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CRC Press eBooks

Quantum Image and Video Representation

Shaocong Lan, Xianhua Song, Ahmed A. Abd El‐Latif, Basma Abd El-Rahiem

Published May 15, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9781003621423-3

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From the quantum images and their preparation methods described in Chapter 2, it can be seen that preparing a quantum image requires a large number of basic quantum gates. For example, to prepare a quantum color image Quantum Image Representation based on HSI (QIRHSI) with a size of https://www.w3.org/1998/Math/MathML" display="inline"> 2 8 × 2 8 pixels and an intensity value range of https://www.w3.org/1998/Math/MathML" display="inline"> 0 ∼ 2 8 − 1 , approximately the number of basic quantum gates required is 2 64 . Therefore, in this chapter, the resources for image preparation will be optimized. The principle of Boolean expression minimization will be used to simplify the quantum circuit in the quantum image QIRHSI. In essence, it is to replace the original preparation of the quantum image with a new unitary transformation that has fewer quantum logic gates.

CRC Press eBooks•May 15, 2026•0 citations
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.
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Quantum image processing is a new and exciting subdiscipline of quantum computation that aims to extend classical image processing applications on a quantum computer.The research starts with a proposal of a representation of images on a quantum computer, named Multi-Channel Representation for Quantum Images (MCQI).This representation encodes the positions and their corresponding colors in the images as a normalized quantum state.For an n by n sized image, 2n qubits and 3 qubits are used to carry the position and color respectively.The preparation procedure of a quantum image is discussed by the multi-channel polynomial preparation, which turns the initial quantum states to the MC-QI quantum states.The image retrieval procedure by quantum measurement is proposed which converts the quantum states to classical images.Furthermore, based on MCQI, some categories of possible processing transformations are suggested.By considering the structure of MCQI representation, the Channel of Interest (CoI), the Channel Swapping (CS), the Color Space Transformation (CST), and Alpha Blending (αB) quantum image processing operators are discussed using unitary transformations with low complexity.All the 4 operators are used to process the information about color in the images.Their complexity are analyzed in terms of the number of basic quantum gates which are needed to build the transformations, and they can be built by 9, 3, 287, 28 basic quantum gates, respectively.Some strategies for designing new transformations from known ones are proposed as well.These strategies can be used to design further algorithms for image processing.Based on the MCQI representation and the four image processing operators, a quantum measurement based double-key double-domain watermarking strategy for multichannel quantum images (MC-WaQI) is developed.In these application, a revised of the original MCQI representation and some restricted versions of the transformations are considered.The research provides the foundation to design other quantum image processing algorithms and can be extend to the following areas:• MCQI representation can be used to build quantum image database,• new frequency operations on quantum images based on quantum Fourier quantum discrete cosine, and quantum wavelet transformations,• building the special effect on color quantum movie,• image data transmission by quantum communication.
To address the limitations of existing models that predominantly represent data in Cartesian coordinate systems and RGB color representations, this paper proposes YCrCbQPI (A Quantum Polar Coordinate Color Image Representation Model Based on YCrCb Color Space, YCrCb-QPI). This model integrates luminance and chrominance separation properties of YCrCb with the geometric invariance of logarithmic polar coordinates. Through a differentiated quantum encoding strategy, more qubits are allocated to critical luminance information while less sensitive chrominance information is assigned simplified encoding. Corresponding quantum state preparation circuits are also designed. Theoretical analysis indicates that compared to traditional RGB polar coordinate models, this model achieves significant savings in color information encoding resources while maintaining comparable visual fidelity. Furthermore, the model inherently possesses the rotation and scaling invariance of polar coordinates, establishing a robust foundation for developing efficient quantum image processing algorithms.
From the quantum images and their preparation methods described in Chapter 2, it can be seen that preparing a quantum image requires a large number of basic quantum gates. For example, to prepare a quantum color image Quantum Image Representation based on HSI (QIRHSI) with a size of https://www.w3.org/1998/Math/MathML" display="inline"> 2 8 × 2 8 pixels and an intensity value range of https://www.w3.org/1998/Math/MathML" display="inline"> 0 ∼ 2 8 − 1 , approximately the number of basic quantum gates required is 2 64 . Therefore, in this chapter, the resources for image preparation will be optimized. The principle of Boolean expression minimization will be used to simplify the quantum circuit in the quantum image QIRHSI. In essence, it is to replace the original preparation of the quantum image with a new unitary transformation that has fewer quantum logic gates.