This research aims to revolutionize complex image clipping using quantum computing, particularly in line clipping algorithms. Traditional methods like Cohen-Sutherland, Liang-Barsky, Cyrus-Beck, and Fast Clipping have limitations in scalability and efficiency. The proposed quantum line clipping algorithm uses quantum computing's unique properties to redefine image processing. It views images as vectors, allowing for computation of pixel distances through quantum inner products. The introduction of and gates within a nine-section quantum display unit plays a pivotal role in decision-making for line clipping, enabling the exclusion of lines beyond the viewport. Comparing this algorithm with classical methods, the quantum algorithm on IBM, Google, and Rigetti's platforms demonstrated superior runtime complexities, demonstrating the immense potential of quantum computation in addressing intricate image clipping challenges. The Quantum Fourier Transform (QFT) acts as a quantum black box, generating high probability amplitudes for substantial vectors. The research also introduces mathematical theorems, such as the quantum image clipping equivalence theorem, which establishes a robust equivalence relation between quantum pixels in frame buffers, the quantum way line clipping equivalence theorem, and the quantum support line clipping optimality theorem. The practical implementation of the proposed quantum line clipping algorithm is presented in Appendix-B, providing valuable resources for researchers and practitioners seeking to explore and experiment with quantum line clipping techniques.

中文翻译：

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量子图像裁剪 - 算法、分析和应用

这项研究旨在利用量子计算彻底改变复杂的图像裁剪，特别是线裁剪算法。Cohen-Sutherland、Liang-Barsky、Cyrus-Beck 和 Fast Clipping 等传统方法在可扩展性和效率方面存在局限性。所提出的量子线裁剪算法利用量子计算的独特属性重新定义图像处理。它将图像视为矢量，允许通过量子内积计算像素距离。在九节量子显示单元中引入 和 门对于线条剪切的决策起着关键作用，从而能够排除视口之外的线条。将该算法与经典方法进行比较，IBM、Google 和 Rigetti 平台上的量子算法表现出了卓越的运行时复杂性，展示了量子计算在解决复杂的图像裁剪挑战方面的巨大潜力。量子傅里叶变换 (QFT) 充当量子黑匣子，为大量向量生成高概率幅度。该研究还引入了数学定理，例如在帧缓冲区中的量子像素之间建立鲁棒等价关系的量子图像裁剪等价定理、量子路线裁剪等价定理和量子支持线裁剪最优性定理。附录 B 中介绍了所提出的量子线裁剪算法的实际实现，为寻求探索和实验量子线裁剪技术的研究人员和从业者提供了宝贵的资源。