Mao-Pei Tsui

Physics-motivated features for distinguishing photographic images and computer graphics

The increasing photorealism for computer graphics has made computer graphics a convincing form of image forgery. Therefore, classifying photographic images and photorealistic computer graphics has become an important problem for image forgery detection. In this paper, we propose a new geometry-based image model, motivated by the physical image generation process, to tackle the above-mentioned problem. The proposed model reveals certain physical differences between the two image categories, such as the gamma correction in photographic images and the sharp structures in computer graphics. For the problem of image forgery detection, we propose two levels of image authenticity definition, i.e., imaging-process authenticity and scene authenticity, and analyze our technique against these definitions. Such definition is important for making the concept of image authenticity computable. Apart from offering physical insights, our technique with a classification accuracy of 83.5% outperforms those in the prior work, i.e., wavelet features at 80.3% and cartoon features at 71.0%. We also consider a recapturing attack scenario and propose a counter-attack measure. In addition, we constructed a publicly available benchmark dataset with images of diverse content and computer graphics of high photorealism.

Using Geometry Invariants for Camera Response Function Estimation

In this paper, we present a new single-image camera response function (CRF) estimation method using geometry invariants (GI). We derive mathematical properties and geometric interpretation for GI, which lend insight to addressing various algorithm implementation issues in a principled way. In contrast to the previous single-image CRF estimation methods, our method provides a constraint equation for selecting the potential target data points. Comparing to the prior work, our experiment is conducted over more extensive data and our method is flexible in that its estimation accuracy and stability can be improved whenever more than one image is available. The geometry invariance theory is novel and may be of wide interest.

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.

Soliton solutions for the Laplacian co-flow of some G2-structures with symmetry

Abstract We consider the Laplacian “co-flow” of G 2 -structures: ∂ ∂ t ψ = − Δ d ψ where ψ is the dual 4-form of a G 2 -structure φ and Δ d is the Hodge Laplacian on forms. Assuming short-time existence and uniqueness, this flow preserves the condition of the G 2 -structure being coclosed ( d ψ = 0 ). We study this flow for two explicit examples of coclosed G 2 -structures with symmetry. These are given by warped products of an interval or a circle with a compact 6-manifold N which is taken to be either a nearly Kahler manifold or a Calabi–Yau manifold. In both cases, we derive the flow equations and also the equations for soliton solutions. In the Calabi–Yau case, we find all the soliton solutions explicitly. In the nearly Kahler case, we find several special soliton solutions, and reduce the general problem to a single third order highly nonlinear ordinary differential equation.

Stability of the minimal surface system and convexity of area functional

Abstract. We study the convexity of the area functional for the graphs of maps with respect to the singular values of their differentials. Suppose that f is a solution to the Dirichlet problem for the minimal surface system and the area functional is convex at f . Then the graph of f is stable. New criteria for the stability of minimal graphs in any co-dimension are derived in the paper by this method. Our results in particular generalize the co-dimension one case, and improve the condition in the 2003 paper of the first author and M.-T. Wang from | ∧2 df | ≤ 1 p−1 to | ∧2 df | ≤ 1 √ p−1 , where p is an upper bound of the rank of df , and the condition in the 2008 paper of the first author and M.-T. Wang from √ det(I + (df)T df) ≤ 43 40 to √ det(I + (df)T df) ≤ 2.