A quantum segmentation algorithm based on local adaptive threshold for NEQR image

TL;DR

The paper tackles image segmentation under uneven illumination by proposing a quantum algorithm that performs local adaptive thresholding on NEQR images. It introduces quantum primitives for comparison, subtraction, and cyclic shifting to compute pixel-wise local thresholds in parallel, achieving a theoretical $O(n^2+q)$ circuit complexity and enabling exponential speedup over classical methods. A complete quantum circuit is constructed to prepare NEQR images, generate neighborhood data via cyclic shifts, compute thresholds through a median-approximation circuit, and binarize to a binary image, with validation on IBM Q simulators. Experimental results on small test images show improved segmentation quality (lower MSE) compared to fixed-threshold methods, demonstrating feasibility in the NISQ era. The work advances quantum image processing by integrating local adaptive thresholding into a practical quantum segmentation framework using relatively modest quantum resources.

Abstract

The classical image segmentation algorithm based on local adaptive threshold can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem gradually emerges. In this paper, a quantum segmentation algorithm based on local adaptive threshold for NEQR image is proposed, which can use quantum mechanism to simultaneously compute local thresholds for all pixels in a gray-scale image and quickly segment the image into a binary image. In addition, several quantum circuit units, including median calculation, quantum binarization, etc. are designed in detail, and then a complete quantum circuit is designed to segment NEQR images by using fewer qubits and quantum gates. For a $2^n\times 2^n$ image with q gray-scale levels, the complexity of our algorithm can be reduced to $O(n^2+q)$, which is an exponential speedup compared to the classic counterparts. Finally, the experiment is conducted on IBM Q to show the feasibility of our algorithm in the noisy intermediate-scale quantum (NISQ) era.

Figures (13)

• Figure 1: An example of a 2×2 image.
• Figure 2: The schematic diagram of the neighborhood window.
• Figure 7: The workflow of our proposed algorithm.
• Figure 8: The implementation circuit of QCS.
• Figure 9: The implementation circuit for calculating the median.