Computational Intelligence in the Reversible Data-Hiding Processes Using Radon Transform

Computational Intelligence in the Reversible Data-Hiding Processes Using Radon Transform

B. Bazeer Ahamed
DOI: 10.4018/978-1-7998-3645-2.ch018
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Data hiding has emerged as a major research area due to the phenomenal growth in internet and multimedia technologies. Securing data transmitted over the internet becomes a challenging issue caused in digitization and networking over the past decade. Data hiding schemes have been adopted to protect digital media content which involves confidential data such as text, video, audio, images, and compression coding. A good reversible data hiding scheme is characterized by the possession of attributes like reversible, imperceptible, high payload capacity, and robustness. By reversible, it's meant that the extraction of the payload as well as the restoration of the host image perfectly from the stego image. Secondly, the imperceptible stego image resemblance against the cover/host image. Finally, robustness counts for the ability to sustain the secret payload against both intentional and unintentional attacks; it has been observed that all the proposed algorithms are more robust and reversible against various attacks in lower bit error rate and higher normalization coefficient.
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An efficient reversible data hiding method must be robust against a wide range of image processing operations such as image enhancement, cropping, rotation, scaling, compression and signal processing operation such as addition of noise (Abdulfetah et al, 2010). However, conventional data hiding algorithms are more sensitive to geometric distortions. Hence, radon transform is introduced to perform rotation, scaling and translation operations on the cover image. These operations change the positioning of the secret bits (Bedi et al, 2013). Without taking inverse Radon Transform, it is very difficult to detect the embedded data and subsequently this increases the security of embedded payload.

In this chapter, the data embedding is performed in a hybrid domain. The cover image is first transformed from spatial domain to radon domain and then this radon image is applied with integer lifting wavelet transform (Chakraborty et al, 2013). Various orthogonal and bi-orthogonal wavelets are used for the implementation of reversible integer lifting wavelet transform. Then the middle bit planes of high frequency lifting coefficients are compressed using arithmetic coding to provide space for embedding secret payload (Cheddad et al, 2010).Radon transform (RT) was introduced in 1917 by the Austrian mathematician Johann Radon. The Radon Transformation is a fundamental tool, which is used in various applications such as radar imaging, geophysical imaging, nondestructive testing and medical imaging (Coltuc, D 2011). The Radon transform is applied to transform the image from the spatial domain to the Radon domain and the inverse radon transform does the reverse. Radon transform is a linear transform and an effective method to analyze signal between the spatial domain and its projection space. It represents the image as a collection of projections along various directions (Gerami et al 2012). It computes the projection of the image intensity along a radial line oriented at a specific angle as shown in Figure 1.

Figure 1.

Projection of image at a specific angle of rotation


For each angle θ and at each distance φ, the intensity of a ray perpendicular to the ρ axis is summed up at R (ρ,θ). Radon transform converts rectangular coordinates (x, y) into polar coordinates R (ρ,θ). The simplest form of discrete Radon transform is to select finite number of the angular variable of projection, then take the summation on the discrete image along the projection line.


Literature Review

Basically reversible data hiding techniques are classified into three categories. They are spatial domain, frequency domain and compressed domain techniques. In spatial domain, pixel values are modified directly to embed the confidential data. Most of the spatial domain techniques are developed based on two principles, i.e., Difference expansion (DE) (Ahamed, B. B., & Ramkumar, T.,2018) and histogram modification (Ahamed, B. B., & Ramkumar, T, 2015). The algorithms based on difference expansion provide high embedding capacity (Hu et al 2008) while the algorithms based on histogram shifting contribute good visual quality to the extracted image (Huang, HC et al, 2010). Frequency domain techniques involve the calculation of frequency coefficients of the image using some reversibility guaranteed transforms like discrete wavelet transform, discrete fourier transform, discrete cosine transform, integer lifting transform, slantlet transform, curvelet transform, discrete radon transform, etc., Then the frequency coefficients are modified to embed secret data. In compression domain, the cover image is compressed to minimize the memory required and the bandwidth space of the embedded image.

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