Quantum Image Segmentation Based on Grayscale Morphology

The classical image segmentation algorithm based on grayscale morphology can effectively segment images with uneven illumination, but with the increase of image data, the real-time problem will emerge. In order to solve this problem, a quantum image segmentation algorithm is proposed in this article, which can use a quantum mechanism to simultaneously perform morphological operations on all pixels in a grayscale image, and which then quickly segments 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 novel enhanced quantum representation images. For a
$2^{n} \times 2^{n}$
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 era.