4. Conclusions

and

Pfr ¼ e

probability Po the suitable value of Th is given.

120 From Natural to Artificial Intelligence - Algorithms and Applications

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

Figure 11. ROC of proposed and conventional hLBPI algorithms.

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

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.

�βPfa (5)

Th ¼ �Ln Pð Þ<sup>o</sup> =α (6)

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 methods, such as the Eigenfaces, Laplacianfaces, and Fisherfaces. Another point that can be observed is that, as in all recognition systems, the accuracy percentage increases when a greater number of training images are used, so one could look for ways to generate training images based on an original image to increase the number of images, and then the system may be able to recognize face images in other types of environments, such as with a lot of lighting or with partial face occlusions. The results obtained with the set A shown in Figure 8 where the system has a good performance both with images with facial expressions and with lighting, as well as when there are images with a partial occlusion of the face such as sunglasses as shown in Figure 9. In both cases, a recognition rate higher than 90% is obtained.

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The evaluation results using the AR databases demonstrate that these algorithms provide good results also when it performs identity verification tasks, providing a theoretical criterion which allows selecting the threshold such that the system be able to provide a previously specified false acceptance or false rejection rate.
