LiuVenkatesanYang

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Background

Since digital images have become ubiquitous in the internet, the image based forgeries have become widespread as well. From the ultra slim model flashing in the cover of a fashion magazines to the manipulated images submitted to the Journal of cell biology, image based forgeries have become very common these days. The U.S Office of Research Integrity reported that there were less than 2.5% of accusations of fraud involving disputed images in 1990. The percentage rose to 26% in 2001 and by 2006, it went up to 44.1% [1]. Image Forgeries are frequently seen in forensic evidence, tabloid magazines, research journals, political campaigns, media outlets and funny hoax images sent in spam emails which leaves no doubts for the viewer as they appear to be visually acceptable without any signs of tampering. This necessitates a good method to detect these kind of forgeries. There are two main interests in Digital Camera Image Forensics. One is source identification and the second is forgery detection. Source identification delas with identifying the source camera with which an image is taken while camera forensics deals with detecting tampering in an image by assessing the underlying statistics of the image.

Few examples of Forged images available on the internet

Introduction

In this class project, we have concentrated on Forgery detection by detecting changes in the underlying statistics of the image. Many digital cameras use color filter arrays in conjunction with a single sensor to record the short, medium and long wavelength information in different pixels of an image. The color information in each individual pixel is obtained by interpolating these color samples using a technique called demosaicing. This interpolation introduces specific correlations which are likely to be destroyed when the image is tampered. The goal of our project is to build a classifier in MATLAB that can take an input image and identify the parts of the image that do not exhibit the expected CFA correlations. We will use the correlation techniques described in [2] to identify parts of the image that are being tampered with.

Methods

Detecting Forgeries using CFA interpolation

We have used a method that detects tampering in images using the correlation in image pixels left by the CFA interpolation algorithm used. [#References - Resources and related work|2] This technique work on the assumption that although digital forgeries may leave no visual clues of having been tampered with, they may, nevertheless, alter the underlying statistics of an image. Most digital cameras, for example, capture color images using a single sensor in conjunction with an array of color filters. As a result, only one third of the samples in a color image are captured by the camera, the other two thirds being interpolated. This interpolation introduces specific correlations between the samples of a color image. When creating a digital forgery these correlations may be destroyed or altered. We describe the form of these correlations, and propose a method that quantities and detects them in any portion of an image 2. We show the general effectiveness of this technique in detecting traces of digital tampering, and analyze its sensitivity and robustness to simple image distortions (compression, noise, and gamma correction).

Interpolation Algorithms

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Results

Results from uncompressed images

Some text. Some analysis. Some figures.

Results from compressed images with different quality factors

Some text. Some analysis. Some figures.

Sensitivity and Robustness Measure

Some text. Some analysis. Some figures. Maybe some equations.

Equations

If you want to use equations, you can use the same formats that are use on wikipedia.
See wikimedia help on formulas for help.
This example of equation use is copied and pasted from wikipedia's article on the DFT.

The sequence of N complex numbers x₀, ..., x_N−1 is transformed into the sequence of N complex numbers X₀, ..., X_N−1 by the DFT according to the formula:

$X_k=\sum _{n=0}^{N-1}{x}_n{e}^{-\frac{2\pi i}{N}kn}k=0,\dots ,N-1$

where i is the imaginary unit and $e^{\frac{2\pi i}{N}}$ is a primitive N'th root of unity. (This expression can also be written in terms of a DFT matrix; when scaled appropriately it becomes a unitary matrix and the X_k can thus be viewed as coefficients of x in an orthonormal basis.)

The transform is sometimes denoted by the symbol $ℱ$, as in $𝐗=ℱ\left\{𝐱\right\}$ or $ℱ\left(𝐱\right)$ or $ℱ𝐱$.

The inverse discrete Fourier transform (IDFT) is given by

$x_n=\frac{1}{N}\sum _{k=0}^{N-1}{X}_k{e}^{\frac{2\pi i}{N}kn}n=0,\dots ,N-1.$

Retinotopic models in group-averaged data projected back into native space

Some text. Some analysis. Some figures.

References - Resources and related work

References

1. Farid, Hany. "Image forgery detection." Signal Processing Magazine, IEEE26.2 (2009): 16-25.

2. Popescu, Alin C., and Hany Farid. "Exposing digital forgeries in color filter array interpolated images." Signal Processing, IEEE Transactions on 53.10 (2005): 3948-3959.

Software

1. MATLAB

Appendix I - Code and Data

Code

File:CodeFile.zip

Data

zip file with my data