Face/Non Face Models & Relative Difference Normalized

dimensionality without much data loss and keeping an adequate detection ratio.

The training and test data used for these experiments are the already introduced in Table 7 and Table 8. Following Figure 59 show the normalized eigenvalues⁵ plots for both databases and for the 1^st and 2^nd stage:

Figure 59. Face detection PCA - Normalized eigenvalues plot: 1^st stage

The eigenvalues for both face databases are similar, although it can be observed that the BioID two first eigenvalues have a higher value than the first two GTAV Internet eigenvalues.

That means that by keeping only two eigenvalues, a better reconstruction can be achieved with BioID face database. Moreover, in both cases, only with this first eigenvalue more than 50% of the information is kept.

5 Normalized Eigenvalues: =

∑

∑

i i

i

λ λ λ λ

Figure 60. Face detection PCA - Normalized eigenvalues plot: 2^nd stage

In second stage, it can also be observed that the BioID first eigenvalues have a higher value than the first two GTAV Internet eigenvalues. But in this case, only the last nine eigenvalues can be considered null.

As explained in previous chapters, these two face databases have different features:

- 16x16 faces: each face from a different person (more face variety), but faces size is smaller as recommended in the literature (see [5]).

- 19x19 faces: faces from only 23 different people, but with a large variety of illumination, background and face size (allows to have desired size of 19x19). The number of available samples (2981) is about the half of the 16x16 face database (6650).

Since test faces are included in face training set, it is normal to always obtain better results with 19x19 images BioID face database, because for each face exists more samples information than in 16x16 face database where each face is unique. Then with the same amount of eigenvalues a better face detection ratio is obtained with 19x19 face database, although this can indicate a worst generalization to other databases.

In order to better see the above eigenvalues, in Appendix III.1.3 a table can be found showing the normalized eigenvalues for 1^st and 2^nd stages for both databases, 16x16 and 19x19 faces.

Different simulations have been done combining the number of eigenvalues (%Info) and the two proposed dissimilarity methods in order to find the best parameters to obtain the best detection ratio.

In the following table, some combinations of eigenvalues are proposed to evaluate the method based on the % of information for both face databases. Notice that the % of information is kept the same for both stages.

16x16 19x19

Number of Eigenvalues Number of Eigenvalues

% Info

1st Stage 2nd Stage % Info

1st Stage 2nd Stage

51% 1 6 58% 1 4

75% 4 23 79% 3 12

90% 14 56 90% 9 28

95% 25 79 95% 18 48

100% 58 135 100% 58 135

100% 59 144 100% 59 144

Table 15. Face detection PCA: number of eigenvalues selection based on %Info for both face DB

Using above combinations of number of eigenvalues, the systems are trained and both test data classified. Next table shows the result of these experiments:

16x16 19x19

Eigenvalues Detection

Ratio Eigenvalues Detection Ratio

Eigenvalues reduction

~%

Info 1st Stage

2nd

Stage Faces Non faces

~%

Info 1st Stage

2nd

Stage Faces Non faces

Ratios Sum

1st Stage

2nd Stage 100% 59 144 0.9940 0.6377 100% 59 144 0.9860 0.6701 3.2878 0% 0%

100% 58 135 0.9940 0.6377 100% 58 135 0.9860 0.6701 3.2878 2% 6%

95% 25 79 0.9940 0.6368 95% 18 48 0.9860 0.6693 3.2861 58% 45%

90% 14 56 0.9940 0.6353 90% 9 28 0.9855 0.6672 3.2820 76% 61%

75% 4 23 0.9935 0.6294 79% 3 12 0.9850 0.6628 3.2707 93% 84%

51% 1 6 0.9835 0.5690 58% 1 4 0.9880 0.5445 3.0850 98% 96%

Figure 61. Face detection PCA: mean detection ratio for different % of information The column Ratios Sum is the sum of the 4 detection ratios (faces and non faces for both databases). This value is calculated to determinate the best global detection ratio.

The row in yellow is the proposed option for the face detection system under study. A good compromise between eigenvalues reduction and global detection ratio is the followed criterion.

The following experiments are based in the above selection and Figure 62 presents the classification result using PCA & Relative Difference Normalized as dissimilarly metric. For each bootstrap iteration of the training process, first plot displays faces (in orange) and non-faces (in blue) detection ratio for 16x16 GTAV Internet database and second for 19x19 BioID database. Detailed information about the plotted values can be found in Table 35 (16x16) and Table 36 (19x19) in Appendix III.1.3.

Figure 62. Bootstrap to improve PCA & RelDiffNorm classification ratio (16x16 &

19x19)

At each bootstrap iteration, face detection rate is decreasing but non-faces detection is increasing, an unavoidable compromise in order to be able to correctly classify such a huge class as non faces set.

As already exposed previous section, best selection should be the intersection between both curves. For instance, taking the first bootstrap iteration for 16x16 case and the second or third iteration for 19x19 case.

Notice that in 19x19 case, although convergence needs more iterations than in 16x16 case, the reached point achieves better results in terms of face correct classification rate. But on the other hand, it is also interesting to observe that when the number of bootstrap iterations increases, faces detection ratio drops more drastically in case of 19x19 faces size. From that, it can be deduced that 16x16 face database is capable of providing more stable results in terms of generalization, as face detection ratio is less affected by the non-faces classes training set.

As a first conclusion, this classification method provides also satisfactory classification rates and it is useful to observe LBP qualities as a face descriptor.

It can also be extracted that GTAV Internet faces seems to have better qualities as a face dataset and it achieves better generalization results due to the fact that contains a wider range of different faces than BioID faces.

As in previous chapter, the reference image (equipop.jpg, see Figure 52) is used to compare both results. In both cases, skin detector is used in order to improve face detection scheme.

Each face candidate is marked with a yellow box and no boxes post processing is applied to keep only one box per face. The result is given by simply applying a boxes mask.

Figure 63. PCA & RelDiffNorm - ref img classification using GTAV Internet training set The result using GTAV Internet as training samples can detect the 10 faces but non faces misclassification is very high. As faces set contains 2000 totally different faces from 2000 different people, face appearance variations is very high and a mean model of the LBP enhanced histogram is not enough to separate faces from non faces, because regions with non flat texture are misclassified as faces.

Next Figure 64 shows the results of classifying the reference image with BioID faces set as training samples.

Figure 64. PCA & RelDiffNorm - ref img classification using BioID training set Compared to previous result, BioID training samples provides better results when classifying non faces, although only 3 from 10 faces are correctly detected. In this case, the price to correctly detect non faces is too high for faces set.

As a conclusion, it is difficult to decide the best face database option and bootstrapping does not offer the desired final converging results. The effort to reduce input vectors does not lead into a better classification ratio. Therefore, it can be concluded that LBP enhanced histograms mean value models together with PCA and relative difference normalized are not able to correctly represent whole faces and non faces samples sets.