Quantum Image Histogram Statistics

Image histogram is a simple but important concept in digital image processing. It is not changed with image translation, rotation, scale, and etc., which makes it be widely used in image feature extraction, image segmentation, image matching, image classification, contrast enhancement and so on. With the development of quantum image processing, it is also necessary to perform the histogram statistics of images on quantum computers. However, since all pixels in a quantum image are stored superposedly, it is difficult to solve the problem of counting the number of pixels with a certain color. This paper proposes a method for calculating the quantum image histogram, based on the quantum adder for superposition states. It uses control qubits to determine whether the color information of a quantum image and the index information of the quantum histogram are equal to a particular value. If this is the case, the quantum adder for superposition states counts the number of pixels with that color. This scheme not only solves the problem of histogram statistics in quantum image processing, but also reduces the complexity of classical histogram statistics from O(22n) to O(2q), where n is related to the image size and q is related to color numbers.