QuatHashing: perceptual hashing with quaternion discrete wavelet transform for reduced-reference visual security assessment

Abstract Visual security assessment (VSA) is an important task of perceptual image encryption and plays a key role in evaluating the effectiveness of encryption schemes. This paper proposes a perceptual hashing algorithm with quaternion discrete wavelet transform (QDWT) for reduced-reference (RR) VSA. The directional complementary sub-band representation is exploited to reorganize the image into horizontal and vertical complementary sub-bands. Since the pixel rearrangement does not discard any information, the distortion introduced by encryption is preserved in the complementary sub-bands while the directional image information is explicitly represented. The complementary sub-bands are modeled as two pure quaternion images and decomposed by QDWT to extract perceptually relevant features from the horizontal and vertical channels. The low-frequency structural features, texture features and multi-scale structural features are further obtained to describe the residual visual information from both directional and multi-scale perspectives. As the human eye is more sensitive to visually salient regions, global and local attention mechanisms are introduced to emphasize these regions and generate compact perceptual feature sequences. The perceptual hash is finally determined by quantizing and combining the horizontal and vertical feature sequences, and the Euclidean distance between the hashes of the reference and encrypted images is used as the final visual security score. Experimental results demonstrate that the proposed QuatHashing achieves more consistent performance than existing IQA and VSA methods, particularly for encrypted images with low and moderate visual quality.