An FFT-based visual quality metric robust to spatial shift

In recent years, several metrics have been developed for measuring image visual quality, including the MSSIM and the visual information fidelity (VIF). However, these metrics are not robust to spatial shifts, meaning that when the reference and distorted images are misaligned by a few pixels, these metrics will produce very low scores, which is undesirable. In this paper, we extend the SSIM metric to make it robust to spatial shifts by first pre-processing the input images with the Fast Fourier transform (FFT). We then apply the magnitude of the transformed Fourier coefficients to the existing metrics because these coefficients are shift-invariant. Our assumption is that if we shift the image by a small amount of pixels, then it will not affect the perceived quality. Experimental results show that the proposed method is attractive for measuring the visual quality of 2D images as it is far less complex than the current approach, which consists in performing global motion estimation to align the input images prior to applying the metrics, and offers better accuracy.