SMWRP, as well as an MSE of 27 points and SSIM with scores of 0.926 points,
which indicates that the stego-images present more degradation in visual quality with respect to SMWRP.
One of the most important advantages to SMWRP is its effectiveness in avoiding the steganalysis that was
applied through StegExpose, where an evasion of more than 90% is obtained, while with LSB it presents an
evasion of 1%, which indicates that it is a steganography method not recommendable when statistical
analysis is applied.
Table 1. Comparison of results between the proposed method and the LSB, when applying
StegExpose in the stego-images
Dataset Resolution Stego-images detected PSNR SNR MSE SSIM CC
UCID SMWRP 512×512 50 42.532 36.742 4.291 0.985 0.999
COCO SMWRP 512×512 35 42.857 36.728 4.049 0.983 0.999
ImageNet SMWRP 512×512 30 43.008 36.954 3.813 0.987 0.999
UCID LSB 512×512 496 33.706 27.330 27.235 0.926 0.992
COCO LSB 512×512 495 33.779 27.607 27.263 0.928 0.994
ImageNet LSB 512×512 491 33.653 27.743 28.112 0.926 0.995
One of the reasons why SMWRP is highly effective in evading steganalysis is that it does not break
the block pattern in the same way that LSB does, where a random pattern is created, which is detected by
analysis such as chi square, RS, among others. Figure 3 shows graphically the results of the PSNR and SNR
evaluation of LSB and SMWRP, for the COCO dataset, where it is possible to verify that the results of the
metrics indicate that visually the alterations are more appreciable in the traditional LSB method. The
previously described is also observed in the results obtained from the UCID dataset, Figures 4 and 5
ImageNet dataset. When analyzing the results of the evaluation of SSIM and CC of LSB and SMWRP, it can
be seen in Figures 6 to 8 it is possible to see that the SMWRP generates alterations to a lesser extent than the
LSB method. The LSB method does not maintain a good performance from the visual aspect of a stego-
image, and it is widely deficient when performing a statistical analysis, as it was demonstrated when the
analysis was applied with the StegExpose tool.
Figure 3. Results obtained from the evaluation of the COCO dataset when evaluating PSNR and SNR

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Figure 4. Results obtained from the evaluation of the UCID dataset with PSNR and SNR
Figure 5. Results obtained from the evaluation of the ImageNet dataset with PSNR and SNR
Figure 6. Results obtained from the evaluation of the COCO dataset with SSIM and CC
Figure 7. Results obtained from the evaluation of the UCID dataset with SSIM and CC
The combination of compression without loss data embedded in digital images with watermarks
using DWT-SVD, has allowed to obtain outstanding results according to what can be observed at the end of
tests, a series of important aspects can be observed in the experimentation process, such as the representation
that SVD makes on the first stego-image, allow to reduce its size so that, in the end, it is possible to increase
data compression. SMWRP allows to distribute the information in such a way that it does not affect the
relationship between the pixels of the final cover image, and thus avoid detection by means of statistical

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techniques. It can be observed that the results obtained in PSNR are higher than 40 dB, as well as the
measurements recorded in the SNR remain above 37 dB and a SSIM superior to 0.980 in all sets, which
indicates that visual stability is preserved in the stego-images, in comparison with the traditional replacement
with LSB, a lower degradation in LSB would be expected because the affected bits per pixel are maximum 3,
compared to SMWRP that presents 4 altered bits per pixel, but due to the compression that is applied the
visual alterations are compensated. The data embedding process involves a double stage, because the original
message is compressed and encoded to be embedded as an image using DWT-SVD and after this, it requires
that the data loss that has originated be recovered, on the one hand , this allows the original message to not be
obtained directly, on the other hand it is a longer process to prepare the message to be embedded, in the
second stage, the replacement of units of the pixels expressed in base 10 allows avoiding the change of the
pixels consecutively, and in this way avoid to the greatest extent possible evading the statistical analysis.
Figure 8. Results obtained from the evaluation of the ImageNet dataset with SSIM and CC
In Figure 9, 18 images are presented, contained in six groups of images that are compared with
cover images, stego-images from SMWRP and the stego-images resulting from LSB method. The most
notorious changes on the effects of embedding the message can be observed in the images of Figures 9(a)
to 9(c), while the images contained in subsections are minus notable Figures 9(d) to 9(f), this trend with more
impact can be observed between the group images of Figures 9(g) to 9(i) and those of the fourth group
Figures 9(j) to 9(l), as well as in the fifth group as shown in Figures 9(m) to 9(o) and sixth group as shown in
Figures 9(p) to 9(r) where LSB stego-images are evidently modified by the embedding process. As can be
seen, the stego-images produced by LSB, present some stripes that visibly affect quality, while in the stego-
images from SMWRP remain more near like the cover images. These visual results are reflected in the data
obtained in the application of the PSNR, SNR, SSIM, CC and MSE metrics. The distribution of the data that
was embedded by LSB, being homogeneous and in large numbers, tends to noticeably alter visual perception,
because more than 3 bits per pixel are modified, making it visually appreciable, on the other hand, in
SMWRP it focuses in locating pixels where large-scale changes are not perceptible, based selectively on the
data being changed.
Figure 10 presents in first place 3 extracts of the images presented in presented in Figures 9(a)
to 9(c), it is possible to visualize the changes that occur when applying the two methods, comparing
Figure 10(a) against Figure 10(b) SMWRP it can be noted that the differences are not visible, because the
modifications in these areas are minor, while comparing Figure 10(a) with Figure 10(c) large changes can be
observed due to that a large amount of data has been entered with LSB. On the other hand, when comparing
the images of Figure 10(d) with Figure 10(e) SMWRP the changes are observed in the central part, but due to
the tonalities found in these areas, there is no impact on the appreciation of digital images. In the red boxes
found in Figures 10(d) to 10(f) can see the differences that exist between the pixels of the stego-images,
where the largest differences stand out in LSB, noting a greater randomness in the tonalities of the pixels.
Finally in Figures 10(g) to 10(i) are extract from ImageNet, in these images is possible see the aggressive
effect from LSB as shown in Figure 9(i) and the modification distribution from SMWRP as shown in
Figure 10(h). During the execution of the tests, the compression process carried out by Lempel–Ziv–Welch
(LZW) and later with DWT-DWT, as well as the recovery of the data recovered from the watermarking
process, generates a time consumption which triples the insertion time with respect to the LSB method, but
SMWRP has the advantage of not visually compromising the result of the steganography process, as well as
avoiding stego-analysis. The results shown in the SSIM and CC metrics for LSB indicate that the images do
not present structural deformations, although visually it is possible to notice the changes in the pixels. While
SMWRP, the scores obtained in both metrics remain above 0.985 points for SSIM and 0.99 for CC.

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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m) (n) (o)
(p) (q) (r)
Figure 9. Visual quality comparison between cover images and stego-image ordered in six groups (a) cover
image, (b) against stego-image SMWRP, and (c) stego-image LSB, (d) cover image, (e) against stego-image
SMWRP, and (f) stego-image LSB, (g) cover image, (h) against stego-image SMWRP, and (i) stego-image
LSB, (j) cover image, (k) against stego-image SMWRP, and (l) stego-image LSB, (m) cover image,
(n) against stego-image SMWRP, and (o) stego-image LSB, and (p) cover image, (q) against stego-image
SMWRP, and (r) stego-image LSB

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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 10. Visual modification difference comparison between images extracts, (a) cover image extract,
(b) against SMWRP stego-imagen extract, and (c) LSB stego-imagen extract, (d) cover image extract,
(e) against SMWRP stego-imagen extract, and (f) LSB stego-imagen extract, and (g) cover image extract,
(h) against SMWRP stego-imagen extract, and (i) LSB stego-imagen extract
The method SMWRP presents an adequate balance with respect to proposals such as [31], as well as
the ability to operate on images with RGB color models, on the other hand, compared to [40], it has the
advantage of embedding a greater amount of data, having a high capacity to evade steganalysis. The
advantage of SVD is in the reduction of the data size and a variable distribution over the image segments
according to the pixel filtering function. Throughout the data analysis, quality check was executed with
advanced metrics such as SSIM, CC to accurately validate the results with respect to the human vision system.
4. CONCLUSION
Watermarks provide many advantages for protection of digital information, since watermarks are
robust against modifications made to the cover images. The characteristics also allow the information
represented by the watermark to be manipulated, since the techniques used for implementation allow the size
of the objects that are embedded to be reduced, particularly in this case digital images. It was observed during
the development of the experiments that the information recovered by means of DWT-SVD had a loss of
approximately 30% with respect to the message that was embedded, but the advantage of the proposal resides
in the fact that when using an RGB image with reduced significant of its original quality as first cover object,
it is possible to compensate the amount of information lost with respect to the final size of the new image that
represents the loss, allowing both objects to be added in order to be embedded in a final stego-image by
steganography.
The initial compression process using LZ77 and B64 is originally capable of reducing up to 50% of
the original size of the message, while by means of the watermark and compression procedure by LZ77 and
B64, it is possible to obtain the reduction of the message converted into an image (first stage of compression)
in a size of 30% with respect to the original. Data embedding mechanism through units’ replacement of
numbers expressed in base 10, corresponding to the pixel values, with respect to LSB allows to significantly
increase the evasion capacity of the classic steganalysis methods that are applied for the mechanisms of bit
substitution embedding. In the tests carried out, the SSIM and CC results for the proposed method always

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obtained scores higher than 0.98, indicating that the modifications made were not significant in the
stego-images. This has been observed that the evasion capacity grows significantly, being up to 93%
effective in evading the analysis executed by StegExpose tool, due to the reduction in randomness that
traditionally occurs when LSB is used. One of the limitations that have been observed with the replacement
of units corresponding to the values of the pixels, is a smaller amount of data that can be embedded, since not
being able to use all the pixels of the cover image to preserve quality otherwise, stego-images drastically
reduce quality, although it is possible to maintain the approval of the steganalysis test.
ACKNOWLEDGEMENTS
We thank CONACYT for the financial support granted to carry out this research project.
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BIOGRAPHIES OF AUTHORS
Hector Caballero was born on May 15, 1988, in Tapaxco, State of Mexico,
Mexico. He received the Ph.D. in Engineering Science degree from Universidad del Estado de
México, México in 2020. His research themes are steganography, biometric systems and
science computing based on natural language. He can be contacted at email:
hcaballeroh045@alumno.uaemex.mx.

 ISSN: 2088-8708
6350
Vianney Muñoz is researcher professor in Image Processing and Computational
Vision at the Autonomous University of the State of Mexico. In 2009 she received her Ph.D.
from Paris 13 University, France. Her research work is about computational vision, image
processing, and video compressing. She can be contacted at email: vmunozj@uaemex.mx.
Marco A. Ramos-Corchado is researcher professor in Artificial Intelligence and
Virtual Reality at the Autonomous University of the State of Mexico. He got his PhD from
Toulouse University in 2007, France. His research themes are artificial life, animation
techniques, distributed systems, and intelligent agents. He can be contacted at email:
maramosc@uaemex.mx.

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