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

TL;DR

The paper addresses the limitation of existing quantum Sobel edge detectors (QSED) that rely on two or four directions, which can miss edge details in high-definition images. It introduces an eight-direction Sobel-based QSED for NEQR images, with full gradient computation in eight directions and integrated quantum pipelines for non-maximum suppression, double thresholding, and edge tracking. The authors provide detailed quantum circuits and show, via simulations, that the method captures more edge information—particularly diagonals—and achieves a lower MSE than previous QSED variants, with a complexity of $O(n^2+q^2)$ for NEQR images. This work advances real-time, high-fidelity quantum image edge detection, while acknowledging that current hardware limitations require ideal-noise simulations and motivating future anti-noise QSED development.

Abstract

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.

Figures (13)

• Figure 1: An example of a 2×2 image
• Figure 2: The pixel neighborhood window
• Figure 3: Eight masks of eight-direction Sobel algorithm
• Figure 11: Workflow of our proposed algorithm
• Figure 12: Quantum circuit realization for gradient value calculation of a quantum image into the ${0^ \circ }$ and ${22.5^ \circ }$ directions