Arithmetic operation belongs to one of the elementary transformations of image. The research on quantum image arithmetic operation is of great value for the rapid realization of image color transformation. In this chapter, quantum color image representation based on the HSI color space (QIRHSI) is used as the image representation model of quantum image arithmetic operation. Based on this model, the intensity inversion, complement, addition and subtraction operations are designed.
Arithmetic operation belongs to one of the elementary transformations of image. The research on quantum image arithmetic operation is of great value for the rapid realization of image color transformation. In this chapter, quantum color image representation based on the HSI color space (QIRHSI) is used as the image representation model of quantum image arithmetic operation. Based on this model, the intensity inversion, complement, addition and subtraction operations are designed.
Arithmetic operations on images are important primary transformations that can be applied to many complicated image operations. We mainly study the intensity-based arithmetic operations on the QIRHSI quantum image representation model to facilitate the development of quantum image processing. The quantum circuits and unitary matrices for four arithmetic operations including reverse, complement, addition, and subtraction are proposed. Finally, the complexity analysis of quantum networks is illustrated to show the effectiveness of the proposed arithmetic operations.
This chapter first presents the general framework structure of quantum image representation, and then introduces some research results on quantum color image representation in our group. In this study, quantum color image representation based on the HSI color space (QIRHSI) is a quantum color image representation based on the hue, saturation, and intensity (HSI) color space in the right-angle coordinate system, novel color quantum image (NCQI) and Color Quantum Image based on Phase Transform (CQIPT) are quantum color image representations based on the RGB color space in the right-angle coordinate system, and MLCPQI is a quantum color image representation based on the RGB color space in the polar coordinate system. In addition, the preparation scheme on a quantum computer and the computational complexity of the prepared image are provided for each quantum color image representation method. Ultimately, a general framework and preparation strategy for quantum video representation are proposed based on quantum image representation.
The negative effects caused by geometric distortion can be removed to the maximum extent possible through appropriate geometric transformations, allowing us to focus on the image content itself in subsequent processing and recognition. Therefore, geometric transformations are often used as a pre-processing step for other image processing applications. In this paper, quantum algorithms are designed to implement geometric transformations, including two-point swapping, circular translation, flipping transformations and right-angle rotation, across a quantum image representation QIRHSI (Quantum Image Representation based on HSI color space) which is built on HSI (Hue-Saturation-Intensity) color space. The above geometric transformations are realized by quantum circuits composed of elementary quantum gates. By analyzing the complexity of the fundamental quantum gates needed for the above geometric transformations, it is found that the global transformations (circular translation, flip transformation and right-angle rotation) are lower than the local transformation (two-point swapping). The proposed geometric transforms are used to facilitate the applications of quantum images with low complexity and high efficiency.
Quantum image processing, as a convergence of quantum computing and image processing, necessitates extensive research into quantum image representations (QIRs), which are among the most significant topics shaping the field of quantum computing (QC) due to their potential opportunities and challenges. This study introduces a novel QIR model based on the hue, saturation, and intensity (HSI) colour model. Our model advances image encoding by uniquely integrating an adjacency matrix to capture spatial pixel relationships with a Fourier transform (FT) representation for pixel intensity. Based on the HSI color space, AFQIRHSI uses a dual-entanglement structure; one state links the adjacency and intensity information, while another efficiently encodes hue and saturation. Named the adjacency Fourier quantum image representation of HSI (AFQIRHSI), this model utilises [Formula: see text] qubits to store a colour digital image of size [Formula: see text]. AFQIRHSI enhances storage capacity by factors of four and two compared to earlier models, such as QIRHSI and EQIRHSI. In this paper, we also present several quantum image operations, including complement colour transformation [Formula: see text], global colour transformation [Formula: see text], quantum image retrieval [Formula: see text], and quantum image detection (QED). Comparative analyses of various quantum image representations are provided, highlighting their similarities and differences. AFQIRHSI offers a robust foundation for advanced quantum image processing applications, particularly in medical imaging and AI-based image classification.
To achieve a certain desired visual effect, the pixel positions of the input image are mapped to positions different from the original ones so as to change the display effect of the original image. This process is called the geometric transformation of the image. Geometric transformations mainly include geometric correction of the image and spatial transformations (scaling transformation, rotation, and affine transformation) [ 1 – 26 ] . This chapter proposes the geometric transformations of the QIRHSI quantum color image, including basic geometric transformations and scaling operations, and further studies the unitary operators of geometric transformations and the corresponding quantum circuits.
A quantum color image encryption algorithm based on geometric transformation and intensity channel diffusion was designed. Firstly, a plaintext image was transformed into a quantum state form using the quantum image representation based on HSI color space (QIRHSI) representation as a carrier. Next, a pseudo-random sequence was generated using the generalized logistic map, and the pixel positions permuted multiple two-point swap operations. Immediately afterward, the intensity values were changed by an intensity bit-plane cross-swap and XOR, XNOR operations. Finally, the intensity channel of the above image was diffused in combination with the pseudo-confusion sequence as produced by the quantum logistic map to perform a diffusion operation on the intensity bit-plane to obtain the ciphertext image. Numerical simulations and analyses show that the designed algorithm is implementable and robust, especially in terms of outstanding performance and less computational complexity than classical algorithms in terms of security perspective.