Improved quantum dilation and erosion operations

To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location (j, i) is stored at the same location (j, i) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.