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.

提出了一种基于八方向 Sobel 算子的新型量子 Sobel 边缘检测算法，通过设计具体的量子电路，不仅减少了边缘信息的损失，还能同时计算量子图像中所有像素的八个方向的梯度值。该算法的复杂度可以降低到 O (n^2 + q^2)，比其他经典或量子算法更低，并且模拟实验证明该算法可以检测出更多的边缘信息，尤其是对角边缘。