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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]

This paper presented a quantum representation and some basic operations for one-dimensional finite length digital signal. For the representation, similar to the existing flexible representation of quantum audio (FRQA), two sets of qubits are used to represent the amplitudes and positions of the signal, respectively, wherein the amplitude is represented by an (n + 1)-bit signed number in twos complement, including one sign bit, m integer bits and n − m fractional bits. The basic operations include the addition, subtraction, multiplication, division, and circular convolution of two digital signals. We designed the quantum circuits that implements these basic operations, analyzed the computational complexity, and verified the correctness of these circuits by simulations on classical computers. [ABSTRACT FROM AUTHOR]