HEMTH: Small Depth Multilevel Thresholding for a Homomorphically Encrypted Image

One of the image segmentation techniques, multilevel thresholding, is widely used in many computer vision applications because of its low computational complexity and efficient data representation. When it is used in cyber-physical systems and internet-of-things, a special technique is required to protect the sensitive information in an image. This paper proposes a novel homomorphic encryption (HE)-based multilevel thresholding method. To implement a comparison operation in the HE domain, which is not a basic homomorphic operation, a numerical method is adopted. Our proposed method executes comparison operations in parallel to perform more iterations and increase accuracy. When the number of iterations in the numerical comparison operation is (5, 3), the proposed three-level thresholding method shows an average peak signal-to-noise ratio of 28 dB compared to a conventional non-HE-based method and takes 3 minutes on a PC.