Log-Polar Based Scheme for Revealing Duplicated Regions in Digital Images

Region duplication is a common type of digital image tampering. This paper presents a log-polar based approach to detect such forgery even if the copied area has been rotated and/or scaled. We compute log-polar fast Fourier transform (LPFFT) on image blocks to approximate the log-polar Fourier transform (LPFT). LPFFT is based on a nearly log-polar system where conversion to log-polar coordinates only involves 1-D Fourier transform and interpolation operations. In addition to rotation and scaling invariance, computation complexity of LPFFT is O(n²logn) , much lower than O(n⁴) of LPFT when n is large. Similarity of the LPFFT results between different blocks provides indication of image tampering. Experimental results show efficacy of the proposed method.