Time Complexity Measurement on CUDA-based GPU Parallel Architecture of Morphology Operation

Operation time of a function or procedure is a thing that always needs to be optimized. Parallelizing the operation is the general method to reduce the operation time of the function. One of the most powerful parallelizing methods is using GPU. In image processing field, one of the most commonly used operations is morphology operation. Three types of morphology operations kernel, na$\ddot{i}$ve, global and shared, are presented in this paper. All kernels are made using CUDA and work parallel on GPU. Four morphology operations (erosion, dilation, opening, and closing) using square structuring element are tested on MRI images with different size to measure the speedup of the GPU implementation over CPU implementation. The results show that the speedup of dilation is similar for all kernels. However, on erosion, opening, and closing, shared kernel works faster than other kernels.