Abstract
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.