The quantum image segmentation algorithm is to divide a quantum image into
several parts, but most of the existing algorithms use more quantum
resource(qubit) or cannot process the complex image. In this paper, an improved
two-threshold quantum segmentation algorithm for NEQR image is proposed, which
can segment the complex gray-scale image into a clear ternary image by using
fewer qubits and can be scaled to use n thresholds for n + 1 segmentations. In
addition, a feasible quantum comparator is designed to distinguish the
gray-scale values with two thresholds, and then a scalable quantum circuit is
designed to segment the NEQR image. For a 2^(n)*2^(n) image with q gray-scale
levels, the quantum cost of our algorithm can be reduced to 60q-6, which is
lower than other existing quantum algorithms and does not increase with the
image's size increases. The experiment on IBM Q demonstrates that our algorithm
can effectively segment the image.

提出了一种改进的 NEQR 图像的双阈值量子分割算法，利用较少的量子比特将复杂灰度图像分割成清晰的三值图像，并且可以对 n 个阈值进行 n+1 次分割，通过设计可行的量子比较器和可扩展的量子电路对 NEQR 图像进行分割，实验结果表明该算法能够有效地进行图像分割。

一种改进的针对 NEQR 图像的双阈值量子分割算法

An improved two-threshold quantum segmentation algorithm for NEQR image

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.

提出了一种基于局部自适应阈值的量子分割算法，该算法利用量子机制为灰度图像中的所有像素同时计算局部阈值，并将图像快速分割为二值图像。设计了几个量子电路单元，包括中值计算、量子二值化等，并通过使用较少的量子比特和量子门设计了一个完整的量子电路来分割 NEQR 图像。对于一个具有 2^n × 2^n 个像素和 q 个灰度级的图像，我们的算法的复杂度可以降低到 O (n^2+q)，与经典方法相比具有指数级的加速。最后，在 IBM Q 上进行实验以展示我们的算法在噪声中等比例量子（NISQ）时代的可行性。