Camera response function signature for digital forensics - Part I: Theory and data selection

Camera response function (CRF) is a form of camera signatures which can be extracted from a single image and provides a natural basis for image forensics. CRF extraction from a single-image is in theory ill-posed. It relies on specific structures in an image that offer glimpses of the CRF. Therefore, the challenges in CRF extraction are first in identifying structures of such property, second in locating such structures in an image, and third in extracting the CRF attributes from the selected structures. In our past work, we proposed that CRF attributes can be found on linear structures in an image and extracted using linear geometric invariants. In this paper, we show additional properties on linear geometric invariants, propose a more robust way to select linear structures in an image, and provide a model-based method to extract CRF attributes from the linear structures. This paper is divided into two parts. Part I is devoted to the theory of linear geometric invariants and the robust selection of linear structures. The linear structure candidates obtained from the method in Part I are used to instantiate the edge profiles for CRF extraction in Part II. The paper as a whole presents a reliable method for CRF extraction, together with rigorous analysis which gives useful insights into the method. In the first half of Part I, a simpler proof that links the equality of linear geometric invariants to a linear-isophote surface is given. As a by-product, the proof leads to an additional way to detect linear-isophote surfaces which uses only the first-order partial derivatives and improves detection reliability. In the second half of Part I, the variance of linear geometric invariants is shown to have a structure which can be used to improve the robustness in detecting linear-isophote surfaces.