Andrey Kuznetsov and Vladislav Myasnikov - Using Efficient Linear Local Features in the Copy-move Forgery Detection Task
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The document proposes a new copy-move forgery detection algorithm using efficient linear local features. The key features of the algorithm are 100% recall, high calculation speed for real-time analysis, and 99.9% precision. It works by using a sliding window to analyze image fragments defined by a structural pattern. Hash values are calculated for each fragment based on linear local features and stored in a hash table. Duplicates are identified by finding hash values with a frequency greater than one. Experiments on satellite images show the algorithm has no false negatives and very low false positives, while being much faster than other methods.
![The proposed approach
5
Problem: there is no copy-move detection algorithm with ~100% precision [1]
The key features of the proposed algorithm:
- 100% recall
- high calculation speed (for real-time image analysis)
- low computational complexity
- 99,9% precision
The main steps of the algorithm
1. Sliding window analysis mode
2. Use special structural pattern
3. Hash values calculation ( based on linear local features)
4. Store hash values in a hash table
1. Christlein, V., Riess, C., Jordan, J., Riess, C., Angelopoulou, E.: An evaluation of popular copy-move forgery detection
approaches. In: IEEE Transactions on InformationForensics and Security. Volume 7(6). (2012). 1841–1854](https://image.slidesharecdn.com/kuznetsovusingefficientlinearlocal-160427211020/85/Andrey-Kuznetsov-and-Vladislav-Myasnikov-Using-Efficient-Linear-Local-Features-in-the-Copy-move-Forgery-Detection-Task-5-320.jpg)
![Linear local features
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(LLF were developed by V. Myasnikov in 2007)](https://image.slidesharecdn.com/kuznetsovusingefficientlinearlocal-160427211020/85/Andrey-Kuznetsov-and-Vladislav-Myasnikov-Using-Efficient-Linear-Local-Features-in-the-Copy-move-Forgery-Detection-Task-10-320.jpg)
![Experiments. Accuracy
14
Method Precision, % Recall, %
Circle 92.1 100
FMT 90.57 100
Lin 94.12 100
Surf 91.49 89.58
Zernike 92.31 100
Our approach 99.9 100
Database [1] contains 48 images with resolution 3000 x 2300 pixels
[1] Image manipulationdataset is created at the Friedrich-Alexander-Universität Erlangen-Nürnberg byV. Christlein et al.](https://image.slidesharecdn.com/kuznetsovusingefficientlinearlocal-160427211020/85/Andrey-Kuznetsov-and-Vladislav-Myasnikov-Using-Efficient-Linear-Local-Features-in-the-Copy-move-Forgery-Detection-Task-14-320.jpg)
Andrey Kuznetsov and Vladislav Myasnikov - Using Efficient Linear Local Features in the Copy-move Forgery Detection Task
- 1. Using efficient linear local features in the copy-move forgery detection task A NDRE Y KUZNE T SOV, V L A DISL AV M YA SNIKOV SA M A RA STAT E A E ROSPA CE UNIV E RSIT Y (SSA U), WWW.SSA U.RU KUZNE T SOFF.A NDRE Y @G M A IL .COM A IST-2016
- 3. Image forgery – what is it? Main forgery types 1. Changing local characteristics 2. Copy-move (plain, transformed) 3. Splicing 4. Objects modelling 3 Copy-move example Protection types 1. Active (digital watermarks) 2. Passive (forgery detection algorithms) Digital data is used everywhere (research, commercial and military purposes)
- 5. The proposed approach 5 Problem: there is no copy-move detection algorithm with ~100% precision [1] The key features of the proposed algorithm: - 100% recall - high calculation speed (for real-time image analysis) - low computational complexity - 99,9% precision The main steps of the algorithm 1. Sliding window analysis mode 2. Use special structural pattern 3. Hash values calculation ( based on linear local features) 4. Store hash values in a hash table 1. Christlein, V., Riess, C., Jordan, J., Riess, C., Angelopoulou, E.: An evaluation of popular copy-move forgery detection approaches. In: IEEE Transactions on InformationForensics and Security. Volume 7(6). (2012). 1841–1854
- 6. Structural pattern 6 A structural pattern is defined as follows: , where the set of coordinates is defined as follows: ( )ba,,Λℵ ( ) ( ) ( )nmbaba nm ,,,,, , Π≡Λℵ Λ∈ ! ( )nmba ,,,Π ( ) ( ) ( ) ( ) ( ) ( )⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ −+−+−+ −++ ≡Π 1,1,,,1 ,1,,,1,,, ,,, bnamnam bnmnmnm nmba ! ! ! Let be an analyzed image( )nmf , – a simplified form of a structural pattern( ){ }( )ba,,0,0ℵ ( ) 5,3,3, =ΛΛℵ 7
- 7. Duplicate 7 There are duplicates by a pattern ( )ba,,Λℵ , if there are at least 2 pairs of coordinates ( )nm ʹʹ, ( )nm ʹʹʹʹ,and that satisfy the following equalities: ( ) ( ) ( ) ( ).,,, ,,, banm nnmmfnnmmf Λℵ∈∀ +ʹʹ+ʹʹ=+ʹ+ʹ The task is to determine for each image pixel, which corresponds to the upper left point of an image fragment (with a form of a structural pattern), a unique integer number: 0 – no copy-move, >0 – copy-move type (m’,n’) 1 2 3 4 5 6 7 8 (m’’,n’’) 1 2 3 4 5 6 7 8 Duplicates
- 9. Linear local features 9 Linear local feature (LLF) over Galois field GF(p): , where ( ){ }( )Amh M m , 1 0 − = ( ){ } 1 0 − = M mmh is a kernel, A is a convolution algorithm over GF(p), p is a prime number A hash value is a result of convolution of an image fragment and a kernel ( ){ } 1 0 − = M mmh
- 10. Linear local features 10 ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) .01~1 ,2,,0~ ,1,1,0~ ,/1,,0 ,/1,1,0 ,10 1 1 1 1 =−++− Θ−+∈=+− Θ−∈=−−− Θ−+∈=− Θ−∈=−− = ∑ ∑ ∑ ∑ = = = = KMMha KMMmmkmha Mmmkmhamh KMMmkmha Mmkmhamh h K K k k K k k K k k K k k ϕ ϕ ϕ ! ! FIR values are calculated using the following system of linear equations (SLE):( ){ } 1 0 − = M mmh ( ){ } 1,0~: +=Θ≠∈=Θ + Knn ϕZ Set of irregularities: SLE are solved to select the optimal convolution kernel 1 2 − −+ K KMC Recursive LLF calculation ( ) ( ) ( ) ( ) 1,0 ~ 1 −= −+−= ∑∑ Θ∈= Nn mmnxknyany m K k k ϕ (LLF were developed by V. Myasnikov in 2007)
- 12. Experiments 12 Let us use a number of false detected duplicates (collisions) as a quality parameter colK Test set: 10 satellite images SPOT-4, 5000x7000, without duplicates ,Precision fptp tp + = ,Recall fntp tp + = Metrics for quality estimation tp – true positive fp – false positive fn – false negative PC used: Intel Core i5 3470, 8GB RAM { }K kka 1= are defined as follows: (a) Fibonacci sequence elements: K=2 – K=3 – K=4 – (b) Polynomial coefficients: ( ) k K k k Ca 1−= 2,1 21 == aa 3,2,1 321 === aaa 5,3,2,1 4321 ==== aaaa
- 13. Experiments. Accuracy 13 0 2000 4000 6000 8000 10x10 9x9 8x8 7x7 6x6 a x b Sliding window size 11×11, Sliding window size 18×18, 9=Λ4=Λ 0 2 4 6 8 10 12 16x16 14x14 12x12 10x10 8x8 7x7 6x6 a x b Results: • a > 8, b > 8 • 6>Λ colKcolK Kcol Proposed solution 2D Rabin- Karp rolling hash(a) (b) 2 240854 1338933 1235 3 242 230 1235 4 232 225 1235
- 14. Experiments. Accuracy 14 Method Precision, % Recall, % Circle 92.1 100 FMT 90.57 100 Lin 94.12 100 Surf 91.49 89.58 Zernike 92.31 100 Our approach 99.9 100 Database [1] contains 48 images with resolution 3000 x 2300 pixels [1] Image manipulationdataset is created at the Friedrich-Alexander-Universität Erlangen-Nürnberg byV. Christlein et al.
- 15. Examples 15
- 16. Experiments. Computational complexity 16 12000 12500 13000 13500 14000 9x9 9x10 11x11 13x13 15x15 Avg. image analysis time, ms a×b Average image analysis time is 12.5 s, because of recursive hash values calculation Method Total time, s Circle 5103.43 FMT 6948.03 Lin 4785.71 Surf 1052.12 Zernike 7065.18 Our approach 420.12
- 17. Results and conclusion 17 Plans for future 1. Designing transformed copy-move detection (affine, JPEG, contrast enhancement, etc.) 2. Compare with GPU-based version of the algorithm Results 1. The algorithm has 0-false negative error 2. Execution speed is very high due to low computational complexity (including recursive hash calculation) 3. False positive error is in average%10 5−