Quantum Circuit Realization of Morphological Gradient for Quantum Grayscale Image

Abstract

In this paper, based on the principle of classical morphology operations, the flat grayscale dilation and erosion operations are proposed for NEQR quantum image model. Furthermore, through combining these two morphology operations, we further realize the morphological gradient operation. As the basis of designing of grayscale morphology operations, a series of quantum circuit designs arepresented, which includes special add one operation UA1(n) and special subtract one operation US1(n) both for an n-length qubits sequence, quantum unitary operation UC, parallel subtractor (PS) module, quantum comparator output the large QCOL and quantum comparator output the small QCOS modules. When designsthe concrete quantum circuit, a sequence of UA1(n) and US1(n) modules are used to obtain the quantum image sets based on the shape of specific structuring element. Then, the searching for maximaor minima in a certain space is involved, which can be solved by cascading a series of QCOL and QCOS modules in certain order. Finally, the PS module can be used to calculate the difference of the maxima and minima for producing the morphological gradient. The circuit’s complexity analysis illustrate that our scheme is very lower to the classical morphology operations.