Experimento N° 1: CELDAS AEROBIAS ESTÁTICAS

There are only two parameters in the proposed method, namely, the dimension of random subspace m and the number of random subspaceL. Fig. 6.2 and Fig. 6.3 show how the true positive (false positive) rate of the method Basic+RSM varies for different values ofmand L, respectively. As shown in Fig. 6.2, the performance of the proposed method improves by increasing the number of random subspaces

off between the performance and computational complexity, we setL= 400 in the following experiments.

Fig. 6.3 indicates the sensitivity of the proposed method to the parameter

m, wheremis the dimension of each random subspace anddis the size of the entire feature spaceT. Note that m∈[1, d] and the performance of the proposed method is as same as that of the PCA-based extraction method [31] whenm=d. Therefore, from Fig. 6.3 we can see that as long asm/d <1, the proposed method can achieve a higher true positive rate than the PCA-based extraction method. In addition, from both Fig. 6.2 and Fig. 6.3 we can see that the performance of the proposed method is not sensitive toL and M. In the rest of this chapter, we empirically set

L= 400 andm/d= 0.45, because these values yield the best result.

6.3.3 Performance Evaluation

In this work, the overall receiver operating characteristic curve [13] is applied to compare the performance of different methods, as shown in Fig. 6.4, Fig. 6.5 and Fig. 6.6. To get convincing results, all the 100×10 intraclass and 100×10×9 interclass samples from 10 cameras are used together to draw the overall ROC curve. It is worth mentioning that the overall ROC curve for the proposed method is obtained in a slightly different manner with the one mentioned in Section 2.5. For a given detection threshold, we count the number of true positive decisions and the number of false positive decisions for each camera in each subspace respectively, and sum them up to obtain the total number of true positive decisions and false positive decisions so as to calculate the true positive ratePtpand false positive rate P_{f p}. Specifically, as the numbers of images captured by each camera are exactly the

L 0 200 400 600 800 1000 1200 Percentage 0 20 40 60 80

100 Canon Ixus70, m/d=0.45, 256x256 pixels

True positive rate False positive rate

Figure 6.2: Performance with respect to the number of random subspaces L on image blocks with size of 256×256 pixels, thresholdτ = 0.08.

m/d 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage 0 20 40 60 80

100 Canon Ixus70, L=400, 256x256 pixels

True positive rate False positive rate

Figure 6.3: Performance with respect to the dimension of the random subspacem

same, we can simply calculate theP_tp andP_{f p} for a threshold as follows Ptp= Pc j=1 PL l=1Tjl T ,Pf p= Pc j=1 PL l=1FjL (c−1)T , i= 1,2, ..., c, (6.9)

wherecis the number of cameras,Lin the number of subspaces andT is the number of query images from all cameras. Tl

j andFjlare the true positive decisions and false

positive decisions made in the subspaceRl with respect to camera Cj, respectively.

By varying the detection threshold from the minimum to the maximum value, we can finally obtain the overall ROC curve for the RSM-based method.

In Fig. 6.4, Fig. 6.5 and Fig. 6.6, the black, blue, and red lines indi- cate the overall ROC performance of Basic/PCAI8, Basic/PCAI8+PCA, and Ba- sic/PCAI8+RSM, respectively. In order to show the detail of the ROC curves with a low FPR, the horizontal axis of all the overall ROC curves are plotted in the logarithmic scale. As analysed above, the performance of PCAFE would decrease when the training set is noisy. But from Fig. 6.4, Fig. 6.5 and Fig. 6.6, we can see that as the post-processing method, PCAFE still can boost the performance of the conventional SPN extraction methods even when the training set are full-filled with scene textures. And this performance gain is more significant when PCAFE is performed on the image block with larger sizes (i.e., 512×512 pixels). On the other had, the proposed RSM method (red lines) constantly achieves the best performance regardless of the size of the image blocks and the SPN extraction algorithms. This observation indicates the superiority of the RSM method over PCAFE on the ROC performance. Based on these results, we can conclude that the PCAFE method can improve the conventional SPN extraction methods even when the training set

Table 6.2: Computational cost (Seconds) of different methods on image blocks with size of 512×512 pixels.

Features Feature

Extraction Matching Total

Basic 0 4.29 4.29

Basic+PCAFE 2.82 0.03 2.85

Basic+RSM 3.96 19.43 23.39

is noisy, and it can be further improved by the proposed RSM method.

Then we evaluate the computational complexity of the SCI identification system based on the proposed methods. Table 6.2 shows the time cost of different methods to match 100 query noise residuals to the aforementioned 10 cameras on 512×512 image blocks. This experiment is conducted on the same PC with an Intel Core i5 3.20GHz processor and 16G RAM. To quantify the efficiency of an identification system, two factors are considered in this experiment. The first one is “Feature extraction” indicating the time cost for PCAFE and RSM to extract features from 100 query noise residuals and 10 reference SPNs. The second factor is “Matching” which relates to the time spent on calculating 100×10 normalized correlations. The overall computational cost is represented as “Total”. The time cost of training and reference estimation are not counted in this experiment as both of them can be performed off-line.

Both PCAFE and RSM require to extract features from the noise residuals, so it is not surprising to see that they require more time in the feature extraction process. The complexity of computing correlation is proportional to the size of the feature vectors. The dimensionality of features extracted by PCAFE is lower than that of the original SPN, thus PCAFE can dramatically reduce the time spent on

False positive rate

10-3 10-2 10-1 100

True positive rate

0 0.2 0.4 0.6 0.8

1 Overall ROC curves, 128x128 pixels

Basic

Basic+PCAFE Basic+RSM

False positive rate

10-3 10-2 10-1 100

True positive rate

0 0.2 0.4 0.6 0.8

1 Overall ROC curves, 128x128 pixels

PCAI8

PCAI8+PCAFE PCAI8+RMS

Figure 6.4: The ROC curves of different methods on image blocks with size of 128×128 pixels.

False positive rate

10-3 10-2 10-1 100

True positive rate

0.5 0.6 0.7 0.8 0.9

1 Overall ROC curves, 256x256 pixels

Basic

Basic+PCAFE Basic+RSM

False positive rate

10-3 10-2 10-1 100

True positive rate

0.5 0.6 0.7 0.8 0.9

1 Overall ROC curves, 256x256 pixels

PCAI8

PCAI8+PCAFE PCAI8+RSM

Figure 6.5: The ROC curves of different methods on image blocks with size of 256×256 pixels.

False positive rate

10-3 10-2 10-1 100

True positive rate

0.7 0.75 0.8 0.85 0.9 0.95

1 Overall ROC curves, 512x512 pixels

Basic

Basic+PCAFE Basic+RSM

False positive rate

10-3 10-2 10-1 100

True positive rate

0.7 0.75 0.8 0.85 0.9 0.95

1 Overall ROC curves, 512x512 pixels

PCAI8

PCAI8+PCAFE PCAI8+RSM

Figure 6.6: The ROC curves of different methods on image blocks with size of 512×512 pixels.

the matching process. The dimensionality of features extracted by RSMmis much lower (i.e., m/d= 0.45), but since the RSM method requires to preform matching in each of the 400 subspaces, it is reasonable to see that SEA requires more running time in matching stage. From the overall computational cost, one can deduce that RSM requires more computational cost than other two methods. Although the RSM-based method can bring performance gain to identification accuracy, from this experiment we can see that it also incurs extra cost in computation.

6.4

Conclusion

In Chapter 4, a PCA-based feature extraction method was proposed to extract a feature set with much lower dimensionality from the original noise residual. Howev- er, the performance of this algorithm degrades when the training set is noisy. It is because the eigenvectors that generated from the training process can be corrupted by the unwanted interferences. Some leading eigenvectors are very likely to represent the interfering artifacts rather than the real SPN signal. Moreover, it is difficult to locate and remove these corrupted eigenvectors from the feature space. To address these problems, an ensemble solution based on RSM is presented to eliminate the impact of various contaminations. The experimental results show that the proposed RSM-based method achieves a superior overall ROC performance than several SPN extraction methods and the PCA-based feature extraction method. However, the proposed RMS-based method would inevitably bring extra efficiency cost to an SCI systems. Therefore, it suggest that the proposed method is more suitable for the cases that a lower false identification rate is preferred.