Accelerating Computation of Zernike and Pseudo-Zernike Moments with a GPU Algorithm

Abstract

Although Zernike and pseudo-Zernike moments have some advanced properties, the computation process is generally very time-consuming, which has limited their practical applications. To improve the computational efficiency of Zernike and pseudo-Zernike moments, in this research, we have explored the use of GPU to accelerate moments computation, and proposed a GPUaccelerated algorithm. The newly developed algorithm is implemented in Python and CUDA C++ with optimizations based on symmetric properties and k × k sub-region scheme. The experimental results are encouraging and have shown that our GPU-accelerated algorithm is able to compute Zernike moments up to order 700 for an image sized at 512 × 512 in 1.7 seconds and compute pseudo-Zernike moments in 3.1 seconds. We have also verified the accuracy of our GPU algorithm by performing image reconstructions from the higher orders of Zernike and pseudo-Zernike moments. For an image sized at 512 × 512, with the maximum order of 700 and k = 11, the PSNR (Peak Signal to Noise Ratio) values of its reconstructed versions from Zernike and pseudo-Zernike moments are 44.52 and 46.29 separately. We have performed image reconstructions from partial sets of Zernike and pseudo-Zernike moments with various order n and different repetition m. Experimental results of both Zernike and pseudo-Zernike moments show that the images reconstructed from the moments of lower and higher orders preserve the principle contents and details of the original image respectively, while moments of positive and negative m result in identical images. Lastly, we have proposed a set of feature vectors based on pseudo-Zernike moments for Chinese character recognition. Three different feature vectors are composed of different parts of four selected lower pseudo-Zernike moments. Experiments on a set of 6,762 Chinese characters show that this method performs well to recognize similar-shaped Chinese characters.