Author Affiliations
1College of Computer Science and Technology, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning , China2Liaoning Key Laboratory of Industrial Intelligence Technology on Chemical Process, Shenyang 110142, Liaoning , Chinashow less
Fig. 1. Schematic of improved fourth-order magic square algorithm and scrambled images.(a) Diagram of the improved fourth-order magic square transformation rules; (b) scramble degree images at each stage of the improved fourth-order magic square transformation
Fig. 2. Scrambling restoration of ORL database. (a) Original image; (b) image scrambled by the proposed scrambling algorithm; (c) restored image
Fig. 3. Pixel point coordinate map in ORL database. (a) Distribution map of adjacent position points of the original image; (b) distribution map of adjacent position points of the scrambled image
Fig. 4. Scrambling restoration of EYaleB database. (a) Original image; (b) image scrambled by the proposed scrambling algorithm; (c) restored image
Fig. 5. Pixel point coordinate map in EYaleB database. (a) Distribution map of adjacent position points of the original image; (b) distribution map of adjacent position points of the scrambled image
Fig. 6. Scrambling stability map
Fig. 7. Relationship between number of iterations and recognition rate. (a) ORL database; (b) EYaleB database
Fig. 8. Similarity number distribution graph of two templates generated with different keys
Parameter | Original matrix | Unmodified transformation matrix | Improved transformation matrix |
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Degree of correlation between adjacent locations | -1.0000 | 0.3398 | 0.2653 |
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Table 1. Matrix adjacent position correlation at each stage of the improved fourth-order magic square transformation
k | Is it periodic |
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10 | No | 50 | No | 100 | No | 1000 | No | 2000 | No |
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Table 2. Periodic experimental demonstration result
Algorithm | Degree of correlation between adjacent locations |
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Original image(ORL) | 0.9817 | Original image(EYaleB) | -0.9822 | Proposed algorithm(ORL) | 0.0194 | Proposed algorithm(EYaleB) | 0.0187 | Original magic square(ORL) | -0.3048 | Original magic square(EYaleB) | 0.1907 | Barker(ORL) | -0.3310 | Barker(EYaleB) | 0.1729 | Arnold(ORL) | 0.2539 | Arnold(EYaleB) | 0.1221 | Algorithm in Ref.[27] | 0.0379 | Algorithm in Ref.[28] | 0.0183 |
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Table 3. Comparison result of different algorithms
Parameter | Method in Ref.[29] | Method in Ref.[30] | Proposed method(ORL) | Proposed method(EYaleB) |
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GAR /% | 96.00 | 96.37 | 97.12 | 96.90 |
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Table 4. Comparison of recognition rate of different methods
Parameter | Method in Ref.[21] | Method in Ref.[31] | Proposed method(ORL) | Proposed method(EYaleB) |
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EER /% | 11.85 | 14.53 | 10.97 | 11.02 |
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Table 5. EER comparison of different methods