A quantum segmentation algorithm based on local adaptive threshold 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.
Lu Wang Wenjie Liu