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

TL;DR

This paper introduces a quantum image edge detection algorithm using an eight-direction Sobel operator, improving edge detail preservation and computational efficiency over previous quantum methods.

Contribution

It proposes a novel quantum Sobel edge detection algorithm based on eight directions, with detailed quantum circuit design and improved edge detection performance.

Findings

Detects more edge details, especially diagonal edges.

Reduces complexity to O(n^2 + q^2), lower than existing algorithms.

Demonstrates improved edge detection in simulations.

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.