3.1. Identification

results are only obtained by the SVM. In this chapter, two different distances were evaluated,

xs � yt

xsxT s yt

where xs is the estimated feature vector of the image under analysis and yt is the center of the t-

In this chapter, the system was evaluated using the identification and verification tasks, wherein identification of the system is required to determine the identity of the person under analysis by comparing the facial characteristics stored in a database with the face characteristics extracted and the verification task, where the system must define if the identity corresponds with the person she/he claims to be [4]. In both tests, the results are compared with another algorithm like the eigenphase [11], Laplacianfaces [29], Fisherfaces, and eigenfaces [28], all of them used in the classification task with the SVM and k-means with Euclidean and

The AR database was expanded with four additional images for each one in the original AR database. These images are shown in Figure 5, where Figure 5a is the original image and

After the expansion, the AR database has 12,000 face images in total, each person has 100 images and the database has 120 persons, where 65 are males and 55 females. The database was divided into two sets, the AR(A) which has 70 images with illumination and expression

cosine distance, the AR Face Database [35] was used for all tests.

Figure 5b–e show the resulting images of the illumination variations.

Figure 5. Effects of illumination transformation applied to form the extended AR database.

<sup>T</sup>

t

yT t

, (2)

, (3)

dst ¼ xs � yt

dst <sup>¼</sup> <sup>1</sup> � xsyT

the Euclidean distance given by:

116 From Natural to Artificial Intelligence - Algorithms and Applications

and the cosine distance is given by.

3. Evaluation results

th class.

Figure 8 shows the recognition performance of the texture descriptors hLBPI and WBP compared with the other classical methods, all of them using the set AR(A) and seven training images for each person.

An important evaluation to obtain also is the ranking of identification, where the ranking (n) denotes the probability that an image belongs to one of n classes with highest probability. That is, a ranking of 10 is the probability that the image belongs to one of the 10 most likely persons. Figures 9 and 10 present the ranking evaluation with the set AR(A) and set AR(B).

In all cases, the training was done using seven images per person belonging to either the AR (A), while the recognition system was tested with images that were not used for training from the AR(A) and AR(B) sets respectively.
