BoinJou

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Introduction

Figure 3

Motivation

Background

CFA Interpolation

A color filter array is an array of color filters placed on top of a camera sensor to capture color information which can then be interpolated to produce color information for neighboring pixels. Different cameras can have different patterns for this CFA color sampling. The most common pattern used is the Bayer pattern.

In Camera Forensics, often, the periodicity of the Color Filter Array is exploited to detect possible tampering in images. But, often when given an image, we don’t know the sampling lattice, and also we don’t know how the interpolation was done. We can use the Expectation-Maximization (EM) algorithm to estimate both of these.

Expectation/Maximization Algorithm

$f(x,y)=\sum _{u,v=-N}^N{\alpha }_{u,v}f(x+u,y+v)+n(x,y)$

where ${\alpha }_{u,v}$ are the interpolation coefficients and n(x,y) is the residual error of the linear model and ideally a Gaussian distribution with zero mean.

The probability that a sample f(x,y) exists given that it is correlated to its neighbors is given by the equation:

$P\{f(x,y)|f(x,y)M_1\}=\frac{1}{\sigma \sqrt{2\pi }}exp[-\frac{1}{2{\sigma }^2}{(f(x,y)-\sum _{u,v=-N}^N{\alpha }_{u,v}f(x+u,y+v))}^2]$

where $\sigma$ is the standard deviation of this Gaussian distribution and is updated in the M-step. The new estimate of the interpolation coefficients is found by minimizing the quadratic error function:

$E(\alpha )=\sum _{x,y}w(x,y){(f(x,y)-\sum _{u,v=-N}^N{\alpha }_{u,v}f(x+u,y+v))}^2$

Methods

Here is a brief outline of our algorithm.

We use a sliding window of size 64x64 to traverse the image with 32 pixel increments. We run the EM algorithm on every block. Then we have a clustering step to localize tampered region using the EM outputs. Finally, we use the cluster maps to classify our image as real or fake.

Localization: Clustering

After running EM on a block, we get two set of useful outputs. First of all, we get a probability map showing which pixels were sampled and which were not, which we take a Fourier Transform of. We also get the estimated alpha values which describe the interpolation weights of neighboring pixels. There is useful information in both of these outputs at different degrees for different images. Our algorithm uses both set of data.

Results

Localization: Clustering

Some text. Some analysis. Some figures.

Classification

Some text. Some analysis. Some figures.

References

References

Software

Appendix I - Code and Data

Code

File:CodeFile.zip

Data

zip file with my data