INVISIBLE WATERMARKING USING DFT AND DFT-DWT HYBRID TECHNIQUES AT VARYING EMBEDDING STRENGTHS

УДК 004.056:004.932

ABSTRACT

Invisible watermarking methods based on the Discrete Fourier Transform (DFT) and a hybrid Discrete Fourier Transform–Discrete Wavelet Transform (DFT-DWT) approach are compared in this article. To embed a binary watermark into a grayscale host image, we employed three alternative techniques: DFT-only, DFT-DWT with an embedding strength of α = 10, and DFT-DWT with α = 20. SSIM, PSNR, and MSE were used to measure imperceptibility, and Bit Error Rate (BER) and correlation were used to measure resilience both before and after JPEG compression. According to the data, the DFT-only approach fails under JPEG compression (BER ≈ 1) but achieves great visual quality (SSIM = 0.9988, PSNR = 51.14 dB). Conversely, the hybrid DFT-DWT technique achieves reduced BER (≈ 0.18) and stronger correlation (≈ 0.31) after compression while maintaining both imperceptibility and robustness. This demonstrates that the combination of DFT and DWT is more effective and dependable in practical settings.

АННОТАЦИЯ

В данной статье мы сравниваем методы невидимого водяного знака, основанные на дискретном преобразовании Фурье (DFT), и гибридный подход, объединяющий дискретное преобразование Фурье и дискретное вейвлет-преобразование (DFT-DWT). Мы использовали три различных метода для внедрения бинарного водяного знака в полутоновое (градации серого) изображение-носитель: только DFT, DFT-DWT с коэффициентом встраивания α = 10 и DFT-DWT с α = 20. Мы оценивали незаметность с использованием метрик SSIM, PSNR и MSE, а устойчивость — с помощью коэффициента битовых ошибок (BER) и корреляции до и после JPEG-сжатия. Результаты показывают, что метод только на основе DFT обеспечивает высокое визуальное качество (SSIM = 0.9988, PSNR = 51.14 дБ), но не выдерживает JPEG-сжатия (BER ≈ 1). С другой стороны, гибридный подход DFT-DWT сохраняет как незаметность, так и устойчивость, достигая более низкого BER (≈ 0.18) и более высокой корреляции (≈ 0.31) после сжатия. Это показывает, что сочетание DFT и DWT работает лучше и более надёжно в реальных условиях.

Keywords: Invisible Watermarking, Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT), Imperceptibility, Robustness

Ключевые слова: невидимое водяное знакирование, дискретное преобразование Фурье (DFT), дискретное вейвлет-преобразование (DWT), незаметность, устойчивость

1. Introduction

In the age of multimedia, invisible watermarking is a crucial method for safeguarding digital media and maintaining image quality while guaranteeing copyright security. By incorporating hidden information into multimedia content, watermarking systems provide for authentication, ownership verification, and protection against unauthorized distribution (Astridefi et al., 2023). Two essential criteria must be addressed by watermarking techniques: robustness and imperceptibility. While robustness refers to the watermark's capacity to withstand common image processing procedures and other attacks, imperceptibility ensures that the added watermark does not diminish the original image's visual quality.

Compared to spatial-domain techniques, frequency-domain watermarking offers superior resistance to signal processing procedures. Because of its stability and resistance to certain geometric transformations, the Discrete Fourier Transform (DFT) is frequently employed. Nevertheless, watermarking techniques that solely rely on the DFT sometimes lack resilience to typical distortions like compression.

Hybrid watermarking methods that use several transforms have been developed to get around this restriction. Watermark information is encoded in more stable areas of the image while retaining high imperceptibility when Discrete Wavelet Transform (DWT) and DFT are combined. Inspired by these benefits, a hybrid DFT-DWT methodology and a conventional DFT watermarking method are empirically compared at various embedding strengths. Using common performance criteria, the suggested assessment looks at watermark robustness and image quality under JPEG compression.

2. Methodology

2.1 Watermark and Host Image

The cover picture for watermark embedding was a grayscale host image (Figure 1) with a resolution of 512 × 512 pixels. The watermark (Figure 2) was a 32 by 32 pixel binary picture with black lettering on a white backdrop. The watermark was transformed into a binary matrix before embedding, with pixel values denoting watermark bits. Embedding the watermark information into the host image while preserving high imperceptibility and resilience against typical image processing operations is the aim of the watermarking procedure.

     Figure 1. Host image                              Figure 2. Watermark

2.2. DFT-Based Watermarking

The host image is first converted into the frequency domain using the Discrete Fourier Transform (DFT) in the DFT-based invisible watermarking technique. The DFT spectrum's chosen magnitude coefficients are altered to embed the watermark.
Watermark information is contained in the mid-frequency region, avoiding the very sensitive low-frequency components and the noise-prone high-frequency components, in order to balance imperceptibility with robustness.

The embedding process can be described as

𝐹′(𝑢,𝑣)=𝐹(𝑢,𝑣)+𝛼𝑊(𝑢,𝑣)

where:

• 𝐹(𝑢,𝑣) represents the original magnitude coefficient of the DFT,
• 𝑊(𝑢,𝑣) represents the watermark bit,
• 𝛼 is the embedding strength,
• 𝐹′(𝑢,𝑣) is the modified magnitude coefficient after embedding.

The image's spatial structure is maintained by preserving the DFT's phase component. The watermarked image is reconstructed using the inverse DFT after embedding.
The embedded watermark bits are estimated during watermark extraction by comparing the DFT magnitude spectrum of the received image with that of the original host image (Senthilkumaran & Abinaya, 2016). DFT watermarking is known to be susceptible to compression attacks, especially JPEG compression, even though it typically offers high visual quality.

2.3. DFT-DWT Hybrid Watermarking

A hybrid watermarking technique that combines DFT and Discrete Wavelet Transform (DWT) was used to increase robustness.

The host image is first subjected to a one-level Haar Discrete Wavelet Transform. Four sub-bands are produced by this decomposition:

LL (approximation)

LH (horizontal details)

HL (vertical details)

HH (diagonal details)

The LL sub-band is comparatively stable under compression attacks and contains the most important image information. Watermark embedding is thus carried out in this sub-band. The LL sub-band is then subjected to a Discrete Fourier Transform (DFT). Like the DFT-only approach, the watermark is embedded by altering the magnitude spectrum with the embedding strength parameter 𝛼. The final watermarked image is produced by applying the inverse DWT after the changed LL sub-band has been rebuilt using the inverse DFT. By combining the frequency-domain robustness of DFT with the multi-resolution localization capacity of DWT, this hybrid technique improves resistance to image processing attacks while preserving good visual quality (Chandra M..).

Two embedding strengths were assessed in this study:

α = 10, representing moderate embedding strength

α = 20, representing stronger watermark embedding

2.3 Experimental Environment

Scientific computing packages such as NumPy, OpenCV, and PyWavelets were used to implement all of the experiments in Python. Standard imperceptibility measurements (SSIM, PSNR, and MSE) and robustness metrics (BER and correlation) were used to assess the watermarking techniques' performance. The watermarked photos were subjected to JPEG compression attacks in order to evaluate robustness under practical circumstances.

3. Experimental Results

3.1 Imperceptibility

Three popular imperceptibility measures were utilized to assess the watermarking approaches' performance: Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index (SSIM).

SSIM provides a perceptually significant assessment of visual quality by measuring image similarity by taking brightness, contrast, and structural information into account. Higher PSNR values indicate better visual fidelity. PSNR measures the ratio between the highest signal power and the distortion created during watermark embedding. Higher similarity is shown by lower values of MSE, which is the average squared difference between the original and watermarked images.

A thorough evaluation of imperceptibility—a crucial prerequisite for invisible watermarking systems—was produced using these metrics (Horé & Ziou, 2010). Excellent visual quality and confirmation that the embedded watermark is still undetectable to the human eye were demonstrated by all evaluated methods' SSIM values remaining above 0.998 and PSNR values exceeding 51 dB (Table 1).

Table 1.

Imperceptibility results

With SSIM values above 0.998 and PSNR values above 51 dB, Table 1's data demonstrate that all watermarking techniques preserve extremely good visual quality. When compared to the DFT-only method, the hybrid DFT-DWT strategy produced somewhat better imperceptibility. It's interesting to note that α = 10 and α = 20 have the same imperceptibility values. This happens because, even when the embedding strength is increased, watermark embedding only alters a small number of frequency coefficients in the LL sub-band, resulting in minimum visual distortion. As a result, the watermarked image's perceived quality is not greatly impacted by raising the embedding strength within this range.

3.2 Robustness

The watermarked photos were subjected to a JPEG compression assault in order to evaluate the resilience of the suggested watermarking techniques. Because JPEG compression is one of the most prevalent distortions that occur during image storage, transmission, and sharing, it was chosen. JPEG compression is a realistic and useful test for watermark robustness since it mostly impacts an image's frequency components, especially the mid- and high-frequency areas (Hu et al., 2023).

Bit Error Rate (BER) and Correlation Coefficient were used to assess robustness.

BER calculates the ratio of erroneously extracted watermark bits to all embedded bits. Higher robustness is shown by lower BER values, whereas watermark recovery failure is indicated by values near 1.

The similarity between the extracted and original watermark patterns is measured by the correlation coefficient. More precise watermark recovery is indicated by higher correlation values.

When combined, these metrics offer a thorough assessment of watermark robustness, with correlation measuring structural similarity following attacks and BER reflecting error sensitivity.

Figure 3. Extracted watermarks before attack(from left to right (DFT only,DFT-DWT( ,DFT-DWT )

Figure 4. Extracted watermarks after attack(from left to right (DFT only,DFT-DWT( ,DFT-DWT )

Table 2.

Robustness results

Even in the clean scenario, the robustness of the DFT-only approach was poor, with a BER of 0.996 and correlation of 0.462; under JPEG compression, it failed completely (BER = 1.0, correlation ≈ 0.000003). The DFT-DWT hybrid approach, on the other hand, shown a notable improvement. The correlation increased to 0.835 and the clean BER decreased to 0.018 for both α = 10 and α = 20, showing accurate watermark retrieval. The hybrid approach retained a moderate level of robustness following JPEG compression, with a correlation of 0.311 and a BER of 0.180. It's interesting to note that raising α from 10 to 20 did not result in additional robustness improvements, indicating that the combination of embedding region and transform had a bigger effect than embedding strength alone. All things considered, the DFT-DWT hybrid approach showed better resistance to JPEG compression while maintaining watermark integrity.

4. Conclusion

In this study, two embedding strengths (α = 10 and α = 20) were used in studies to compare invisible watermarking strategies using DFT and a hybrid DFT-DWT methodology. The findings showed that although the DFT-only approach offers good imperceptibility, it is not robust, especially when JPEG compression is applied, where watermark retrieval completely fails. The DFT-DWT hybrid approach, on the other hand, maintains excellent visual quality while greatly increasing robustness. The practically equal performance of the α = 10 and α = 20 configurations indicates that the mix of transform domains is more important than the embedding strength alone. In clean settings, the hybrid approach continuously produced low BER and strong correlation while maintaining a moderate level of robustness following JPEG compression. These results demonstrate how well DWT and DFT work together for real-world watermarking applications that need to be both invisible and resistant to attacks. Future research could investigate adding SVD to this hybrid model or using deep learning methods for improved robustness against a wider variety of distortions and blind detection.

References:

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2. N. Senthilkumaran and S. Abinaya Digital Image Watermarking Using Dft Algorithm Advanced Computing: An International Journal (ACIJ), Vol.7, No.1/2, March 2016
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