A continuous-variable quantum-inspired algorithm for classical image segmentation
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RESEARCH ARTICLE
A continuous-variable quantum-inspired algorithm for classical image segmentation Akram Youssry1,2 · Ahmed El-Rafei3 · Ri-Gui Zhou4 Received: 1 May 2019 / Accepted: 9 October 2019 © Springer Nature Switzerland AG 2019
Abstract The probabilistic nature of quantum particles, state space, and the superposition principle are among the important concepts in quantum mechanics. A framework was previously developed by the authors that allowed to take advantage of these quantum aspects in the field of image processing. This was done by modeling each image’s pixel by a two-state quantum system which allowed efficient single-object segmentation. However, the extension of the framework to multiobject segmentation would be highly complex and computationally expensive. In this paper, we propose a classical image segmentation algorithm inspired by the continuous-variable quantum theory that overcomes the challenges in extending the framework to multi-object segmentation. By associating each pixel with a quantum harmonic oscillator, the space of coherent states becomes continuous. Thus, each pixel can evolve from an initial state to any of the continuous coherent states under the influence of an external resonant force. The Hamiltonian operator is designed to account for this force and is derived from the features extracted at the pixel. Therefore, the system evolves from an initial ground state to a final coherent state depending on the image features. Finally by calculating the fidelity between the final state and a set of reference states representing the objects in the image, the state with the highest fidelity is selected. The collective states of all pixels produce the final segmentation. The proposed method is tested on a database of synthetic and natural images, and compared with other methods. Average sensitivity and specificity of 97.86% and 99.61% were obtained respectively indicating the high segmentation accuracy of the algorithm. Keywords Quantum-inspired algorithms · Coherent states · Quantum harmonic oscillator · Signal processing
Akram Youssry
[email protected]; [email protected] Ahmed El-Rafei [email protected] Ri-Gui Zhou [email protected] 1
Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW 2007, Australia
2
Electronics and Communication Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt
3
Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt
4
College of Information Engineering, Shanghai Maritime University, Shanghai, China
1 Introduction Quantum image processing has been an active area of research recently. The usual tasks of image processing are performed utilizing the theory of quantum mechanics. This includes image representation (Yan et al. 2016), image matching (Jiang et al. 2016), similarity analysis (Zhou et al. 2018b), interpolation (Zhou et al. 2018a), denoisi
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