# Fractional Differential Texture Descriptors Based on the Machado Entropy for Image Splicing Detection

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## Abstract

**:**

## 1. Introduction

## 2. Fractional Entropy

_{i}is the probability of occurrence, and Γ(.) and ψ(.) refer to the gamma and digamma functions, respectively.

_{i}is the probability distribution of the image pixel’s intensity.

## 3. Construction of Fractional Masks

_{α}(P

_{i}), we obtain

#### 3.1. Texture Feature Extraction

// Input |

// I: an Input image |

// α, µ are fractional parameters of the proposed masks |

// Output: |

// T: Texture features |

1. Construct 2D fractional mask coefficients in the following eight directions: 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. |

2. Split output image into blocks equal to fractional mask window size. |

3. For each block, compute the output image’s block in which each pixel of the image’s block is convolved with the fractional masks on eight directions. |

4. For each output block, compute the gray-level co-occurrence matrix: Contrast; Homogeneity; Energy, and Entropy [25]. |

Save the texture features vector T for all image blocks as the final texture features. |

## 4. Dimension Reduction Method

## 5. Experimental Results and Discussion

#### 5.1. Classification

- Radial basis function is used as a kernel function
- Grid search method is applied to obtain the best value for c and γ parameters so that the SVM classifier can accurately predict unknown data.

#### 5.2. Comparison with Other Methods

## 6. Conclusions

## Acknowledgments

**PACS Codes:**07.05.Pj

## Author Contributions

## Conflict of Interests

## References

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**Figure 1.**Standard deviation distributions of extracted features. Rows indicate the standard deviation distributions of features extracted from gray-scale images. The first column indicates the original features. The second column shows the features after applying kernel PCA.

**Table 1.**Detection accuracy of the fractional feature extraction method with the original dimension of 1764.

Dimensionality | True positive (%) | True negative (%) | Accuracy (%) | |
---|---|---|---|---|

Number of features | 1764 | 74.74 | 55.92 | 70.33 |

**Table 2.**Detection accuracy of the fractional feature extraction method with kernel principal component analysis (PCA) in different dimensions.

Dimension | True positive (%) | True negative (%) | Accuracy (%) | |
---|---|---|---|---|

Features + Kernel PCA | 200 | 88.46 | 76.97 | 82.72 |

150 | 88.46 | 84.87 | 86.67 | |

100 | 89.74 | 86.84 | 88.29 | |

90 | 91.03 | 88.82 | 89.92 | |

80 | 91.03 | 89.47 | 90.26 | |

70 | 88.46 | 90.13 | 89.30 | |

60 | 90.38 | 89.47 | 89.93 | |

50 | 89.74 | 89.47 | 89.61 | |

40 | 92.31 | 91.45 | 91.88 | |

30 | 91.67 | 90.13 | 90.91 | |

20 | 91.03 | 78.95 | 84.99 | |

10 | 100 | 0 | 50.65 |

Feature Extraction Methods | Dimensionality | TP (%) | TN (%) | Acc (%) |
---|---|---|---|---|

Expanded DCT Markov [29] | 100 50 | 89.92 89.60 | 90.21 90.45 | 90.07 90.02 |

DWT Markov [29] | 100 50 | 87.58 86.71 | 85.39 85.70 | 86.50 86.21 |

Expanded DCT Markov + DWT Markov [29] | 100 50 | 93.28 92.28 | 93.83 93.13 | 93.55 93.55 |

HHT + Moments of Characteristic Functions with Wavelet Decomposition [30] | 110 78 | 80.03 73.91 | 80.25 76.49 | 80.15 75.23 |

Run-length and edge statistics based model [31] | 163 139 | 83.23 83.87 | 85.53 76.97 | 84.36 80.46 |

Fractional features + Kernel PCA (Proposed) | 40 | 92.31 | 91.45 | 91.88 |

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**MDPI and ACS Style**

Ibrahim, R.W.; Moghaddasi, Z.; Jalab, H.A.; Noor, R.M.
Fractional Differential Texture Descriptors Based on the Machado Entropy for Image Splicing Detection. *Entropy* **2015**, *17*, 4775-4785.
https://doi.org/10.3390/e17074775

**AMA Style**

Ibrahim RW, Moghaddasi Z, Jalab HA, Noor RM.
Fractional Differential Texture Descriptors Based on the Machado Entropy for Image Splicing Detection. *Entropy*. 2015; 17(7):4775-4785.
https://doi.org/10.3390/e17074775

**Chicago/Turabian Style**

Ibrahim, Rabha W., Zahra Moghaddasi, Hamid A. Jalab, and Rafidah Md Noor.
2015. "Fractional Differential Texture Descriptors Based on the Machado Entropy for Image Splicing Detection" *Entropy* 17, no. 7: 4775-4785.
https://doi.org/10.3390/e17074775