3. Exposing Splicing Forgeries in Digital Images through the Discrepancies in Dichromatic Plane Histograms
on this observation, the authors proposed to extract texture [81] and gradient-based [82] de- scriptors from the face regions of the IM. The IM is converted to YCbCr colour space, and the Y channel is utilized for computing both the descriptors. Then, the features are classified in a pair-wise manner using a support vector machine (SVM) classifier. More specifically, for each face-IM pair, computed using the same illumination estimation method, the same type of features extracted from the two face-IMs are concatenated and classified using the SVM. In their follow-up work, Carvalhoet al.[41] proposed to extract three types of features from the face-IMs, namely texture, shape and colour features. More specifically, the authors proposed to compute three texture descriptors in [81], [83], [84], two shape descriptors in [85], [86], and four colour descriptors in [87], [88], [89], [90]. Also, in this work, Carvalhoet al. proposed to convert the IM to three different colour spaces, namely Lab, HSV, and normalized RGB colour spaces. Similar to [9], here also, the features are classified in a pair-wise manner by concate- nating similar features of the two face-IMs computed from the same type IM converted to the same colour space. Thek-nearest neighbour classifier is utilized for classifying the features. Al- though these methods are very effective, their performances drop in low-resolution and highly compressed images. This is because in the case of low-resolution and highly compressed im- ages, the IM computation becomes less accurate and hence the features computed from them become less discriminative.
3.2 Background
Figure 3.1: Surface and body reflections from a non-homogeneous surface according to the DRM.
the surface and the body. Shafer [78] proposed the DRM to explain the reflections from non- homogeneous substances. Homogeneous substances, e.g., metals and many crystals, do not exhibit the two types of reflections as exhibited by the non-homogeneous surfaces.
According to the DRM [78], the total radiance of the light reflected from a non-homogeneous material is the sum of radiances of the light reflected from thesurfaceand thebody. Figure 3.1 shows these two reflections. Thesurfaceorspecularreflection is the mirror-like reflection at the surface of the object. Thebodyordiffused reflection occurs when the incident light penetrates through the surface and suffers scattering by the colourant particles present beneath the surface.
The scattered light finally re-emitted through the surface. Thus, the total radiance L(θ, λ) is given by
L(θ, λ)=mi(θ)Ci(λ)+mb(θ)Cb(λ) (3.1) whereθis the angle between the incident light and the viewing directions;λis the wavelength of light;Ci andCbare the spectral power distributions, andmiandmbare the geometric factors of surface and body reflections, respectively. The two vectorsCiandCbspan a two-dimensional space, known as thedichromatic plane. In RGB colour space, Equation (3.1) can be expressed as
fR(x) fG(x) fB(x)
= mi
fR(x) fG(x) fB(x)
i
+mb
fR(x) fG(x) fB(x)
b
(3.2)
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3. Exposing Splicing Forgeries in Digital Images through the Discrepancies in Dichromatic Plane Histograms
where fR(x), fG(x), and fB(x) are the sensor responses for the red, green and blue colour channels respectively at the pixel location x, and the subscripti andbrepresent the interface and body reflection components respectively. According toneutral interface reflection[92], the spectral power density of the interface reflection is the same as that of the illuminant source. Thus, the RGB values of an object lie on the dichromatic plane defined by the illuminant colour and the object colour, as expressed by Equation (3.2). Under uniform illumination, the dichromatic planes of two differently coloured surfaces in the same scene intersect at the illumination colour.
This is because the illumination colour is common for both the dichromatic planes estimated from the two surfaces. Therefore, the intersection of different dichromatic planes gives the estimate of the illuminant colour. However, in real-life noisy images, this method fails to give the true illuminant colour. This is because the noise may cause the pixels, belonging to a single dichromatic plane, to lie on multiple dichromatic planes. Hence, the intersection of these planes may not give the true illuminant colour.
3.2.2 Dichromatic Plane Histogram (DPH)
In [77], the authors proposed to use the 2D Hough transform [93] to find the dichromatic planes in the RGB colour space. According to the DRM, all the dichromatic planes pass through the origin. Therefore, in the RGB space, the equation of the dichromatic plane is given as
fR(x) sin(θ) cos(φ)+ fG(x) sin(θ) sin(φ)+ fB(x) cos(θ)=0 (3.3) whereθandφare respectively the polar and azimuth angles of the plane in a spherical coordinate system. All the pixels satisfying Equation (3.3) for a specific pair of (θ, φ) lie on the same dichromatic plane defined by the pair (θ, φ). A DPH, Hd(θ, φ), represents the distribution of pixel values lying on different dichromatic planes. Hd(θ, φ) is created by applying a 2D Hough transform, where each bin represents the number of pixels belonging to a dichromatic plane specified by the pair (θ,φ). Therefore,Hd(θ, φ) gives the likelihood of the presence of different dichromatic planes in an image corresponding to different pairs of angles (θ, φ). In this chapter, the DPH is used as the illumination-signature, as shown in the following section.
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