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.

中文翻译：

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量子图像直方图统计

图像直方图是数字图像处理中一个简单但重要的概念。它不随图像平移、旋转、缩放等变化而改变，使其广泛应用于图像特征提取、图像分割、图像匹配、图像分类、对比度增强等方面。随着量子图像处理的发展，也需要在量子计算机上进行图像的直方图统计。但是，由于量子图像中的所有像素都是叠加存储的，因此很难解决对某种颜色的像素进行计数的问题。本文提出了一种基于叠加态量子加法器的量子图像直方图计算方法。它使用控制量子位来确定量子图像的颜色信息和量子直方图的索引信息是否等于特定值。如果是这种情况，叠加态的量子加法器会计算具有该颜色的像素数。该方案不仅解决了量子图像处理中直方图统计的问题，而且将经典直方图统计的复杂度从O(22n)降低到O(2q)，其中n与图像大小有关，q与颜色数有关.