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A novel secured Euclidean space points algorithm for blind spatial image watermarking

Abstract

Digital raw images obtained from the data set of various organizations require authentication, copyright protection, and security with simple processing. New Euclidean space point’s algorithm is proposed to authenticate the images by embedding binary logos in the digital images in the spatial domain. Diffie–Hellman key exchange protocol is implemented along with the Euclidean space axioms to maintain security for the proposed work. The proposed watermarking methodology is tested on the standard set of raw grayscale and RGB color images. The watermarked images are sent in the email, WhatsApp, and Facebook and analyzed. Standard watermarking attacks are also applied to the watermarked images and analyzed. The finding shows that there are no image distortions in the communication medium of email and WhatsApp. But in the Facebook platform, raw images experience compression and observed exponential noise on the digital images. The authentication and copyright protection are tested from the processed Facebook images. It is found that the embedded logo could be recovered and seen with added noise distortions. So the proposed method offers authentication and security with compression attacks. Similarly, it is found that the proposed methodology is robust to JPEG compression, image tampering attacks like collage attack, image cropping, rotation, salt-and-pepper noise, sharpening filter, semi-robust to Gaussian filtering, and image resizing, and fragile to other geometrical attacks. The receiver operating characteristics (ROC) curve is drawn and found that the area under the curve is approximately equal to unity and restoration accuracy of [67 to 100]% for various attacks.

Introduction

Authentication, tamper detection, broadcast monitoring, and copyright protection are the important applications of watermarking [2]. Image watermarking is significant to prove the authentication or ownership of the digital images. It provides copyright protection to the digital images and it is used to detect tampering of digital images [22]. In the proposed work, the watermarking system is designed significantly involving all the above applications. The watermarking systems are categories into two types, they are spatial and frequency domain watermarking, and the trade-off parameters are robustness, imperceptibility, payload, and security [8]. In the literature, it is a challenge to propose a spatial domain watermarking system by maintaining the trade-off parameters. The authors have taken up the challenge to provide a better spatial domain watermarking system.

In digital image watermarking spatial domain watermarking is simple and embedding the logo in the least significant bit offers less robustness, the robustness is increased by embedding the logo in the intermediate significant bits [10]. Kutter and Petitcolas [17] suggest embedding 80 bits of watermark data in the host image for good quality of perception and the recovery of watermark it sufficient to obtain greater than 80% of the watermark. Yinyin et al. [33] thinks that embedding 2 bits in every pixel increases the payload and processing the two images for image integrity makes the work very complex. Chuan et al. [3] develop watermark from MSB and embedding them as reference bits and authentication bits, but according to the benchmarking techniques by Kutter and Petitcolas in [17], the watermark needs to be independent with the host image and it was violated. Shabir et al. [25] developed a watermarking scheme to embed the logo in the intermediate significant bits of the host image at specific spatial locations using a random vector address, the average peak signal-to-noise ratio (PSNR) of five standard images embedding logo in the 4th significant bit is 45.084 dB.

Works on the authentication and tampering are studied in which, few authentication oriented are presented here, Kostopoulos et al., [14] generate authentication codes and embed in the 4 × 4 blocks of host image where the residual histogram is produced. The PSNR values range from 51.454 dB to 48.826 dB depending upon the images. Yinyin et al. [33] implemented reversible data hiding and image authenticated using two images and tampered images are detected. Hong and Chen in [9] made the comparison between pixel pair matching and optimal pixel adjustment process and diamond process. Nikolaidis and Pitas in [20] used watermark casting for protecting the copyright of the digital content and provides robustness against JPEG and low-pass filter attacks. When discussing tampering literature, Zhang and Wang in [31] propose fragile watermarking and use two different types of bits known as reference bits and check bits to obtain the tampered regions from the host image. Similarly, the same author with other co-authors Zhang et al. in [32] proposed recovery of the tampered area from the host image using two methods in which the first method recovers 5 MSB’s digits, and the second method uses restoration methods to recover the data.

Abraham and Paul in [13] works on the spatial color image watermarking scheme, in which out-off the three color frames red, green, and blue, only the blue color frame is used for watermark embedding and the other two color frames red and green are not disturbed. The watermark is embedded in the least significant bit of the blue color frame using a spatial mask, another spatial mask is used for red and green frames to retain the color information.

Wang and Su in [29] the color image is QR decomposed and matrix R is used for copyright protection of the color image in spatial domain. R. Sinhal in [22] converted RGB to grayscale image and embedded the 2 × 4 watermark in the LSB domain in a structure. Chun-Chi Lo and Yu-Chen Hu in [4] worked on the tampered images and the preserving the image integrity. George Voyatzis and Ionnis Pitas in [7] proposed the concepts of robust watermarking with various attacks and stated that geometrical attacks are still a problem to solve. Huynh-The et al. [11] work on the binary watermark bits; they are embedded in the DWT blocks HL4 and LH4 to provide imperceptibility and robustness in the color images. Liu in [16] work on YCbCr color model images, they were tamper-proofed. Using dual-option parity check and morphological operations it was recovered. Sajjad et al. [23] proposed image tampering and restoration using SVD. Lei-Doa and Bao-Long in [15] resist the geometric attacks in the spatial domain, the watermark is embedded in the circular regions of the even–odd quantization.

Qingtang Su et al. in [21] proposed color image watermarking in YCbCr color space and performed watermark embedding in the Y component using the DC component of each 8 × 8 sub-block in the spatial domain similar to DCT transform, this work was robust against signal processing attacks and geometric attacks, it does not specify the pitfalls of the method for the future scope. It does not add the security parameter to the proposed algorithm.

Dipti Prasad Mukherjee et al. [5] work on a new algorithm in the spatial domain, which provides buyer authentication with the multimedia objects, it provides robust against the standard Stirmark attack.

Image authentication scheme is proposed by Zhaxoia et al. in [35] using random values authentication codes are generated and induced in the user-defined seed using Hilbert curve mapping. Authors thought authentication of digital images in the natural way using the concept of moles on the human body. Moles on the human body are considered as one of the basic identification marks (authentication) for a person. In the same analogy, authors thought of establishing moles like watermarks all over the image to provide authentication where these watermark points are invisible and the moles are visible. Mathematical investigation behind moles on the human body is still under research, so author’s proposed the points of watermarks (as like moles) on the digital image mathematically using geometric and arithmetic series. The authors thought of generating geometric sequences instead of any predefined curves. So, in the proposed work the geometric sequences were derived to retain the image authentication with added security concept.

The knowledge behind the Euclidean Space points and their axioms are obtained from [28] the idea behind discrete mathematics in the form of Geometric and Arithmetic Sequence came into play in the author’s mind using from [6]. In the same way, the implementation idea of the Diffie–Hellman key exchange protocol was initiated in [27] explains the similarities and differences between watermark security and cryptography security.

Using the above knowledge, Euclidean Space point’s (ESP) algorithm is designed in the second section. In the third section, the digital watermark embedding scheme in the raw host image is described along with the Diffie–Hellman key exchange protocol algorithm. The blind watermark recovery is described in the fourth section. Testing the proposed work and comparing with the existing methods on the standard raw digital grayscale, and RGB color images are carried out in the fifth section. The results and discussion is carried out with different perspective in the spatial domain with the conclusion of the proposed work.

Methods: Euclidean space point’s (ESP) algorithm and Diffie–Hellman key exchange protocol

Aim

The proposed work objective is:

  1. a)

    To design and develop a New Euclidean Space Points (ESP) Algorithm using discrete mathematics and algebra.

  2. b)

    To implement blind spatial domain image watermarking system for image authentication and copyright protection using the developed ESP algorithm and Diffie–Hellman key exchange protocol algorithm for security purpose.

  3. c)

    To test the authentication and copyright protection of the proposed watermarking system by sending the watermarked images in the Email, WhatsApp, and Facebook platform.

  4. d)

    To test the proposed watermarking system with various attacks.

  5. e)

    To restore the watermark logo after the attacks.

  6. f)

    To analyze and evaluate the proposed watermarking system using quality metrics and statistical methods.

Design

Euclidean space point’s (ESP) algorithm basics

The Euclidean space point’s (ESP) algorithm is designed first by choosing the size of the host image in which the watermarking is desired. Using discrete mathematics, in (discrete mathematics), geometric sequence (GS), and arithmetic sequence (AS) are generated and arranged along the x and y-spatial Cartesian coordinate system using the axioms of the Euclidean plane (UChicago REU, 2013). The generation of GS and AS is described in the ESP algorithm with example values. The points of intercept (POI), of the GS (along with the x-axis), and AS (along the y-axis) in the host image define the ESP to embed the watermark in the spatial domain.

Proposed Euclidean space point’s (ESP) algorithm

  1. Step 1

    : Let the set \({\varvec{x}}=\left({\varvec{x}}_{11},{\varvec{x}}_{21},{\varvec{x}}_{31,}\ldots {\varvec{x}}_{\varvec{n}1}\right)\) and \({\varvec{y}}=\left({{\varvec{y}}}_{11},{{\varvec{y}}}_{21},{{\varvec{y}}}_{31},\dots .,{{\varvec{y}}}_{{\varvec{n}}1}\right)\) are the possible sets of all ordered n-tuples in x-coordinates and y-coordinates. Let \({\varvec{X}}={{\varvec{R}}}_{{\varvec{x}}}^{{\varvec{n}}}\bigcup {{\varvec{R}}}_{{\varvec{y}}}^{{\varvec{n}}}={{\varvec{R}}}^{{\varvec{n}}}\) and the elements of \({{\varvec{R}}}_{{\varvec{x}}}^{{\varvec{n}}}\) and \({{\varvec{R}}}_{{\varvec{y}}}^{{\varvec{n}}}\) are the points in the spatial coordinates. The axioms of the Euclidean spaces are defined in [28].

    $$\mathrm{If }\, x, \mathrm{ and }\, y \in {R}^{n}, a \in R$$
    1. a)

      Vectors additions \(\left({x}_{11}+{y}_{11}, {x}_{21}+{y}_{21}, \dots ., {x}_{n1}+{y}_{n1}\right).\)

    2. b)

      Multiplication by a real number ‘a’.

      $$\alpha x=\left({\alpha x}_{1}, {\alpha x}_{2}, \dots , {\alpha x}_{n}\right)\mathrm{ and }ay=\left(a{y}_{1}, {\alpha y}_{2}, \dots . {\alpha y}_{n}\right).$$
    3. c)

      Vector product \(\left({x}_{1}{y}_{1}+{x}_{2}{y}_{2}+ \dots .+ {x}_{n}{y}_{n}\right).\)

  1. Step 2

    : Geometric sequence is obtained using the recursive Eq. (1):

    $${x}_{11}=x* {r}^{N},$$
    (1)

    where r is the common ratio and \(N \in \left\{0, 1, . . . R\right\}\). The first term is \({x}_{0}= x*{r}^{0}\), the second term is\({x}_{1}= {x}_{0}*{r}^{1}\), the third term is \({x}_{2}= {x}_{1}*{r}^{2}\) and so forth. For example, let r = 2, \({x}_{0}= x=1\), and \(R=\left\{0, 1, 2, 3, . . . 9\right\}\). Thus the sequence \({x}_{11}\) (2) is obtained [10], with the cardinality of 10:

    $${x}_{11}=\left\{1, 2, 4, 8, 16, 32, 64, 128, 256, 512\right\}.$$
    (2)
  2. Step 3

    : Arithmetic sequence is obtained using the recursive Eq. (3):

    $${{y}_{11}=y}_{n}= {y}_{n-1}+d,$$
    (3)

    where d is a common difference, the first term is \({y}_{0}= y\), the second term is \({y}_{1}= {y}_{0}+d\), the third term is \({y}_{2}= {y}_{1}+d\) and so on. For example, let d = 2 and \({y}_{0}= y=1\), thus sequence (4) is obtained [6] with the cardinality of 10:

    $${y}_{11}=\left\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\right\}.$$
    (4)
  3. Step 4

    : To obtain more point locations on the host image, these set points \(\left({x}_{11}, {y}_{11}\right)\), are

    Improved using the Euclidean space points axioms defined in i(a), i(b), and i(c).

    Using the axiom i(b),

    let ‘a’ = 19 (Secret Key) we obtained another \({x}_{12}\) sequence (5) where:

    $${x}_{12}=a* {x}_{11}=19*{x}_{11}$$
    $${x}_{12}=\left\{19, 38, 76, 152, 304, 608, 1216, 2432, \mathrm{4864,9728}\right\}.$$
    (5)

    Similarly \({y}_{12}\) sequence (6) is obtained using the axiom i (b), \({y}_{12}=a*{y}_{11}=19*{y}_{11}\)

    $${y}_{12}=\left\{19, 57, 95, 133, 171, 209, 247, 285, \mathrm{323,361}\right\}.$$
    (6)

    Using the above axiom i (a) we get \({x}_{13}\) sequence (7), \({x}_{13}= {x}_{11}+{y}_{11}\)

    $${x}_{13}=\left\{2, 5, 9, 8, 15, 25, 43, \mathrm{77,143}, 273, 531\right\}.$$
    (7)

    From axiom i (c) we get the sequence, \({y}_{13}\) sequence (8), \({y}_{13}= {x}_{11}*{y}_{11}\)

    $${y}_{13}=\left\{1, 6, 20, 56, 144, \mathrm{352,832}, 1920, \mathrm{4352,9728}\right\}.$$
    (8)

    Here \(\{{x}_{11}\}, \{{x}_{12}\} and \{{x}_{13}\}\) are the possible sets of points in the \(x\)-coordinate. Similarly, \(\{{y}_{11}\}, \{{y}_{12}\} and \{{y}_{13}\}\) are the possible sets of points in the y-coordinate.

  4. Step 5

    If these coordinate points exceed the size of the host image, the location point processing is described below:

    1. a)

      If the size of the host image is M X N then the location points are restricted to the maximum (M, N), by applying modulus M on the x-coordinates points and modulus N on the y-coordinate points.

    2. b)

      The redundant location point values in the x and y-coordinates are removed.

    3. c)

      The set of processed x-coordinates and y-coordinates are taken as the location points to embed the watermark.

This set of sequences can further be expanded, but the designed algorithm takes only the axioms from the sequences (3) and (4) so that the processing time and the complexity can be reduced. An example of the ESP algorithm with (Tables 1, 2, and 3) is explained in the Supplementary material. In this algorithm, to initialize the security to the Euclidean Space points, the secret key is shared between the end-users using Diffie–Hellman key exchange protocol, which is explained in the next upcoming section.

Table 1 Full-reference quality metric and No-reference quality metrics—analysis on standard set of images
Table 2 Analysis of Facebook Images and Logo recovery in 4th, 5th, and 6th-bit planes
Table 3 Visual quality metrics of watermarked RGB color image vs. host RGB color image

Proposed watermark embedding scheme using ESP algorithm

In the proposed work, the host image is selected, and based on the size of the host image (different image sizes are chosen), the Euclidean Space points are designed using the ESP Algorithm. The main objective of the proposed work is to attain a blind and simple watermarking algorithm, imperceptibility of the watermark in the spatial domain, robust watermark for any attack, increased payload, and also to provide security to the watermark to preserve the owner copyrights or authentication. To achieve the mentioned parameters a block diagram is proposed which is shown in Fig. 1, the block diagram performs Euclidean space point’s based spatial domain watermarking and it is analyzed with both the grayscale image and RGB color model image. The proposed block diagram and algorithm are analyzed with the grayscale images and also with the RGB color model images.

Fig. 1
figure 1

Euclidean space points spatial domain watermarking

Proposed block diagram

In the proposed block diagram Fig. 1, the grayscale host image is first chosen in which the watermark is to be embedded. Next according to the size of the host image Euclidean space points are generated using the ESP algorithm. After obtaining the Euclidean space points, the grayscale intensity values of the host image at the POI are obtained and these grayscale intensity values of the host image are converted into its eight binary equivalent digits.

The watermark image or Logo is converted into a binary logical image using Otsu’s adaptive threshold method [26]. The binary digits of the logical logo are embedded in one of the bit planes or positions of POI obtained from the Euclidean space points and the watermarked image is obtained. The analysis was done on the host image by embedding the logo binary digits in every bit position of the POI. The watermarked image performance was obtained and it is described in the results and discussion.

In the second stage of the work, the RGB color image model is chosen as the host image. In this second proposed methodology, the RGB host image is processed by separating the red, green, and blue frames. The ESP algorithm is obtained according to the size of the Blue frame to obtain POI to embed the watermark logo. Intensity values of the blue frame at POI are obtained and converted to 8-bit binary digits. The binary digits of the logical logo are embedded in every bit position of POI and analyzed by merging the two frames. Similarly, the green color frame and red color frames are processed separately and analyzed. The results are described in the “Results and discussion” section. After individual frame processing, red, green, and blue frames are embedded with Logo2 at the same time and combined to get the RGB watermarked image.

According to the concept of cryptography algorithm, public keys are shared in the public domain and private keys are shared securely. In the ESP algorithm, the initial x-coordinate value \(\left({x}_{0}\right)\), the initial y-coordinate value \(\left({y}_{0}\right)\), the common ratio value \(\left(r\right)\), the common difference value \(\left(d\right)\) and secret key value \(\left(a\right)\) could be defined by the sender to obtain security of the Euclidean space points. This provides security to the Euclidean Space points where the watermark logo is going to reside. The concept of sharing private keys using Diffie–Hellman key exchange protocol is explained in the next section.

Diffie–Hellman key exchange protocol algorithm

The security of the secret key Diffie–Hellman key exchange protocol (DHKEP) [24] is one of the best algorithms to share the secret key securely in an unsecured channel [30].

The procedure of key exchange protocol is as follows:

  1. i.

    Let the two users be transmitter ‘T’ and receiver ‘R’ in a treaty to share the secret key.

  2. ii.

    In the treaty both ‘T’ and ‘R’ users agree on two prime numbers ‘P’ and ‘G’ and these are in the public domain. Choose P as a large number.

  3. iii.

    G is the primitive root modulo P.

  4. iv.

    Let ‘T’ and ‘R’ users choose privately ‘a’ and ‘b’—a large random number or secret key or private key.

  5. v.

    ‘T’ computes \(A= {G}^{a}mod P\) and sends to ‘R’ and ‘R’ computes \(B= {G}^{b}mod P\) and sends to ‘T’. Both ‘T’ and ‘R’ computes the shared key \(K= {G}^{ab}mod P,\)

where ‘T’ computes \(K={B}^{a} \mathrm{mod} P= {\left({G}^{b}\right)}^{a} \mathrm{mod} P ,\) and ‘R’ computes \(K={A}^{b} \mathrm{mod} P= {\left({G}^{a}\right)}^{b} \mathrm{mod} P\). ‘T’ and ‘R’ share the shared key ‘K’ to exchange the secret key securely. This algorithm is the discrete logarithmic problem and it is equally as hard as RSA. In this proposed work P = 7919, G = 3041, a = 19 and b = 17, A = 2753, B = 4886.

Proposed blind watermark extraction methodology

Figure 2 shows the proposed blind watermark extraction block diagram at the receiver end. In the transmission section, the host image could be either the grayscale image or the RGB color image. In the receiver section, after obtaining the watermarked image, the watermark logo can be removed and checked based on the required strategies. To prove the authentication of the sender at the transmission end the watermark logo could be recovered from the watermarked image without using the original logo or partial logo or original image, so the recovery of the watermark logo is very blind, so it is called blind watermarking. The logo is recovered by generating the secret key value ‘a’ from the shared keys between the two parties ‘T’ and ‘R’ using the Diffie–Hellman key exchange protocol.

Fig. 2
figure 2

Blind recovery of watermark

Then the Euclidean space points are generated at the receiver end. The key value provides security to the location points of Euclidean space points where the logo was embedded. After obtaining the Euclidean space points from the secret key value, POI is obtained on the watermarked image, the intensity values of the POI from the watermarked image are obtained from all the specific locations of POI, and it is converted into its binary equivalent digits. As per the end–end user treaty, the bit where the digital bit of logo is embedded is obtained and all the digital bits are processed to form the logical digital binary logo, and hence the logical digital binary logo is recovered blindly without the use of any host image information or original watermark logo information and it proves the authentication or ownership of the user. Similarly, the logo is recovered from the RGB color image, and analysis was done and it is described in the “Result and discussion” section.

Results and discussion

The Euclidean space points (point of intercept of GS and AS) are obtained and shown in Fig. 3. The complete proposed work is implemented using custom MATLAB R2018a coding.

Fig. 3
figure 3

Euclidean space points—for 512 × 512 host image with the initial values x0 = y0 = 1, r = 5, d = 2, secret key = 19

In the proposed work, the host image is selected and the Euclidean space points are generated using the ESP algorithm according to the size of the host image. Depending upon the initial values and secret key value the Euclidean space points are obtained, these points spread over the entire region of the host image, and it is an advantage that, when the watermark spreads over the entire region of the host image, authentication of the digital image could be obtained from every corner of the image.

Measure of imperceptibility

The proposed watermarking scheme is applied on the data set (ImageProcessingPlace.com), in [12] which there are 166 raw images they are Gray Scale Data Set: Tiff_Sequence_Images: 64 images, Tiff_Texture_Image: 64 images, Tiff_Misc_Images: 25 images, and Standard_PNG_Images: 13 images, and JPG_Football_images: 44 images. ImageProcessingPlace.com data sets are the Image databases and it is selected because:

  1. a)

    These are the standard test images found frequently in literature.

  2. b)

    Almost all the images are uncompressed with higher resolution.

  3. c)

    Image databases are used for digital image processing using MATLAB, and they are in the DIP4E and DIPUM3E Faculty and Students Support Packages.

  4. d)

    In one place faculty and students can select different image data base according to their work.

  5. e)

    These databases are used in more than 50 countries worldwide.

  6. f)

    More than 1K research institution, industries, and educational institutes use DIP and DIPUM image databases.

Most of the books, journals and publishers used these image databases

In Fig. 4, ‘10’ standard grayscale images of size 512 × 512 and ‘3’ standard color images of size 512 × 512 are shown as few example images. Logo2 is 64 × 64 which is the same proposed in [13]. In this proposed work, the grayscale Logo1.jpg or Logo2.jpg is used and is converted to a logical binary logo. The ESP algorithm is used to obtain the point of intersection of GS and AS according to the size of the host image. The length of the GS and AS is 90 without excluding zeros and redundant values. By removing the zeros and redundant values, the length of the GS and AS is 73, so 73 POI-ESP are obtained to embed the watermark of size 32 × 32 logical binary logo, that is 1024 bits are required and for the 64 × 64 logical binary logo 4096 bits are required to embed the binary logo in the host image. To obtain better imperceptibility of the watermark these 73 POI-ESP are not sufficient to embed the watermark. So, from GS and AS a maximum of 73 × 73 array of POI is developed to hide the watermark in the host grayscale image. The 73 × 73 POI of the host image is converted into 8-bit binary digits, and the logical binary digits of Logo1 are embedded in every bit and analyzed. The analysis is carried out with 166 raw grayscale images (*.tiff and *.png) and 44 *.jpg images. The proposed methodology is analyzed with two types of quality metrics are Full-reference quality metrics and No-reference quality metrics.

Fig. 4
figure 4

Images: up to down. From left to right: first row: cameraman.tif, Lena.tif, Mandril_gray.tif, Pepper.tif, Pirate.tif, second row: Walkbridge.tif, Woman_blonde.tif, Woman_blackhair.tif, White_Page.tif, Black_Page.tif, third row: Lena_Color.tif, Mandril_Color.tif, and Pepper_Color.tif (grayscale and color host images of size 512 × 512), Logo1.jpg and Logo2.jpg (Grayscale images of size 64 × 64)

Evaluation of image watermarking quality metrics

Image watermarking could degrade the quality of the host image to a certain degree, to test the watermarked image quality metric equal to the subjective perception of quality by a human observer [36] it can be done using two methods are Full-reference quality metrics and No-reference quality metrics. In the Full-reference quality metric, there are three algorithms used to check the quality of the image, they are image mean square error (MSE), image peak signal-to-noise ratio (PSNR), and image Structural Similarity Index (SSIM). MSE and PSNR are simple to calculate it is given in Eq. 9 from [19] peak Val is the maximum intensity value of the image, and Eq. 10, but they are very less compared to the quality of human perception:

$$\mathrm{PSNR}= 10 {\mathrm{log}}_{10}\frac{{\mathrm{Peak} \mathrm{Val}}^{2}}{\mathrm{MSE}},$$
(9)
$$\mathrm{MSE}= \sum_{k=1}^{3}\sum_{i=1}^{M}\sum_{j=1}^{N}\frac{\mathrm{WI}\left(i, j\right)-I\left(i, j\right)}{3*M*N},$$
(10)

where WI(i, j) is the watermarked image and I(i, j) is the host image.

SSIM metric consists of luminance, contrast, and structural information of the digital image. The human visual system (HVS) perception is good at observing structures that are used in SSIM, so the metric SSIM is more related to the subjective quality score of human beings. Structural Similarity Index [26] is given in Eq. 11:

$$\mathrm{SSIM}= {\left[l\left(I,\mathrm{WI}\right)\right]}^{\alpha }* {\left[c\left(I, \mathrm{WI}\right)\right]}^{\beta }* {\left[s\left(I, \mathrm{WI}\right)\right]}^{\gamma }.$$
(11)

SSIM is based on the computation of three terms; they are luminance, contrast, and structural. They are computed using Eqs. (12), (13), and (14):

$$l\left(I, \mathrm{WI}\right)= \frac{2{\mu }_{I}{\mu }_{\mathrm{WI}}+{C}_{1}}{{\mu }_{I}^{2}+{\mu }_{\mathrm{WI}}^{2}+{C}_{1}},$$
(12)
$$c\left(I, \mathrm{WI}\right)= \frac{2{\sigma }_{I}{\sigma }_{\mathrm{WI}}+{C}_{2}}{{\sigma }_{I}^{2}+{\sigma }_{\mathrm{WI}}^{2}+{C}_{2}},$$
(13)
$$s\left(I, \mathrm{WI}\right)=\frac{{\sigma }_{I\mathrm{WI}}+{C}_{3}}{{\sigma }_{I}{\sigma }_{\mathrm{WI}}+{C}_{3}},$$
(14)

where \({\mu }_{I}, {\mu }_{\mathrm{WI}},{\sigma }_{I}, {\sigma }_{\mathrm{WI}, }\mathrm{and} {\sigma }_{I\mathrm{WI}}\) are the local means, standard derivations, and cross-covariance for images I (host image) and WI (Watermarked image).

If \(\alpha = \beta = \gamma =1 (\mathrm{default})\)

$${C}_{3}=\left. {C}_{2} \right/2$$
(15)

Substituting Eqs. 12, 13, 14, and 15 in 10, we obtain equation from [32]:

$$\mathrm{SSIM}\left(I, \mathrm{WI}\right)=\frac{\left(2{\mu }_{I}{\mu }_{WI}+{C}_{1}\right)\left({2\sigma }_{IWI}+{C}_{2}\right)}{\left({\mu }_{I}^{2}+{\mu }_{WI}^{2}+{C}_{1}\right) \left({\sigma }_{I}^{2}+{\sigma }_{WI}^{2}+{C}_{2}\right)}.$$
(16)

The formula to calculate the correlation coefficient is given in Eq. (17):

$$\mathrm{CC}= \frac{\sum_{M}\sum_{N}\left({I}_{M, N}-\overline{I } \right)\left({WI}_{M, N}-\overline{W }\right)}{\sqrt{\left(\sum_{M}\sum_{N}{\left({I}_{M, N}-\overline{I } \right)}^{2}\right)\left(\sum_{M}\sum_{N}{\left({WI}_{M, N}-\overline{W }\right)}^{2}\right)}},$$
(17)

where \(\overline{I }\) is the mean of the original image and \(\overline{W }\) is the mean of the watermarked image. The correlation coefficient value ranges from − 1 to 1. ‘M’ and ‘N’ are the number of rows and columns of the host image I(M, N) and watermarked image WI(M, N). The bit error rate is the ratio of no. of bits in error to that of total no. of bits.

The watermark Logo1 or Logo2 is embedded in all the bit planes of Fig. 4 images (Table4 in Supplementary material) at the specific ESP of I(M, N). Full Reference Quality Metric is measured, it is observed that using the proposed ESP algorithm and embedding methodology in the spatial domain gives the average PSNR of 46.21356 dB and 40.3028 dB between I and WI at the 5th-bit plane or position due to the logical binary logo of size 32 × 32 and 64 × 64, respectively. At the 4th bit plane, the PSNR is 52.53392 and 46.4826, respectively. The PSNR is above 45 dB even if the watermark binary logo is embedded in the 4th-bit plane. In all the 166 raw grayscale images (*.tiff and *.png) the 64 × 64 size binary watermark logo ‘Logo2’ is embedded in the 4th bit plane of the host image at the specific ESP, and whereas in the 44 *.jpg images, the watermark is embedded in the 6th-bit plane instead of 4th plane because in compressed images *.jpg, the embedded watermark in the 4th-bit plane could not be recovered properly.

Table 4 PSNR comparison of the proposed method with the other methods on Lena (512 × 512) image

No-reference quality metrics

In the No-reference quality metrics evaluation method, there are two algorithms, the first algorithm is Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE), and the second algorithm is Natural Image Quality Evaluator (NIQE) from [1]. BRISQUE model is trained with the set of images with the known distortion, whereas NIQE can evaluate the quality of the images with arbitrary distortion. BRISQUE is opinion-aware that is the subjective quality score that correlates with HVS but NIQE is opinion-unaware. Figure 5 shows the relationship between the average SSIM and the average BRISQUE score of all the 10 standard grayscale images.

Fig. 5
figure 5

Average SSIM vs. average BRISQUE score

The BRISQUE value is low for good images and high for the distorted images. The proposed ESP algorithm and embedding methodology satisfy the relationship between BRISQUE and SSIM. Table 1 gives the values of the Full-reference quality metric and No-reference quality metrics of all the standard sets of images.

In all the raw images, that is *.tiff, *.tif, and *.png the watermark Logo2 is embedded in the 4th bit plane of a specific ESP location. In the compressed images (*.jpg), Logo2 is embedded in every 4th, 5th, and 6th-bit plane to check the blind recovery of Logo2 at the receiver end. The average Full-reference quality metrics and average No-reference quality metrics of all the images between the ‘I’ and ‘WI’ are measured. According to the measurement in Table 1, as the MSE (mean square error) more the PSNR (peak signal-to-noise ratio) is less. Similarly, the BER (bit error rate) is high for high MSE.

Watermarked image analysis via Email, WhatApp, and Facebook

All the raw watermarked images (WIs) are zipped, attached in a folder, and sent to the personal email. The WIs from email (E_WI) are downloaded and extracted through the compressed folder. Performance metric analysis on the images WI and E_WI is done and it is found that the PSNR is infinite dB, SSIM is unity, BER is zero, and NC is unity. All the embedded logos are perfectly recovered from all the sets of images. Similarly, all the WIs are sent individually in WhatsApp and downloaded from WhatsApp the metric analysis between WI and W_WI is done the result values are as same as email.

In the same way, the WIs are uploaded to the authors' Facebook (FB) book account and downloaded individually. It is shown in Fig. 6. The observations made in the analysis are the following:

  1. a)

    The input data set raw images are in the format *.tiff, *.tif, *.png, the output image downloaded from FB is *.jpg.

  2. b)

    If the size of the WI to the FB is M x N (less than 1024 X 1024 pixels), occupied space say XX KB (below 1 MB) of memory in the drive, the F_WI size is as same as input image with fewer data storage (approximately XX/4 KB). That is the memory compression is carried in FB. The embedded logo is blindly recovered.

  3. c)

    If the size of the WI to the FB is greater than say 1024 X 1024 pixels and occupying more than 1 MB of storage, then the F_WI size is different from that of the WI, and memory compression takes place it is approximately equal to XX/2.

  4. d)

    In this proposed work, if the size of the image is altered to a greater extent, the logo could not be perfectly recovered.

  5. e)

    Authentication is tested from the F_WI images, it is observed that the binary watermark logo embedded 4th bit of host image could be partially recoverable with very low SSIM and PSNR. Then logo is embedded in the 5th and 6th-bits, found that the logo from F_WI could be recovered blindly.

Fig. 6
figure 6

Analysis of watermarked image via E-mail, WhatsApp and Facebook

So for this proposed algorithm, 5th-bit logo embedding is advisable for the Facebook image authentication, because the 6th-bit offers very low PSNR (less than 40dB) between I and F_WI from Table 2.

It is analyzed by comparing the histograms of WI and F_WI. The histogram difference between the WI and F_WI is similar to exponential noise. It is submitted in Annexure (Table 5) since the numbers of tables are more in this work:

  1. f)

    All the Logos from WI are recovered blindly. So the proposed work falls in the category of blind image watermarking.

Table 5 Confusion matrix to test the algorithm and watermarking scheme

Attacks and tests for image authentication

To test the proposed scheme for image authentication, the WI tampers with various attacks. The watermark logo is obtained from the tampered watermarked image without the reference of the host image (Blind Watermarking) and compared with the original logo as shown in Fig. 7. The tampered watermarked image obtained at the receiver section is processed with the ESP algorithm and the watermark logo is extracted. The tampered image can be recovered using the steps followed in Fig. 7.

Fig. 7
figure 7

Image authentication and recovery from tampered watermarked image

The tampered image is recovered using the host image as a reference, at first the tampered image and the host image are subtracted to get the residual tampered region. Next, the residual tampered image region coordinates are collected and mapped with the coordinates of the host image. The intensity values of the coordinates from the host image are collected and the intensity values are replaced in the residual region to recover the tampered region. The PSNR between the recovered watermarked image and the watermarked image is infinity. In the proposed watermarking scheme even if the watermarked image tampers more than 90%, detection of the watermark is done as shown in Fig. 8h. Figure 8a–o shows the extraction of the watermark logo from the tampered watermarked images with different percentages of tampering. Tampering on the watermarked image was tested on the standard Lena image of size 512 × 512 with the tampering rate from 0.59 to 95% the proposed work provides the PSNR of the watermark logo in the range of [81.2441 to 52.9996]. This shows that the proposed ESP algorithm, the watermarking embedding and recovering scheme offers very good image authentication.

Fig. 8
figure 8

Recovery of watermark from tampered watermarked images for image authentication

Imperceptibility in color images

RGB color image model analysis: Lena.png image is processed by embedding Logo2.jpg in individual color frames and the PSNR of the watermarked image and RGB host image is calculated and shown in Table 3. The proposed work performance is very excellent compared with the other existing methods. Table 3 is evident for its performance. The BRISQUE score for the good quality image should be a low value, the ESP algorithm and the watermarking scheme provide the best watermarking, and the relationship between the PSNR, SSIM, and BRISQUE also satisfies the relation. Another observation is that the embedding can be carried out up to the 4th-bit position and 5th-bit position in the POI where the watermark would be still imperceptible.

The restoration process of RGB color images

In the practical view, when the digital images are transmitted in the channel, images may lead to different attacks by the intruders it may be an intentional or unintentional attack. The proposed work needs to offer good robustness and security to the intruders. So to check the performance of the proposed algorithm 10 standard sets of raw images from (ImageProcessingPlace.com) are taken. Different types of attacks are performed on the watermarked image and the performance of the proposed ESP algorithm and the watermarking scheme was tested using the performance metrics SSIM, cross-correlation function (CC), mean square error (MSE), and bit error rate (BER). Figures 9, 10, 11, 12, 13 show the visual quality metrics on the recovered watermark before and after restoration. The Logo2 is embedded in all three color frames Red, Green, and Blue. The average SSIM of Logo2 before restoration that is after all attacks on the RGB color watermarked image is 0.979294 and after restoration is 0.995141. The restoration process enhances the correlation coefficient value to a greater extent. The restoration process was done as follows:

Fig. 9
figure 9

Attacks vs. visual metrics—correlation coefficient

Fig. 10
figure 10

Attacks vs. visual metrics—SSIM

Fig. 11
figure 11

Attacks vs. bit error rate

Fig. 12
figure 12

Attacks vs. mean square error

Fig. 13
figure 13

Attacks vs. accuracy of logo obtained after restoration

Input Host image: RGB Color Model image.

  • Step 1: Store all the three color frames separately as ‘R’, ‘G’, and ‘B’ of the host image.

  • Step 2: After watermarking and transmitting from the transmitter section in Fig. 1, store the watermarked image in the receiver section.

  • Step 3: Let ‘R_A’, ‘G_A’, and ‘B_A’ be the three color frames after an attack.

  • Step 4: Restoration process: Let ‘Res_A’, ‘Res_G’, and ‘Res_B’ be the restored frames.

  • Calculate Res_A = R – R_A; Res_G = G – G_A; and Res_B = Res_B – B.

  • Step 5: Using the restored frames Logo2 can be obtained with acceptable visual quality.

Using the above restoration process, the average correlation coefficient on all the attacks was increased by 0.450106 times.

The average mean square error and average bit error rate on all the attacks were decreased by 0.232843 and 953.7059.

The accuracy is calculated by using the formula from [18] after the restoration process, it is given in Eq. (18):

$$\mathrm{Accuracy}= \frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}},$$
(18)

where TP: true positive, TN: true negative, FP: false positive, and FN: false negative.

Figure 12 shows that after the restoration process, the watermark Logo2 can be obtained with an accuracy of more than 67%. So the proposed ESP algorithm, watermarking scheme, and restoration scheme work more accurately.

Watermark restoration

The watermark Logo2 was better restored after the restoration process.

In Fig. 14, watermark Logo2 after the attack and restored watermark Logo2 from the watermarked image is shown with all different kinds of attacks. The proposed watermarking scheme and the algorithm are immune to salt-and-pepper noise and sharpening filter that is before restoration.

Fig. 14
figure 14

Attacks and recovery of Logo2 before and after restoration

Comparison with the existing methods

Comparison of average PSNR values of 10 standard grayscale images with the other existing methods is presented in Table 4. The proposed ESP algorithm and watermarking methodology were analyzed by embedding a logical binary logo individually in every bit position of the host image. In Fig. 2 of Chuan Qin et al. in [3] at page 236, the watermark bits are used to recover MSB layers of the tampered image but watermark bits can authenticate the tampered images without recovering them since the purpose of watermarking is to provide image authentication.

In [3] tampering of Lena 512 × 512—the grayscale image at 6.84% leads to a PSNR of 44.16 dB and the recovered image has the PSNR of 46.37 dB which at the embedding mode (6, 2). In Table 4 the proposed method is compared with the particular references [3, 22, 31], and [32] because all these existing methods are purely based on spatial domain image watermarking technique as the proposed work, in which the PSNR metric is calculated depending upon the different significant bits i.e. from ISB to LSB. In a similar manner, the existing techniques calculated PSNR metric after restoration technique from tampering attack.

Comparison of statistical performance with the existing methods

In [33], the confusion matrix and its analysis were carried out to find the TPR (true positive rate) and FPR (false positive rate) to check the quality of the proposed work. Similarly, for the proposed work statistical performance was carried out. The confusion matrix was constructed and is shown in Table 5.

The formula for TPR and FPR is calculated from [18] and it is given in Eqs. (19) and (20):

$$\mathrm{True positive rate} \left(\mathrm{TPR}\right)= \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}},$$
(19)
$$\mathrm{False positive rate} \left(\mathrm{FPR}\right)= \frac{\mathrm{FP}}{\mathrm{FP}+\mathrm{TN}}.$$
(20)

Using the above confusion matrix, Eqs. (19) and (20), Table 6 values are calculated for the proposed work and compared with the existing works.

Table 6 Comparison of statistical parameters with the existing methodologies

In Table 6 the statistical parameters TP, TN, FP FN, TPR and FPR are calculated for the proposed work to check the performance of the proposed watermark embedding and blind recovery using ESP algorithm with the other existing methods in [4], [33], [34] and [35]. In the existing methodologies similar statistical parameters were used to analyze the watermarking system, so these reference were chosen for comparison. From Table 6 it is evident that TPR is higher and FPR is lower for the proposed methodology than all other existing methods in [4], [33], [34] and [35]. So the proposed methodology is better than the other existing methodologies.

The proposed system is compared with Chun-Chi Lo et al. [4], and Zhaoxia Yin et al. [35]. It is found that the TPR value is high and the FPR value is very less compared with all the other existing methodologies, which confirms that the proposed ESP algorithm and the watermarking scheme is better than the other existing schemes. The receiver operating characteristics (ROC) curve is drawn in Fig. 15 for the 10 standard grayscale images and it is shown that the area under the ROC is nearly equal to unity. Similarly, raw RGB color images (17.png images and 10 raw.tif) were also analyzed with the ESP algorithm and the proposed watermarking methodology. The comparison of the proposed work is carried out with the standard Lena.tif (512 × 512 × 3) image and is shown in Table 7.

Fig. 15
figure 15

ROC curve using proposed system

Table 7 Comparison of color images with the existing methods

In Table 7, the proposed method is compared with [11, 13, 16, 22] and [34] existing methods because in these existing methods spatial domain watermarking on color images are focused. The proposed work has excellent image subjective quality than the other mentioned existing methods.

Jobin Abraham and Varghese Paul in [13] used masks to adjust the color variation after watermark embedding and the same Logo2 was used in embedding but the PSNR was very low compared with the proposed work and in this work, there is no need for such mask. The work is done in [11] and [16] also does not require such a mask, the proposed ESP algorithm and watermark embedding scheme provides very high PSNR at the LSB level. The PSNR 69.1941 dB is achieved when the Logo2 is embedded in the 4th bit plane of Lena image of size (512 × 512).

Conclusion

Blind and semi-fragile spatial domain watermarking is proposed for image authentication. The ESP algorithm is developed with fixed initial values and a secret key. The points of intercept, of GS and AS make the algorithm to be more secured where the confusion probability will be more. It is difficult for the intruder to identify the watermark presence in the host image since the logo is embedded appending the Diffie–Hellman key exchange protocol with the ESP algorithm. According to the proposed methodology embedding the logo is better in the 4th bit plane for the raw images and the 5th-bit plane for compressed images, where the authentication could be done perfectly. The proposed ESP spreads over the entire region of the host image, so the image authentication could be done from any corner of the image. The image authentication is tested by sending the WI in the E-mail, WhatsApp, and Facebook. It is observed that using this proposed method, image authentication in E-mail and WhatsApp can be done perfectly with 100% accuracy the SSIM of the original Logo and recovered Logo is unity. In FB, to obtain better image authentication, the embedding is done in the 5th-bit plane of the host image, because after downloading the WI from the FB the WI is in the compressed format. So the image authentication is done with more accuracy. Image tampering attacks are done on the WI with the tampering attack ranging from 0.59 to 95%, the proposed work provides the PSNR of the watermark logo in the range [81.2441 to 52.9996] dB. The proposed work is robust to JPEG compression from it can withstand up to 7:1 compression ratio as given in Table 2. Similarly, the work is robust to tampering, image cropping, salt-and-pepper noise, sharpening filter, semi-robust to Gaussian filtering, rotation (1°), and image resizing, and fragile to other geometrical attacks. Logo detection is 100% after averaging filter attack, tampering WI with 32 × 32 grayscale image attack, and sharpening filter attack. The average accuracy of logo detection is more than 65% for all the attacks. The proposed ESP algorithm and the watermark embedding scheme provide higher imperceptibility, security, and robustness to the raw and compressed grayscale images. Similar to the RGB images, it offers higher imperceptibility with a higher payload and the logo recovery rate is very high. Overall, the proposed methods provide the best image authentication compared with the other existing methods.

Future scope

The proposed work is handcrafted over different image data set of various sizes and it is working well for the grayscale images and also with the color images, but the downloaded colored watermarked images from the FB give poor authentication. After embedding the watermark logo in all three color frames separately, the PSNR between the host image and FB_WI is 45 dB which is acceptable. But the authentication is not satisfactory for the author, where the SSIM is very low. The downloaded watermarked image from FB is checked with the original WI image, it is observed that about 48.19% of pixels are affected in FB color image. So another spatial watermarking method is to be developed for color images to maintain authentication in FB. Deep Neural Networks (DNN)-based spatial domain watermarking with the handcrafted ESP algorithm is the future scope of this proposed work.

Availability of data and materials

MALTAB Coding – Individually for Every Image Set.

Image Data Set (*.tiff, *.tif, *.png, *.jpg).

Example of the Proposed ESP Algorithm and Complete Quality Metric Analysis of images.

Abbreviations

*.jpeg:

Joint Photo Experts Group—Image Format

*.jpg:

Joint Photo Graph—Image Format

*.png:

Portable Network Graphics—Image Format

*.tif:

Tagged Image File

*.tiff:

Tagged Image File Format

AS:

Arithmetic sequence

BER:

Bit error rate

BRISQUE:

Blind/referenceless image spatial quality evaluator

CC:

Cross correlation

dB:

Decibels

DHKEP:

Diffie–Hellman key exchange protocol

ESP:

Euclidean space points—algorithm developed for the proposed work

FB:

Facebook

FN:

False negative

FP:

False positive

FPR:

False positive rate

GS:

Geometric sequence

I(M, N):

Input image, of size M—rows and N—columns

ISB:

Intermediate significant bit

JPEG:

Joint Photograph Experts Group

KB:

Kilo byte

LSB:

Least significant bit

MSB:

Most significant bit

MSE:

Mean square error

NIQE:

Natural image quality evaluator

POI:

Point of intercept

PSNR:

Peak signal-to-noise ratio

RGB:

Red green and blue frames—from a color image

ROC:

Receiver operating characteristics

SSIM:

Structural similarity

TN:

True negative

TP:

True positive

TPR:

True positive rate

WI(M, N):

Watermarked image of size M, N

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Acknowledgements

I extend my sincere thanks and gratitude to Dr. P. Suhail Parvaze, Ph. D, IIT Madras, and Research Consultant for Philips India, for his valuable suggestions and to improve the quality of the paper.

Funding

The proposed work was not applied to any of the organization, so there is no funding applicable for this work.

Author information

Authors and Affiliations

Authors

Contributions

Contribution of the first author: designed, developed and MATLAB implementation of the three modules they are (i) new ESP algorithm (ii) DHKEP, and the watermarking system. (iii) Testing and analysis. Contribution of the second author: (i) discussed the literature survey and its outcomes (ii) suggested the test to send in Email, WhatsApp and Facebook. (iii) Watermark restoration process. Both authors read and approved the final manuscript.

Corresponding author

Correspondence to Shaik Hedayath Basha.

Ethics declarations

Competing interests

Image authentication scheme [35] is proposed using Hilbert curve mapping which is complex instead of that the authors proposed simple ESP algorithm using geometric and arithmetic sequences with added security.

Compared with [35] our system is simple, semi-robust and secure.

In RGB watermarking, Jobin Abraham and Varghese Paul [13] used spatial mask to recover the distorted Red and Green Frames, In this work No such Spatial Masks are required.

The False Positive Rate of the proposed system is less compared with [3, 33] and [35] works.

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Basha, S.H., B, J. A novel secured Euclidean space points algorithm for blind spatial image watermarking. J Image Video Proc. 2022, 21 (2022). https://doi.org/10.1186/s13640-022-00590-w

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Keywords

  • Authentication
  • Attacks
  • Image analysis
  • Euclidean space points (ESP)
  • Tampering
  • Watermarking