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In this section, 75 nasal curves found on the four components (depth, SNx, SNy and SNz) shown

in Figure 6.1 are evaluated under identification scenarios. To make a comparison between different types of captures, 360 captures of 18 subjects are selected from the Photoface, FRGC and Bosphorus databases, respectively.

(a) Depth (b) SNx (c) SNy (d) SNz

Figure 6.1: 75 nasal curves representations on the depth and surface normals components 6.3.1 Recognition Performance for 75 Nasal Curves

In Chapter 4, instead of using 50 points, each curve is resampled to only 15 points and the results demonstrated that using fewer points on the nasal and cheek regions can produce a comparable recognition performance, even though the dimensionality of the feature space is greatly reduced. Therefore, in this chapter, 75 nasal curves with 15 points per curve are extracted for recognition. To make a comparison of the recognition performances generated from different types of captures, the subset (360 captures of 18 subjects) of each database is employed for evaluation.

To reduce the dimensionality and find the most discriminative curves or curves combination, FSFS was applied to the 75 curves, combined with the leave-one-out cross validation and nearest neighbour classifier. The R1RRs obtained from set of captures for the three databases

and different components (depth, SNx, SNy and SNz) are shown in Figure 6.2, which describes

the changes of R1RRs when the number of selected curves varies from 1 to 30. The recognition

performances are not provided when more curves are selected as all the R1RRs reduce for ≥ 30

curves.

The R1RRs for the FRGC database, shown in red, outperform those for the Bosphorus (blue)

and Photoface (black) databases for the reason that the captures from Bosphorus and Photoface databases contain more expression variations. In addition, for all three databases, features

extracted from the surface normals (SNx, SNy and SNz) are shown to be more discriminative

than those from the depth component. Only the features extracted from the depth component were explored in [7] and so there is potential to further evaluate the surface normals or combine both depth and surface normals to build a stronger feature set.

The L9L1 curve, from the nasal root to tip, is always first selected (except for the SNx map)

and makes a significant contribution to the overall recognition performance. L9L1 is located on the central profile of human face, which can better and more robustly describe the nasal surface changes. However, in the SNx map, this curve suffers significant feature-level changes

as long as it is not localized accurately, for example the sign of the points on the L9L1. For the depth, SNy and SNz components of the FRGC database and the SNy component of the Photoface

database, all the R1RRs of L9L1 exceed 80%.

Figure 6.2: R1RRs against the number of curves selected by the FSFS and leave-one-out. Four

components, depth, SNx, SNy and SNz, from each subset (360 captures of 18 subjects) of the Photoface,

FRGC and Bosphorus databases are used in this experiment. Only the first 30 selected curves are provided for recognition performance comparison.

6.3.2 Recognition Performance for the Landmarks Localized by the Constant Distance For the Photoface captures, the nasal root and two alar grooves are not always robustly localized, as few local nasal structures are provided in the reconstructed depth map. Therefore, instead of using the NCM landmarking [7] employed in Section 6.3.1, this section uses two constant distances, Drtp (from the tip to root) and Daap (from the tip to alar grooves), to localize

the root and alar grooves, resulting in 75 curves on a fixed sized nasal region. For Daap, the

nose tip is located in the centre, which results in an isosceles triangle covering the whole nasal region. This means that whatever is the real size of nasal region, all the captures use the same window to crop the nasal region.

The R1RRs shown in Figure 6.3 are calculated by the same settings, as for Figure 6.2. This

enables a direct comparison with the recognition performances by using the NCM landmarking for the Photoface database from Figure 6.3. It is clear that the features extracted from the fixed sized nasal region described by green curves outperform the region found by NCM landmarking, which proves the conclusion stated in [138]. The constant distance is likely to preserve the within-class similarity and between-class scatter, as the captures from the same subject contain similar geometric distributions after pose calibration.

Figure 6.3: A comparison of R1RRs between fixed sized (constant distance) and calculated (NCM

landmarking) nasal region in the Photoface database using depth (D), SNx (X), SNy (Y) and SNz (Z)

6.3.3 Classification Evaluation Using the Features Extracted from the SNy Map

Compared with the other two databases, the recognition performance of the features extracted from the SNy map in the Photoface database is apparently better than those from the depth, SNx

and SNz maps. Using only 9 selected curves on the SNy map, the R1RR can reach 98.84%, which

demonstrates the potential of extracting discriminative features for face recognition from the Photoface captures. Compared to the SNx and SNz components, these 9 curves on the SNy map

produce a higher recognition performance. Therefore, instead of using the less accurate depth map of the Photoface captures, it is very promising to investigate new discriminative features on the surface normals components.

A further classification evaluation is explained in this section to demonstrate the recognition performance of features extracted from the SNy map. KFA [139] with the polynomial kernel is

applied for nonlinear projection and dimensionality reduction. Instead of using 18 subjects with 20 captures per subject, this evaluation takes all the captures in the Photoface database into account and tests the recognition performance using from 1 to 10 of training samples. Figure 6.4 shows the R1RRs against the number of training samples per subject.

Figure 6.4: R1RRs against the number of training samples using the selected curves from the SNy map

of the Photoface captures. All the captures in the Photoface database are used in this evaluation. When the training set only contains one or two samples for each subject, the R1RRs (62.22%

and 85.79%, respectively) are very comparable to the results reported in [9]. Furthermore, the efficiency is much improved using the proposed method as only the human nasal region and a small number of features (135 values) are considered for face recognition. When the number of training samples increases to 10, the R1RR reaches 97%, demonstrating that the recognition

identity. Instead of exploiting other feature selection and classification strategies, there is great potential for improved performance by fusing with the features extracted from other components.