Bivariate Hahn moments for image reconstruction

Wu, Houming; Yan, Sen

doi:10.2478/amcs-2014-0032

Cited by 10 publications

(6 citation statements)

References 29 publications

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“…The computation of the discrete orthogonal moments by using K p,N n (x), t N n (x), H α,β,N n (x), C α n (x) and M β,γ n (x) presents numerical fluctuations [10,37,63,67]. Therefore a more stable version of them should be used.…”

Section: Discrete Orthogonal Polynomialsmentioning

confidence: 99%

Hiding data inside images using orthogonal moments

Soria-Lorente¹,

Berres²,

Avila-Domenech³

2019

Preprint

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In this contribution we propose a novel steganographic method based on several orthogonal polynomials and their combinations. The steganographic algorithm embeds a secrete message at the first eight coefficients of high frequency image. Moreover, this embedding method uses the Beta chaotic map to determine the order of the blocks where the secret bits will be inserted. In addition, from a 128-bit private key and the steps of a cryptography algorithm according to the Advanced Encryption Standard (AES) to generate the key expansion, the proposed method generates a key expansion of 2560 bits, with the purpose to permute the first eight coefficients of high frequency before the insertion. The insertion takes eventually place at the first eight high frequency coefficients in the transformed orthogonal moments domain. Before the insertion of the message the image undergoes a series of transformations. After the insertion the inverse transformations are applied to the original transformations in reverse order. The experimental work on the validation of the algorithm consists of the calculation of the Peak Signal-to-Noise Ratio (PSNR), the Universal Image Quality Index (UIQI), the Image Fidelity (IF), and the Relative Entropy (RE), comparing the same characteristics for the cover and stego image. The proposed algorithm improves the level of imperceptibility and security analyzed through the PSNR and RE values, respectively.

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Section: Discrete Orthogonal Polynomialsmentioning

confidence: 99%

Hiding data inside images using orthogonal moments

Soria-Lorente¹,

Berres²,

Avila-Domenech³

2019

Preprint

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“…The use of strongly non-separable polynomials and their moments would increase the computing complexity while (probably) not bringing any advantages. Almost nobody has used non-separable polynomials for image analysis purposes; [37] is one of very few exceptions.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Rotation of 2D orthogonal polynomials

Yang

Flusser

Kautský

2018

Pattern Recognition Letters

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Orientation-independent object recognition mostly relies on rotation invariants. Invariants from moments orthogonal on a square have favorable numerical properties but they are difficult to construct. The paper presents sufficient and necessary conditions, that must be fulfilled by 2D separable orthogonal polynomials, for being transformed under rotation in the same way as are the monomials. If these conditions have been met, the rotation property propagates from polynomials to moments and allows a straightforward derivation of rotation invariants. We show that only orthogonal polynomials belonging to a specific class exhibit this property. We call them Hermite-like polynomials.

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“…In practice, the parameters η and γ used in the fusion Rule of the texture components, are chosen equal (Wu and Yan, 2014). For our applications, we choose η = γ = 25.…”

Section: Fig 2 Flowchart Of the Novel Methodsmentioning

confidence: 99%

“…Constants η and γ influence the form and the symmetry of the Hahn polynomial. The details of the calculation of these polynomials are available in Wu and Yan (2014).…”

Section: Fusion Rule For Texture Componentsmentioning

confidence: 99%

“…These descriptors are determined through discrete orthogonal moments that are obtained from bivariate Hahn polynomials. These polynomials recently introduced by Wu and Yan (2014) characterize the local variations of an image and the moments deriving from it, are robust to noises. In addition, these moments present a numerical stability, what permits to construct algorithms numerically stable (Wu and Yan, 2014 …”

Section: Fusion Rule For Texture Componentsmentioning

confidence: 99%

See 1 more Smart Citation

Application of Morphological Component Analysis to Optical Image Fusion

Loum¹,

Armand²,

Ghislain³

et al. 2017

American Journal of Applied Sciences

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Abstract:The image fusion technique is widely used in remote sensing. Its purpose is to provide comprehensive information without arte facts by combining the partial information from different source images. In this study, we propose a new model of images fusion with very high spatial resolution. We use the separation capacities of the Morphological Component Analysis (MCA) to extract the smooth and texture components of our images. These morphological components are then fused separately using the decomposition in the Laplacian pyramids for the smooth part and bivariate Hahn polynomials for texture part. Finally the image fusion is obtained through linear combination of merged smooth and texture components. The experiments carried out on IKONOS, LANDSAT and Quick Bird remote sensing images show the good performances of our method which has been compared to conventional methods. The performances obtained in our experiments are characterized by a small global metric such as ERGAS equals to 3.88 for IKONOS image and 3.65 for QuickBird image compared to 8.70 for IKONOS image and 6.97 for QuickBird for conventional HIS algorithms. We also have a mean loss of 15% for spectral information com pare to those of the conventional methods which revolve around 25%. The degradation of spatial information in order of 17% in contrast to conventional HIS algorithms which oscillate around 21%.

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Bivariate Hahn moments for image reconstruction

Cited by 10 publications

References 29 publications

Hiding data inside images using orthogonal moments

Hiding data inside images using orthogonal moments

Rotation of 2D orthogonal polynomials

Application of Morphological Component Analysis to Optical Image Fusion

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