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Adaptive robust image watermark approach based on fuzzy comprehensive evaluation and analytic hierarchy process

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Abstract

In this paper, we propose a novel image watermark approach using fuzzy comprehensive evaluation (FCE) and analytic hierarchy process (AHP) for determining the watermark embedding strength adaptively in the block-based discrete cosine transform (DCT) domain. By exploiting the brightness, energy and uniform characteristics of the DCT coefficients, we synthesize this information availably. The experimental results show that novel approach has not only the good robustness to commonly image processing such as Gaussian noise, cropping, mean filtering, median filtering, rotation and rescaling but also the very strong resistant ability to translation and rotation attacks.

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Abbreviations

I :

A gray-level original image

N 1 :

Row number of an original image

N 2 :

Column number of an original image

J :

8 × 8 Block

W :

A binary original watermark image

M 1 :

Row number of an original watermark image

M 2 :

Column number of an original watermark image

key0 :

Pre-determining key

W P :

The permuted watermark image

F :

The DCT coefficients of I

μ :

Parameter of generating logistic maps

int(x):

Integer part of x

α (i, j) :

Parameter controlling the watermark strength of block (i, j)

\({\hat{{I}}}\) :

The watermarked image

F′:

The watermarked DCT coefficients

I w :

A possibly watermarked image

W′:

The extracted watermark

m (i, j) :

Average value of the absolute value of the block F (i, j)

ω(m (i, j)):

Modified index

L :

The total number of DCT 8 × 8 blocks

O :

The evaluation object set

U :

The evaluation index set

\({\vec {x}_j }\) :

The eigenvalue of the three evaluation index

X :

The eigenvalue matrix of the L evaluation indexes

r kj :

The membership degree of the kth index for O j

r i :

The ith single-object evaluation of the O i

\({\underline{A}}\) :

The weighting coefficient set of the three evaluation indexes

a i :

The relative importance of index u i

\({\underline{C}}\) :

The fuzzy comprehensive evaluation set of the U

c j :

The result of fuzzy comprehensive evaluation of the object O j

R :

The fuzzy evaluation matrix

B :

The judgment matrix

S(i):

The affection of the various evaluation indexes to comprehensive evaluation

\({\bar{{r}}_i}\) :

Sample average value of ith evaluation index

b L :

The relative important parameter

\({\bar{{B}}}\) :

The normalized judgment matrix

DCT:

Discrete cosine transform

FCE:

Fuzzy comprehensive evaluation

AHP:

Analytic hierarchy process

PSNR:

Peak signal to noise ratio

NC:

Normal correlation

HVS:

Human visual system

DC:

Direct coefficient

AC:

Alternating coefficient

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Authors and Affiliations

  1. Department of Computer Science, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Cong Jin

Authors
  1. Cong Jin
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Correspondence to Cong Jin.

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Jin, C. Adaptive robust image watermark approach based on fuzzy comprehensive evaluation and analytic hierarchy process. SIViP 6, 317–324 (2012). https://doi.org/10.1007/s11760-011-0256-2

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  • DOI: https://doi.org/10.1007/s11760-011-0256-2

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