A Study On Quaternion Transforms For Color Image Processing

As a basic visual feature, the color helps to perceive and recognize objects from complex scenario, and also plays an important role in image retrieval, face detection and recognition, object segmentation, and so on. Moreover, with the increasing development of image sensor and computer technology, the color image processing has received much attention in signal processing community during the past years.The traditional color image processing approaches, such as transforming it into grayscale image, separately processing or representing it by vector after decomposing into single channel, can not fully exploit the correlation between color channels. With the help of quaternion representation, the multiple channels can be encoded into an entirety. In such a way, not only the three channels can be treated simultaneously, but also the spectrum relationship between them can be taken into consideration. In this dissertation, based on the quaternion matrix representation, some holistic transforms of color images and their applications were investigated. The main contributions are summarized as follows:(1) Rotation angle estimation based on quaternion orthogonal moments and their feature descriptorsFirstly, the conventional Bessel-Fourier moments were extended to quaternion type, named quaternion Bessel-Fourier moments. Then, the importance of phase information contained in quaternion orthogonal moments (including Bessel-Fourier moments, Zernike moments, pseudo-Zernike moments and Fourier-Mellin moments) was investigated in terms of color image reconstruction. Based on the relation between quaternion moments of original image and those of the rotated one, the algorithm of rotation angle estimation using the iteration of quaternion orthogonal moments was derived. Finally, taking the proposed quaternion Bessel-Fourier moments for example, the feature descriptors that were invariant to geometric transformation was defined by combining with the above rotation angle estimation algorithm, and further applied to color objects recognition. Experimental results show that the reconstructed color images through the proposed quaternion Bessel-Fourier moments achieve the smallest error. For color objects recognition, the proposed feature descriptors have better robustness compared with the existing quaternion orthogonal moment invariants.(2) Color face recognition based on local features and ensemble learningThe robust color face recognition approach based on local features and ensemble learning was proposed. In pre-processing stage, the color face images were divided into non-overlapping patches. Then, the quaternion pseudo-Zernike moments were used to extract image features. Meanwhile, by combining with the image entropy, the adaptive quaternion pseudo-Zernike moments were introduced to describe the features. In the classifier stage, the ensemble learning classifier was utilized. It can be observed from the experimental results that in comparison with the approach using global features, the proposed local features based color face recognition approach shows better robustness in terms of illumination, facial expression or other conditions, which can improve the recognition accuracy.(3) Quaternion Gyrator transform and its application to color image encryptionTheoretically, the quaternion Gyrator transform was introduced and its fast computation algorithms were derived, including the direct algorithm via quaternion Fourier transforms and another indirect one through the traditional Gyrator transform of single channel grayscale image. The quaternion Gyrator transform was then applied for color image encryption. On the one hand, the single color image encryption algorithm based on double random phase encoding and quaternion Gyrator transform was proposed. On the other hand, through the phase retrieval process, the encryption of double or even more color images can be transformed into single-channel architecture to transmit. In addition, as there are four parts in quaternions, the above two algorithms can realize the hybrid encryption of color and grayscale images. The experimental results have shown that the proposed encryption algorithms outperform the existing algorithms in terms of system complexity, security and robustness.(4) Combining encryption techniques for color image watermarkingBy using quaternion representation of color image, the digital watermarking algorithms combining with the encryption techniques were developed. For color watermark image, single or double images were respectively investigated. Using the quaternion Gyrator transform, the single color image was first encrypted through double random phase encoding or the double color images were encrypted through phase retrieval process, then they were fused into quaternion Gyrator transformed host image, the watermarked color image can be obtained through inverse transform. Moreover, these algorithms can embed the color and grayscale watermarks simultaneously. For the binary watermark image, the color image watermarking algorithm constructed on image invariant features and visual cryptography was addressed. Firstly, the quaternion pseudo-Fourier-Mellin transform was defined and its geometric invariants were derived, then the feature matrix was constructed. Combining it with the (2,2) visual cryptography, the distribution and reconstruction schemes of watermark image were designed. The experimental results have demonstrated the feasibility of the proposed watermarking algorithms as well as their better robustness.