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In this paper, a design method of quantum circuits for threshold segmentation of gray-scale image is proposed, which is a quantum counterpart of classical optimum global thresholding using Otsu's method. First, we design a quantum circuit to obtain the histogram of the pixels distribution. Then, on this basis, we design the quantum circuits of some sub-modules, such as the cumulative histogram, cumulative mean, multiplication, division, the between-class variance and so on. Finally, all the between-class variances corresponding to each gray-level are sorted. At this time, the gray-level corresponding to the maximum of the between-class variance is the Otsu's threshold. For all the operations involved in the classical Otsu's threshold selection, we designed the corresponding quantum circuits, analyzed the computational complexity, and verified the correctness of these circuits by simulations on classical computers. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the quantum image spatial filtering, and focused on the design method of quantum weighted averaging filter and its application in image de-noising. To this end, we first designed the quantum circuits for some auxiliary modules, such as swapping two numbers, comparing two numbers, computing the weighted average of some integers, etc. Next, we constructed a weighted averaging filter of size 3 × 3 using auxiliary modules. The spatial filtering directly on the image itself can be accomplished by using designed filter. We provided the quantum circuits that implements the filtering task and presented the results of several simulation experiments on some gray images with different noises. The significance of this paper is to explore the quantum realization method of image filtering in spatial domain. [ABSTRACT FROM AUTHOR]