Geometric transformations, such as resizing and rotation, are almost always needed when two or more images are spliced together to create convincing image forgeries. In recent years, researchers have developed many digital forensic techniques to identify these operations. Most previous works in this area focus on the analysis of images that have undergone single geometric transformations, e.g., resizing or rotation. In several recent works, researchers have addressed yet another practical and realistic situation: successive geometric transformations, e.g., repeated resizing, resizing-rotation, rotation-resizing, and repeated rotation. We will also concentrate on this topic in this paper. Specifically, we present an in-depth analysis in the frequency domain of the second-order statistics of the geometrically transformed images. We give an exact formulation of how the parameters of the first and second geometric transformations influence the appearance of periodic artifacts. The expected positions of characteristic resampling peaks are analytically derived. The theory developed here helps to address the gap left by previous works on this topic and is useful for image security and authentication, in particular, the forensics of geometric transformations in digital images. As an application of the developed theory, we present an effective method that allows one to distinguish between the aforementioned four different processing chains. The proposed method can further estimate all the geometric transformation parameters. This may provide useful clues for image forgery detection.

In this letter, we propose a blind and effective method to estimate the image rotation angle. It operates by exploiting the hidden periodicities in the rotated image using the 2-D spectrum of its second order statistics. The expected positions of rotation-related peaks as well as their trajectory paths in the 2-D spectrum are first derived. Based on the peaks found around those paths, the rotation angle is then estimated using a much simpler formula than those of the state-of-the-art 2-D method. Through both theoretical analyses and experimental results on a large set of natural images, the proposed scheme is demonstrated to give more accurate estimate than previous methods.

Recently, the median filtering (MF) detector as a forensic tool for the recovery of images' processing history has attracted wide interest. This paper presents a novel method for the blind detection of MF in digital images. Following some strongly indicative analyses in the difference domain of images, we introduce two new feature sets that allow us to distinguish a median-filtered image from an untouched image or average-filtered one. The effectiveness of the proposed features is verified with evidence from exhaustive experiments on a large composite image database. Compared with prior arts, the proposed method achieves significant performance improvement in the case of low resolution and strong JPEG post-compression. In addition, it is demonstrated that our method is more robust against additive noise than other existing MF detectors. With analyses and extensive experimental researches presented in this paper, we hope that the proposed method will add a new tool to the arsenal of forensic analysts.