A new general model for quantum image histogram (QIH)

An image histogram diagram illustrates the frequency of intensity values occurring in an image. A histogram figure has two dimensions including the x-axis and the y-axis. The color values are demonstrated by the former, and the latter indicates the number of pixels having the corresponding color values. Because quantum image processing (QImP) has been developed rapidly in recent years, in this paper, a new general approach to construct quantum image histogram (QIH) for quantum grayscale and RGB images is proposed, which is based on two kinds of quantum images named novel enhanced quantum representation of digital images (NEQR) and novel colored quantum images (NCQI). QIH manipulates two entangled qubit sequences with the aim of storing and preparing image histogram information, constructing a quantum model for illustrating image histogram. This model requires \((q+2n+1)\) qubits based on NEQR image and \(3\times (q+2n+1)\) qubits based on RGB image to construct the image histogram, when size of image is \(2^{n}\times 2^{n}\) with gray (color) range \(2^{q}\). Moreover, our constructive polynomial preparation proves that the time complexity of QIH is not more than \(O(nq2^{2n+q})\). To the best of our knowledge, this is the first general approach for encoding histogram information based on quantum RGB and grayscale images, and it may open a new window to further statistical analysis procedures related to QImP. For instance, a practical use of QIH as a strict criterion to evaluate quantum data hiding algorithms is also discussed in this paper.