Feature Selection Using the Bosphorus Database

4.5.1 Motivation and Feature Selection

Instead of using the whole face region, extracting features on the cheek/nose region, which is relatively robust under various expressions, provides an effective approach for 3D face recognition. The 113 curves found in Figure 4.3 provide a comprehensive coverage of the cheek/nose region. However, selecting all the curves as features produces a high dimensionality feature vector which is unlikely to have a good classification performance [95, 96]. This so- called “curse of dimensionality” requires a large number of training samples to be added to the classifier when the dimensionality increases. To address these, feature selection is used to find a subset of curves that can produce a high recognition performance.

There are a lot of feature selection methods for dimensionality reduction. FSFS is applied to reduce the feature space dimensionality in this chapter for the reason that it provides a simple and effective way of selecting the curves step by step. FSFS starts from an empty set and first selects the best single curve, in terms of classification performance. Then, other curves which produce the highest R1RR based on the leave-one-out method, when combined with the

previously selected curves, are iteratively added to the set. The recognition rate of each single curve is calculated by the nearest neighbour city-block distance that has been shown to have a better discriminatory power when the feature space is sparse [74]. The feature selection employs the Bosphorus database, as the majority of its captures contain little noise, enabling relatively accurate landmarking and curve drawing.

4.5.2 Feature Selection Results of 75 Nasal Curves

The feature selection results of 75 curves are shown in Figure 4.4 and the number of points on each curve is resampled to 50. To produce the best recognition performance, 21 curves are selected by FSFS to build a feature vector whose R1RR reaches to 82.5%. This implementation

outperforms the result in [7] to some extent as they achieved the highest R1RR, ~82.5%, when

28 curves are selected, which are using more curves than this implementation. Furthermore, for the recognition performance of each single curve, the most discriminative curve is the nasal bridge one (L9L1) with the highest R1RR, 45.65%, which is much higher than the one recorded

in [7], ~38%.

Figure 4.4: R1RRs against the number of curves selected by the FSFS algorithm using 75 nasal curves

4.5.3 Feature Selection Results of 38 Curves on the Cheek/Nose Region

Using the detected cheek landmarks and their neighbouring nasal landmarks, 38 curves are found mainly on the cheek region for recognition performance evaluation. A constant distance of 40 pixels, was used to localize two cheek landmarks, which is a reasonable setting for 3D captures in the Bosphorus database and could be further evaluated in the following sections. R1RRs against the number of curves selected by the FSFS algorithms is shown in Figure 4.5

and Table 4.1. To achieve the highest R1RR, 6 curves which produce 82.77% of the R1RR are

selected by the FSFS method. It is higher than that of 21 nasal curves (82.5%), which produce the highest R1RR in 75 nasal curves selection. If only using 4 curves, they achieve 82.5% of

R1RR, which is the same as the performance of 21 nasal curves but using a very small sized

feature vector. This result is very promising and shows great potential of extracting expression invariant features on the adjoining regions between the nose and cheeks.

Figure 4.5: R1RRs against the number of curves selected by the FSFS algorithm using 38 curves

Table 4.1: R1RRs using the curves selected by FSFS

Curves selected by FSFS R1RR 1 L18L22 58.31% 2 L18L22, L20L24 76.98% 3 L18L22, L20L24, L19L23 81.18% 4 L18L22, L20L24, L19L23, L1L20 82.50% 5 L18L22, L20L24, L19L23, L1L20, L17L21 82.31% 6 L18L22, L20L24, L19L23, L1L20, L17L21, L16L18 82.77%

(a) Three horizontal curves (b) CMC curves

Figure 4.6: Three horizontal curves across the cheek/nose region and their recognition performance tested under identification scenarios

As can be seen from Table 4.1, the three curves (L18L22, L20L24, L19L23) across the cheek/nose region shown in Figure 4.6 are the most significant curves of the 38 curves when selected by FSFS. The R1RR of each selected curve is higher than the best curve selected on

the nasal region, L9L1. Moreover, using all the three horizontal curves the R1RR is 81.18%,

which is comparable with the recognition performance of 21 selected nasal curves found in Section 4.5.3, despite the fact that 18 fewer curves are used.

4.5.4 Feature Selection Results of 113 Curves on the Cheek/Nose Region

FSFS has been successfully applied on the nasal (75) and cheek (38) curves selection, which shows the potential for using small subset of curves to produce higher recognition performance. In this section, the combination of the cheek/nose curves (75+38) is further evaluated by using the FSFS method. The number of points of each curve is resampled to 50 and the distance between L20 and L9 is set to 40 (pixels). The feature selection results from 113 curves on the cheek/nose region using the FSFS algorithm is shown in Figure 4.7. The selected curves and their corresponding R1RRs are provided in Table 4.2.

Table 4.2: Curves selected by FSFS

Curves selected by FSFS R1RR 1 L18L22 58.31% 2 L18L22, L20L24 76.98% 3 L18L22, L20L24, L9L1 82.65% 4 L18L22, L20L24, L9L1, L4L12 84.66% 5 L18L22, L20L24, L9L1, L4L12, L15L5 85.68% 6 L18L22, L20L24, L9L1, L4L12, L15L5, L19L23 86.24% 7 …L1L20 87.07% 8 …L1L20, L3L6 87.53% 9 …L1L20, L3L6, L16L10 87.72% 10 …L1L20, L3L6, L16L10, L14L6 87.98% 11 …L1L20, L3L6, L16L10, L14L6, L17L21 88.10% 12 …L1L20, L3L6, L16L10, L14L6, L17L21, L9L16 88.10% 13 …L1L20, L3L6, L16L10, L14L6, L17L21, L9L16, L1L14 88.36% L18L22, L19L23, L20L24, L9L1 84.35%

Figure 4.7: Rank one recognition rate against the number of curves selected by the FSFS algorithm using 113 curves on the cheek/nose region

To achieve the highest recognition performance, 13 curves were finally selected using FSFS to construct feature space. They are L18L22, L20L24, L9L1, L4L12, L15L5, L19L23, L16L18, L3L6, L16L10, L14L6, L17L21, L9L16 and L1L14. The R1RR of those features is 88.36%,

which shows that this feature combination can achieve good recognition performance. Therefore, using features from both the nasal region and its adjoining cheek region is beneficial for expression robustness. Finally, 4 curves are selected to form a low dimensionality rejector whose aim is to effectively and quickly eliminate a large number of ineligible candidate faces from the gallery.