3.2. Verification

In the case of verification, the percentage of error is divided into two: false acceptance and false rejection. False acceptance occurs when an individual claims to be the person who is not and

Figure 6. Examples of (a) images from the AR(A) set. (b) Images from the AR(B) set.

Figure 7. The identification rate obtained using different numbers of training images.

this is mistakenly accepted by the system. False rejection occurs when an individual provides their identity and the system erroneously rejects this statement.

The performance of most face verification systems depends on a suitable selection of the threshold value to diminish both the false acceptance and the false rejection. After many tests, it was concluded that this relationship, this threshold, is used to decide if the person is who she/he claims to be; next, it is explained, how the threshold can be obtained with an exponential function as shown in Figure 12, where you can select the point that has the lowest value of both false acceptance and false rejection. Thus, we can assume that the false acceptance

Figure 8. Recognition performance of the evaluating approach using: SVM, Euclidean distance, and cosine distance in the classification stage. The performance of hLBPI, eigenphases, eigenfaces, Laplacianfaces, and Fisherfaces are also shown

Pfað Þ¼ Th e

�αTh (4)

Face Recognition Based on Texture Descriptors http://dx.doi.org/10.5772/intechopen.76722 119

probability is given by:

Figure 9. Ranking evaluation of image set AR(A).

for comparison.

Figure 11 shows the receiver operating characteristics (ROC) when the hLBPI and WBP algorithms are used for the verification task using the set AR(A). Figure 11 shows that both algorithms have a similar performance with a false rejection and false acceptance, and they are very low.

Figure 8. Recognition performance of the evaluating approach using: SVM, Euclidean distance, and cosine distance in the classification stage. The performance of hLBPI, eigenphases, eigenfaces, Laplacianfaces, and Fisherfaces are also shown for comparison.

Figure 9. Ranking evaluation of image set AR(A).

this is mistakenly accepted by the system. False rejection occurs when an individual provides

Figure 11 shows the receiver operating characteristics (ROC) when the hLBPI and WBP algorithms are used for the verification task using the set AR(A). Figure 11 shows that both algorithms have a similar performance with a false rejection and false acceptance, and they are

their identity and the system erroneously rejects this statement.

Figure 7. The identification rate obtained using different numbers of training images.

118 From Natural to Artificial Intelligence - Algorithms and Applications

very low.

The performance of most face verification systems depends on a suitable selection of the threshold value to diminish both the false acceptance and the false rejection. After many tests, it was concluded that this relationship, this threshold, is used to decide if the person is who she/he claims to be; next, it is explained, how the threshold can be obtained with an exponential function as shown in Figure 12, where you can select the point that has the lowest value of both false acceptance and false rejection. Thus, we can assume that the false acceptance probability is given by:

$$P\_{\hat{f}^\hbar}(Th) = e^{-\alpha \hat{T} \hbar} \tag{4}$$

and

$$P\_{\sharp^\*} = e^{-\beta P\_{\sharp^\*}} \tag{5}$$

Then from Eqs. (4) and (5) it follows that <sup>α</sup> ¼ �Ln Pfað Þ Th <sup>=</sup>Th where Pfað Þ Th is the false acceptance percentage, calculated from a threshold Th. Hence, for a desired false acceptance probability Po the suitable value of Th is given.

$$\text{Th} = -\text{Ln}(P\_o)/\alpha \tag{6}$$

4. Conclusions

This chapter presented the application of different texture descriptors for tasks ranging from feature extraction to face recognition, which are based on the LBP algorithm, specifically the hLBPI and WBP. The evaluation results demonstrate that these algorithms provide good recognition rates. In most situations, the accuracy of recognition with the WBP is slightly lower than the accuracy with the hLBPI because the feature vector estimation of the WBP does not require PCA and uses non-overlapping blocks. This fact results in an important computational complexity reduction of approximately 2NML=9 relative to hLBPI, where L is the feature vector size. If an L with a big value is used, it produces a more exact feature vector, although this causes the computational complexity to increase. Also, the evaluation results were compared with other

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Figure 12. Relationship between the false acceptance rate and the threshold value.

Figure 13. Relationship between the false acceptance rate and false rejection rate.

Figure 13 shows the results of an exponential function and some experimental results of the relationship between the false acceptance rate and false rejection rate in this chapter.

Figure 10. Ranking evaluation of image set AR(B).

Figure 11. ROC of proposed and conventional hLBPI algorithms.

Figure 12. Relationship between the false acceptance rate and the threshold value.

Figure 13. Relationship between the false acceptance rate and false rejection rate.
