Quantum image edge detection based on eight-direction Sobel operator for NEQR

Quantum Sobel edge detection (QSED) is a kind of algorithm for image edge detection using quantum mechanism, which can solve the real-time problem encountered by classical algorithms. However, the existing QSED algorithms only consider two- or four-direction Sobel operator, which leads to a certain loss of edge detail information in some high-definition images. In this paper, a novel QSED algorithm based on eight-direction Sobel operator is proposed, which not only reduces the loss of edge information, but also simultaneously calculates eight directions' gradient values of all pixel in a quantum image. In addition, the concrete quantum circuits, which consist of gradient calculation, non-maximum suppression, double threshold detection and edge tracking units, are designed in details. For a 2^n x 2^n image with q gray scale, the complexity of our algorithm can be reduced to O(n^2 + q^2), which is lower than other existing classical or quantum algorithms. And the simulation experiment demonstrates that our algorithm can detect more edge information, especially diagonal edges, than the two- and four-direction QSED algorithms.