Hybrid Color Image Watermarking Algorithm Based on DSWT-DCT-SVD and Arnold Transform

Garg, Palak; Dodeja, Lakshita; Priyanka, .; Dave, Mayank

doi:10.1007/978-981-13-2553-3_31

Cited by 8 publications

(2 citation statements)

References 5 publications

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“…Orthogonal transformations have very useful properties in solving science and engineering problems. Just like the Fourier and Chebyshev series which are effective methods to project a periodic function into a series of linearly independent terms, orthogonal polynomials provide a natural way to solve the related problems, such as compression and protection in image processing [1]- [3], pattern recognition [4], [5] and feature capturing [6], [7]. It also can be applied for temporal video segmentation [8], face recognition [9], and character recognition [10].…”

Section: Introductionmentioning

confidence: 99%

A General Method for Generating Discrete Orthogonal Matrices

Chan

2021

IEEE Access

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Discrete orthogonal matrices have applications in information coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize continuous orthogonal functions that have been discovered. The need of such continuous functions is restrictive. Polynomials, as the simplest class of continuous functions, are widely studied for their orthogonalality, to serve the purpose of generating orthogonal matrices. However, beginning with continuous orthogonal polynomials still takes much work. To overcome this complexity while improving the efficiency and flexibility, we present a general method for generating orthogonal matrices directly through the construction of certain even and odd polynomials from a set of distinct positive values, bypassing the need of continuous orthogonal functions. We present a constructive proof by induction that not only asserts the existence of such polynomials, but also tells how to iteratively construct them. Besides the derivation of the method as simple as a few nested loops, we discuss two well-known discrete transforms, the Discrete Cosine Transform and the Discrete Tchebichef Transform, how they can be achieved using our method with the specific values, and show how to embed them into the transform module of video coding. By the same token, we also give the examples for generating new orthogonal matrices from arbitrarily chosen values. The demonstrative experiments indicate that our method is not only simpler to implement, but also more efficient and flexible. It can generate orthogonal matrices of larger sizes, compared with those existing methods.

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Section: Introductionmentioning

confidence: 99%

A General Method for Generating Discrete Orthogonal Matrices

Chan

2021

IEEE Access

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“…Orthogonal transformations have very useful properties in solving science and engineering problems. Just like the Fourier and Chebyshev series which are effective methods to project a periodic function into a series of linearly independent terms, orthogonal polynomials provide a natural way to solve, such as compression and protection in image processing [4,6,16], pattern recognition [19,24] and feature capturing [12,14]. Among various types of transformers, matrix transformers are most widely used due essentially to their simplicity and explicitness, especially for the transformations on real intervals (R → R).…”

Section: Introductionmentioning

confidence: 99%

A General Method for Generating Discrete Orthogonal Matrices

Chan,

Ke,

2021

Preprint

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Discrete orthogonal matrices have several applications, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize continuous orthogonal functions that have been discovered. The need of certain continuous functions is restrictive. To simplify the process while improving the flexibility, we present a general method to generate orthogonal matrices directly through the construction of certain even and odd polynomials from a set of distinct positive values, bypassing the need of continuous orthogonal functions. We provide a constructive proof by induction that not only asserts the existence of such polynomials, but also tells how to iteratively construct them. Besides the derivation of the method as simple as a few nested loops, we discuss two well-known discrete transforms, the Discrete Cosine Transform and the Discrete Tchebichef Transform. How they can be achieved using our method with the specific values, and introduce how to embed them into the transform module of video coding. By the same token, we also show some examples of how to generate new orthogonal matrices from arbitrarily chosen values.

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