An improved two-threshold quantum segmentation algorithm for NEQR image

The quantum image segmentation algorithm is to divide a quantum image into several parts, but most of the existing algorithms use more quantum resource(qubit) or cannot process the complex image. In this paper, an improved two-threshold quantum segmentation algorithm for NEQR image is proposed, which can segment the complex gray-scale image into a clear ternary image by using fewer qubits and can be scaled to use n thresholds for n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n+1$$\end{document} segmentations. In addition, a feasible quantum comparator is designed to distinguish the gray-scale values with two thresholds, and then a scalable quantum circuit is designed to segment the NEQR image. For a 2n×2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^n} \!\times \! {2^n}$$\end{document} image with q gray-scale levels, the quantum cost of our algorithm can be reduced to 60q-6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q{-}6$$\end{document}, which is lower than other existing quantum algorithms and does not increase with the image’s size increases. The experiment on IBM Q demonstrates that our algorithm can effectively segment the image.