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<p>As digital images increasingly face challenges related to copyright protection, tampering detection, and efficient retrieval, the need for advanced and robust hashing techniques that fully exploit color information has become critical. To address these issues, this paper proposes a novel color image hashing scheme based on the singular value decomposition of split quaternion matrices (SVDSQ). Utilizing the split quaternion matrix model of color images, our approach captures the intrinsic relationship among the color channels, enhancing feature representation. SVDSQ offers several advantages, including the use of a special singular value form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a+b\textrm{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mtext>k</mtext> </mrow> </math></EquationSource> </InlineEquation>, which provides an accurate geometric description in Cartesian coordinates, superior reconstruction performance, and improved computational efficiency compared to traditional quaternion SVD schemes. This scheme incorporates multi-scale feature extraction to derive robust image features across different scales, ensuring resilience against various digital operations. By applying Euclidean distance computations on the extracted features, this paper generates a compact and discriminative color image hash. This hash demonstrates exceptional robustness to image modifications, such as noise, compression, and resizing, while maintaining high discriminative performance for efficient image retrieval and copyright protection. The proposed scheme represents a significant advancement in color image hashing and offers a scalable, efficient solution for real-world applications.</p>

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Multi-scale feature extraction and color image hashing based on SVD of split quaternion matrices

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Gang Wang,
  • Chuan Jiang,
  • Zhenwei Guo,
  • V. I. Vasil’ev

摘要

As digital images increasingly face challenges related to copyright protection, tampering detection, and efficient retrieval, the need for advanced and robust hashing techniques that fully exploit color information has become critical. To address these issues, this paper proposes a novel color image hashing scheme based on the singular value decomposition of split quaternion matrices (SVDSQ). Utilizing the split quaternion matrix model of color images, our approach captures the intrinsic relationship among the color channels, enhancing feature representation. SVDSQ offers several advantages, including the use of a special singular value form \(a+b\textrm{k}\) a + b k , which provides an accurate geometric description in Cartesian coordinates, superior reconstruction performance, and improved computational efficiency compared to traditional quaternion SVD schemes. This scheme incorporates multi-scale feature extraction to derive robust image features across different scales, ensuring resilience against various digital operations. By applying Euclidean distance computations on the extracted features, this paper generates a compact and discriminative color image hash. This hash demonstrates exceptional robustness to image modifications, such as noise, compression, and resizing, while maintaining high discriminative performance for efficient image retrieval and copyright protection. The proposed scheme represents a significant advancement in color image hashing and offers a scalable, efficient solution for real-world applications.