Quantum Image Segmentation Based on Grayscale Morphology

TL;DR

This work addresses the challenge of real-time image segmentation under uneven illumination by introducing a quantum image segmentation algorithm based on grayscale morphology. It leverages the NEQR quantum image representation and dedicated quantum circuit modules to perform dilation, erosion, and hat transforms in parallel across all pixels, followed by binaryzation. The authors formalize circuit components, analyze complexity to show a potential $O(n^2+q)$ cost, and validate feasibility with IBM Q simulations in the NISQ era. The approach promises an exponential speedup over classical methods for large-scale images and highlights the practicality of quantum morphology-based segmentation while signaling avenues for adaptive structuring elements in future work.

Abstract

The classical image segmentation algorithm based on grayscale morphology can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem will emerge. In order to solve this problem, a quantum image segmentation algorithm is proposed in this paper, which can use quantum mechanism to simultaneously perform morphological operations on all pixels in a grayscale image, and then quickly segment the image into a binary image. In addition, several quantum circuit units, including dilation, erosion, bottom hat transformation, top hat transformation, etc., are designed in detail, and then they are combined together to construct the complete quantum circuits for segmenting the NEQR images. For a 2^n * 2^n image with q grayscale levels, the complexity of our algorithm can be reduced to O(n^2+q), which is an exponential speedup than 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 (6)

• Figure 1: The schematic diagram of the structuring windows.
• Figure 2: Segmentation of unevenly illuminated image.
• Figure 6: The workflow of our proposed algorithm.
• Figure 12: The Schematic of original image.
• Figure 13: The probability histograms of bottom hat transformation and top hat transformation.