Quantum image edge extraction based on classical Sobel operator for NEQR

As the basic problem in image processing and computer vision, the purpose of edge detection is to identify the point where the brightness of the digital image changes obviously. It is an indispensable task in digital image processing that image edge detection significantly reduces the amount of data and eliminates information that can be considered irrelevant, preserving the important structural properties of the image. However, because of the sharp increase in the image data in the actual applications, real-time problem has become a limitation in classical image processing. In this paper, quantum image edge extraction for the novel enhanced quantum representation (NEQR) is designed based on classical Sobel operator. The quantum image model of NEQR utilizes the inherent entanglement and superposition properties of quantum mechanics to store all the pixels of an image in a superposition state, which can realize parallel computation for calculating the gradients of the image intensity of all the pixels simultaneously. Through constructing and analyzing the quantum circuit of realization image edge extraction, we demonstrate that our proposed scheme can extract edges in the computational complexity of \(\mathrm{O}({n^2} + {2^{q + 4}})\) for a NEQR quantum image with a size of \({2^n} \times {2^n}\). Compared with all the classical edge extraction algorithms and some existing quantum edge extraction algorithms, our proposed scheme can reach a significant and exponential speedup. Hence, our proposed scheme would resolve the real-time problem of image edge extraction in practice image processing.