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。