Decision-theoretic model to identify printed sources

Abstract

When trying to identify a printed forged document, examining digital evidence can prove to be a challenge. Over the past several years, digital forensics for printed document source identification has begun to be increasingly important which can be related to the investigation and prosecution of many types of crimes. Unlike invasive forensic approach which requires a fraction of the printed document as the specimen for verification, noninvasive forensic technique uses the optical mechanism to explore the relationship between the scanned images and the source printer. To explore the relationship between source printers and images obtained by the scanner, the proposed decision-theoretical approach utilizes image processing techniques and data exploration methods to calculate many important statistical features, including: Local Binary Pattern (LBP), Gray Level Co-occurrence Matrix (GLCM), Discrete Wavelet Transform (DWT), Spatial filters, the Wiener filter, the Gabor filter, Haralick, and SFTA features. Consequently, the proposed aggregation method intensively applies the extracted features and decision-fusion model of feature selections for classification. In addition, the impact of different paper texture or paper color for printed sources identification is also investigated. In the meantime, the up-to-date techniques based on deep learning system is developed by Convolutional Neural Networks (CNNs) which can learn the features automatically to solve the complex image classification problem. Both systems have been compared and the experimental results indicate that the proposed system achieve the overall best accuracy prediction for image and text input and is superior to the existing approaches. In brief, the proposed decision-theoretical model can be very efficiently implemented for real world digital forensic applications.

Appendix: Formulas of feature filters

Brief description of the formulas for ten feature filter sets is shown below:

Feature Filter	Image quality Measures	Formula
GLCM	Region of interest R (ROI) GLCM	$R=\sum \limits_{\left(i,j\right)\in ROI}^1$ $GLCM\ \left(i,j\right)=\frac{1}{\sum \limits_{\left(i,j\right)} Img\left(i,j\right)} Img\left(i,j\right)$ where (i, j) indicates the spatial location of image. Img (i, j) is the probability from location (i, j).
DWT	Dilation 3 wavelet functions	Ψ(H)(x, y), Ψ(V)(x, y), and Ψ(D)(x, y), When the wavelete function is sparable by f(x, y) = f1(x), f2(y), then these functions rewritten to ϕ(x, y) = ϕ(x), ϕ(y) Ψ(H)(x, y) = Ψ(x), ϕ(y) Ψ(V)(x, y) = ϕ(x), Ψ(y) Ψ(D)(x, y) = Ψ(x), Ψ(y) whereΨ(H)(x, y),Ψ(V)(x, y), and Ψ(D)(x, y) are called horizontal, vertical, and diagonal wavelets
Gaussian	G (x, y)is Gaussian matrix element at position (x, y)	$\mathrm{G}\ \left(x,y\right)=\frac{1}{2\uppi {\sigma}^2}{e}^{-\frac{1}{2\uppi {\sigma}^2}}$ where G (x, y)is Gaussian matrix element at position (x, y), σ is the standard deviation.
LoG	Log(x, y)  is the high-frequency Laplacian filter	$\mathrm{Log}\left(x,y\right)=-\frac{1}{\uppi {\sigma}^4}\left[1-\frac{1}{\uppi {\sigma}^4}\right]{\mathrm{e}}^{-\frac{1}{\uppi {\sigma}^4}}$
Unsharp	fs(x, y) is the sharped imaged from unsharp mask	${f}_s\left(x,y\right)=f\left(x,y\right)-\overline{f}\ \left(x,y\right)$ where $\overline{f}\ \left(x,y\right)$is a blured version of f(x, y)
Wiener	H(u, v)is function of Wiener filter	g(x, y) = f(x, y) + n (x, y) $H\left(u,v\right)=\frac{P_f\left(u,v\right)}{P_f\left(u,v\right)+{\sigma}^2}$ Where σ2is variance from the noise in Eqs. (9), Pf(u, v)is the signal power spectrum
Gabor	sx & sy are the variance along x and y axis, f is the frequency of sinusoidal function and θ is the orientation of Gabor function	$G\left(x,y\right)=\frac{f^2}{\uppi \upgamma \upeta}\exp \left(-\frac{f^2}{\uppi \upgamma \upeta}\right)\exp \Big(\mathrm{j}2\uppi f{x}^{\prime }+$ ϕ) x′ = x cos(θ) + y sin(θ) y′ = y cos(θ) − x  sin(θ)
Haralick	Angular second moment Contrast Correlation Sum of squares (variance) Inverse different moment Sum average Sum varince Sum entropy Entropy Difference variance Difference entropy Info. measure of correlation 1 Info. measure of correlation 2 Max. correlation coefficient	∑i∑jp(i, j)2 ${\sum}_{\mathrm{n}=0}^{{\mathrm{N}}_{\mathrm{g}}-1}{n}^2\left\{{\sum}_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{g}}}{\sum}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{g}}}p\left(i,j\right)\right\},\left|i-j\right|=n$ $\frac{\sum_i{\sum}_j(ij)p\left(i,j\right)-{\mu}_x{\mu}_y}{\sigma_x{\sigma}_y}$ ∑i∑j(i − μ)2p(i, j) ${\sum}_i{\sum}_j\frac{i}{1+{\left(i-j\right)}^p}p\left(i,j\right)$ ${\sum}_{i=2}^{2{N}_g}{ip}_{x+y}(i)$ ${\sum}_{i=2}^{2{N}_g}{\left(i-{f}_s\right)}^2{p}_{x+y}(i)$ $-{\sum}_{i=2}^{2{N}_g}{p}_{x+y}(i)\mathit{\log}\left\{{p}_{x+y}(i)\right\}$ −∑i∑jp(i, j) log(p(i, j)) variance of px − y(i) $-{\sum}_{i=0}^{N_g-1}{p}_{x-y}(i)\log \left\{{p}_{x+y}(i)\right\}$ $\frac{ HX Y-{ HX Y}_1}{\max \left\{ HX, HY\right\}}$ ${\left(1-\exp \left[-2.0\left( HXY2- HXY\right)\right]\right)}^{\frac{1}{2}}$ HXY1 =  − ∑i∑jp(i, j) log(p(i, j)) where HX and HY are the entropies of px and py, HXY1 =  − ∑i∑jp(i, j) log {px(i)(p)y(j)}, and HXY2 =  − ∑i∑jpx(i)py(j) log {px(i)(p)y(j)} (the second largest eigenvalue of Q)1/2 where$Q\left(i,j\right)={\sum}_k\frac{p\left(i,k\right)p\left(j,k\right)}{p_x(i){p}_y(k)}$
Fractal	Δ(x, y): fractal feature vector	$\Delta \left(x,y\right)=\left\{\begin{array}{c}1,\\ {}\\ {}0,\end{array}\right.{\displaystyle \begin{array}{c} if\exists \left({x}^{\prime },{y}^{\prime}\right)\in {N}_4{\left[x,y\right]}_{,}\\ {} Ib\left({x}^{\prime },{y}^{\prime}\right)=0\wedge Ib\left({x}^{\prime },{y}^{\prime}\right)=1,\\ {} otherwise\end{array}}$ where N4[x, y],is the set of pixels that are 4-connected to (x, y) from the image. ∆(x, y) uses the value 1 if the pixel at position (x, y) in the binary image Ib(x′, y′) that has the value 1 and having one neighboring pixel with the value 0. Otherwise, ∆(x, y) takes the value 0.
LBP	LBPP, R(xc, yc) LBP features where P sampling points on a circle of R radius	${LBP}_{P,R}\left({x}_c,{y}_c\right)={\sum}_{p=0}^{P-1}\mathrm{s}\left({g}_{\mathrm{p}}-{g}_c\right){2}^ps(x)=\left\{\begin{array}{c}1, ifx\ge 0;\kern1em \\ {}0, otherwise.\end{array}\right.$