# Blind Color Image Watermarking Using Fan Beam Transform and QR Decomposition

^{1}

^{2}

^{*}

## Abstract

**:**

^{*}a

^{*}b

^{*}color model and FBT is applied to b

^{*}component. Then the b

^{*}component of the original image is split into m × m non-overlapping blocks and QRD is conducted to each block. Watermark data is placed into the selected coefficient of the upper triangular matrix using a new embedding function. Simulation results suggest that the presented algorithm is extremely robust against numerous attacks, and also yields watermarked images with high quality. Furthermore, it represents more excellent performance compared with the recent state-of-the-art algorithms for robustness and imperceptibility. The normalized correlation (NC) of the proposed algorithm varies from 0.8252 to 1, the peak signal-to-noise ratio (PSNR) varies from 54.1854 to 54.1892, and structural similarity (SSIM) varies from 0.9285 to 0.9696, respectively. In contrast, the NC of the recent state-of-the-art algorithms varies from 0.5193 to 1, PSNR varies from 38.5471 to 52.64, and SSIM varies from 0.9311 to 0.9663, respectively.

## 1. Introduction

^{*}component of original image employing an insertion operation; (iii) the process of detecting watermark is blind; and (iv) it yields a significant trade-off for imperceptibility and robustness. Experimental results suggest that the introduced algorithm shows significance resistance against diverse attacks. Besides, it yields watermarked images with high quality. Furthermore, it shows more excellent result in comparison with the recent state-of-the-art algorithms [19,20,21] for imperceptibility and robustness. It is because watermark information is inserted into the first row fourth column of the upper triangular matrix acquired from the FBT coefficients of b

^{*}component of original image using a new embedding equation.

## 2. Background Information

#### 2.1. Fan Beam Transform

^{2}. Also consider a point S as source and ${v}_{\theta}$ as unit vector in a direction θ ∈ [0, 2π] on the plane. Then, FBT, denoted by F, applies on function f as follows:

#### 2.2. QR Decomposition

## 3. Proposed Watermarking Algorithm

#### 3.1. Watermark Embedding Process

^{*}a

^{*}b

^{*}color model which is represented by I.

^{*}component of L

^{*}a

^{*}b

^{*}color model I is selected, because human visual system is less sensitive to b

^{*}component. Then, FBT is applied to b

^{*}component to obtain FBT coefficients which are represented by C with size U × V.

_{q}is calculated which is represented by

_{q}is the determinant of each block B

_{q}. Then n blocks with larger determinants are selected, where ${E}_{select}=\left\{{E}_{s},1\le s\le n\right\}$ represents the determinant of corresponding selected blocks represented by $G=\left\{{G}_{s},1\le s\le n\right\}$.

_{s}is selected for inserting watermark.

_{s}. Let

_{1}= −0.5Δ, T

_{2}= 0.5Δ

_{1}and T

_{2}are magnitudes and Δ is the quantization step size. The element ${r}_{s;(1,4)}$ is selected because it is likely to be greater than those of the elements in other rows which allows a greater modified range. Moreover, this element has an indirect effect on the first row fourth column element of each block.

^{’*}component.

^{*}a

^{*}b

^{’*}color model I

^{’}is transformed into RGB color model to obtain the watermarked image A

^{’}.

Algorithm 1: Watermark Inserting Procedure |

Declaring variables: |

A: original RGB image |

$I$: converted L^{*}a^{*}b^{*} image |

Y: watermark sequence |

C: FBT coefficients |

B: block with size m × m |

G: selected block with size m × m |

Q: unitary matrix with size m × m |

R: upper triangular matrix with size of m × m |

${r}_{s;(1,4)}$ = selected element for embedding watermark |

FBT and QRD: transformation and decomposition used in the algorithm |

Watermark Embedding Procedure: |

Read the host image and watermark image |

A.bmp (original image with size 512 × 512) |

W.bmp (color watermark image with size of 16 × 16) |

for i = 1: N |

j = 1: N do |

Separate W into R, G, and B components and convert them into binary sequence |

end for |

return the watermark sequence |

for k = 1: M |

l = 1: M do |

A is transferred from RGB to L^{*}a^{*}b^{*} color model |

end for |

Select b^{*} channel and apply FBT to obtain C |

for i = 1: r |

Separate C into r blocks B |

end for |

Calculate determinant of each block B and select largest n blocks |

for p = 1: N × N |

Insert watermark using Equation (5) when y(p) = 0 |

Insert watermark using Equation (6) when y(p) = 1 |

end for |

Perform inverse QRD |

Perform IFBT to get modified channel b* |

The modified L^{*}a^{*}b^{’}^{*} color model is transformed into RGB color model |

return watermarked image A’ |

#### 3.2. Watermark Detection Process

^{*}a

^{*}b

^{*}color model I*. Then b

^{*}component is selected and FBT is applied on it to get FBT coefficients C*.

^{*}matrices using the following equation

Algorithm 2: Watermark extracting procedure |

Declaring variables: |

A*: attacked watermarked RGB image |

I*: attacked watermarked L^{*}a^{*}b^{*} image |

Y*: extracted watermark sequence |

C*: modified FBT coefficients |

B*: modified block with size m × m |

G*: modified selected block with size m × m |

Q*: modified unitary matrix with size m × m |

R*: modified upper triangular matrix with size m × m |

${r}_{s;(1,4)}^{\ast}$ = selected element for extracted watermark |

FBT and QRD: transformation and decomposition used in the algorithm |

Watermark extraction procedure: |

Read the attacked watermarked image |

A*.bmp (attacked watermark image with size of 512 × 512) |

for k = 1: M |

l = 1: M do |

A* is transferred from RGB to L^{*}a^{*}b^{*} color model |

end for |

Select b^{*} channel and apply FBT to obtain C* |

for i = 1: r |

Separate C* into r blocks B* |

end for |

Calculate determinant of each block B* and select largest n blocks |

for p = 1: N × N |

Extract watermark using Equation (7) |

end for |

Separate the extracted bits into 8-bits per group |

Convert each group into decimal value to get the R, G, B components |

Combine the R, G, and B components to get the watermark image |

#### 3.3. Performance Assessment of Proposed Algorithm

^{’}, W, W

^{*}, µ, σ indicate the original host image, watermarked host image, watermark image, watermark image after extraction, local mean, and standard deviation of the image, respectively.

## 4. Simulation Results and Discussion

^{*}component of original host image.

- JPEG compression: the watermarked images were compressed using JPEG compression (QF = 90);
- Cropping: the watermarked images were cropped (25%) from the top;
- Rotation attack: the watermarked images were rotated by 45° and the rotated images were re-rotated in a counter-clockwise for extraction;
- Gaussian noise: the watermarked images were attacked by Gaussian noise with variance 0.1;
- Speckle noise: the watermarked images were attacked by speckle noise with variance 0.01;
- Salt and pepper noise: Salt and pepper noise with variance 0.01 is performed to the watermarked images;
- Poisson noise: the watermarked images were attacked by Poisson noise with scaling factor 1e
^{12}; - Contrast adjustment: the watermarked images were attacked by contrast adjustment;
- Sharpening: the watermarked images were attacked by sharpening with tolerance 0.1;
- Median filtering: the watermarked images were attacked by 3 × 3 median filter;
- Wiener filtering: the watermarked images were attacked by 3 × 3 wiener filter.

^{*}component of original image.

## 5. Conclusions

^{*}component of original image using a new embedding equation. The experimental results suggested that the presented algorithm is not only robust against many attacks such as salt and pepper noise, Gaussian noise, rotation, JPEG compression, cropping, wiener filtering, median filtering, and sharpening etc., but also yield watermarked images with good quality. Furthermore, it outperforms state-of-the-art algorithms in respect of imperceptibility and robustness. These results verify that the presented algorithm can be effectively utilized for copyright protection of color image.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Host images (

**a**) Lena, (

**b**) F16, (

**c**) TTU, and (

**d**) House; watermarked images (

**e**) Lena, (

**f**) F16, (

**g**) TTU, and (

**h**) House; difference between host images and watermarked images: (

**i**–

**l**).

**Figure 5.**Analysis of the proposed method under no attack, JPEG compression (QF: 90%), cropping (25%) and rotation (45°) attacks.

**Figure 6.**Analysis of the proposed method under salt and pepper noise (0.01), Gaussian noise (0.1), speckle noise (0.01) and Poisson noise attacks.

**Figure 7.**Analysis of the proposed method under contrast adjustment, sharpening (0.1), wiener filtering, and median filtering attacks.

**Table 1.**Comparative analysis between the suggested algorithm with various recent methods in terms of imperceptibility.

Image | Parameter | Su et al. [19] | Su et al. [20] | Khanam et al. [21] | Proposed Method |
---|---|---|---|---|---|

Lena | PSNR | 40.5079 | 39.4428 | 50.0467 | 54.1854 |

SSIM | 0.9534 | 0.9416 | 0.9542 | 0.9696 | |

F16 | PSNR | 41.6091 | 37.1729 | 51.6431 | 54.1875 |

SSIM | 0.9540 | 0.9311 | 0.9426 | 0.9664 | |

TTU | PSNR | 39.4805 | 39.6781 | 50.7542 | 54.1892 |

SSIM | 0.9537 | 0.9458 | 0.9331 | 0.9285 | |

House | PSNR | 39.7134 | 41.1739 | 48.3143 | 54.1823 |

SSIM | 0.9663 | 0.9524 | 0.9372 | 0.9579 | |

Average | PSNR | 40.3277 | 39.3669 | 50.1896 | 54.1861 |

SSIM | 0.9568 | 0.9427 | 0.9418 | 0.9595 |

**Table 2.**Comparative analysis between the proposed algorithm and several state-of-the-art methods for robustness.

Attack Type | Su et al. [19] | Su et al. [20] | Khanam et al. [21] (With Key) | Khanam et al. [21] (Without Key) | Proposed Method |
---|---|---|---|---|---|

Gaussiannoise (0.1) | 0.9625 | 0.8823 | 1.0 | 0.9351 | 1.0 |

Specklenoise (0.01) | 0.9663 | 0.9647 | 1.0 | 0.9349 | 1.0 |

Cropping (25%) | 0.6482 | 0.8619 | 1.0 | 0.8352 | 0.8252 |

Sharpening (tol = 0.1) | 0.9935 | 0.9882 | 1.0 | 0.8594 | 1.0 |

Rotation (45°) | 0.9361 | 0.9225 | 1.0 | 0.5193 | 1.0 |

Wiener filtering | 0.9578 | 0.9765 | 1.0 | 0.6771 | 1.0 |

Salt and pepper noise (0.01) | 0.9478 | 0.9733 | 1.0 | 0.9944 | 1.0 |

Median filtering | 0.9419 | 0.8997 | 1.0 | 0.9459 | 1.0 |

JPEG Compression (90%) | 0.9998 | 0.9791 | 1.0 | 0.7876 | 1.0 |

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**MDPI and ACS Style**

Dhar, P.K.; Hazra, P.; Shimamura, T.
Blind Color Image Watermarking Using Fan Beam Transform and QR Decomposition. *Symmetry* **2020**, *12*, 486.
https://doi.org/10.3390/sym12030486

**AMA Style**

Dhar PK, Hazra P, Shimamura T.
Blind Color Image Watermarking Using Fan Beam Transform and QR Decomposition. *Symmetry*. 2020; 12(3):486.
https://doi.org/10.3390/sym12030486

**Chicago/Turabian Style**

Dhar, Pranab Kumar, Pulak Hazra, and Tetsuya Shimamura.
2020. "Blind Color Image Watermarking Using Fan Beam Transform and QR Decomposition" *Symmetry* 12, no. 3: 486.
https://doi.org/10.3390/sym12030486