Using the Shape Index for Nose Recognition

Although many published works have considered the SI as a new type of 3D face representation to generate discriminative features, it is still an under-explored representation [18]. Huang et

al. [142] used a multi-scale local binary pattern depth map together with the SI map to increase

the distinctiveness of smooth range faces. Vijayan et al. [132] also explored the use of the SI map for 3D face recognition of twins. In [19], a comparison of a series of 3D facial features showed that the SI map outperformed the depth map but was worse than the point cloud and surface normals.

Despite some advantages, using the original SI map may encounter some unexpected problems. For example, the SI coefficients calculated on the planar region are relatively noisy as the curvatures of such regions are low, which makes it hard to extract robust features on such regions. Therefore, the original SI map is not an appropriate representation for describing all the face, especially for the cheeks. To avoid this drawback, the SI features can be restricted to the less flat regions, for example on the nasal region.

To smooth the original SI map, some effective filters that have successfully been applied to image denoising can provide a good solution to address this problem, for example the median filter. In addition, the curvedness [35], a positive number that specifies the amount of curvature, can remove the noisy data by thresholding the original SI map. In the next section, the discriminative SI features are extracted from the nasal region and the recognition performances obtained by using different SI smoothing approaches are also discussed.

6.4.1 Median Filtering the SI Map

Figure 6.5(a) and (b) demonstrate the original SI map of one sample capture selected from the Bosphorus database. The noisy points, shown in both the frontal and side views, might affect the region segmentation and feature extraction. A recent summary and evaluation of different denoising methods applied to 3D face recognition suggests that the median filter is a good choice for denoising [135]. Therefore, the median filter is employed to smooth the original SI map and the resulting denoised SI map is shown in Figure 6.5(c) and (d). Experiments have shown that 3×3 is a suitable size of median filters for denoising both the depth and SI maps.

(a) Original SI (b) Frontal view

(c) Denoised SI (d) Frontal view (denoised)

Figure 6.5: Median filter applied to the original SI map calculated from one sample capture selected from the Bosphorus database.

The set of nasal curves used in the previous section is also extracted from both original and denoised SI maps and the corresponding recognition performances are shown in Figure 6.6 (blue curves). The R1RR is much higher when the median filter is applied and, in particular,

the R1RR of the curve L9L1 increases by ~17% after denoising. To compare the recognition

performance of features extracted from both original and denoised SI maps among different databases, a subset of the FRGC v.2, Bosphorus and Photoface databases are used for evaluation, which employs the same number of captures and experimental settings (FSFS based feature selection of 75 nasal curves) as the comparisons described in Section 6.3.

In general, as can be seen from Figure 6.6, the recognition performance of the Photoface captures, shown by black curves, outperforms the Bosphorus (blue) and FRGC v.2 (red) databases. The R1RRs of the curve L9L1 experience ~20% improvement for all three databases.

However, for the combination of curves, using the denoised SI map brings more recognition performance improvement in the FRGC v.2 and Bosphorus databases, which is about 5-10% higher than using the original one. In contrast, the median filter brings less improvement when more than 4 curves are selected in the Photoface database. Denoising is of limited benefit as the captures in the Photoface database are relatively smoothed.

Figure 6.6: A comparison of the recognition performance of the 75 curves extracted from both original and denoised SI maps among three databases. The curves are sequentially selected by FSFS.

6.4.2 Curvedness Thresholding

The curvedness can be considered as a rotation invariant gradient operator, which measures the degree of regional curvature. It has true geometrical significance as it is coordinate independent. Therefore, curvedness has the potential to be considered as a new and effective representation of the 3D facial surface to describe curve degree of each point.

In Figure 6.7, the original capture from the Bosphorus database is thresholded by different curvedness values. With the thresholds increasing, the regions contain a high degree of curved surfaces are more prominent, for example the nasal alar grooves and mouth. To remove the noise points on the relatively flat regions in the SI map, the threshold 0.1 is first applied. Each point in the SI map is first smoothed by the median filter and used for feature extraction if the curvedness is bigger than 0.1. However, as can be seen from Figure 6.8, using the curvedness thresholding did not improve the recognition performance. Data loss might be the main reason for this phenomenon as some useful features are removed during the thresholding phase. Therefore, although curvedness thresholding can provide a good approach to smooth the SI map, some discriminative information might be lost and selecting an appropriate threshold for face recognition is still a challenging issue. In comparison, the median filter or other effective filters are more suitable for low complexity SI map denoising.

(a) original (b) 0.1 (c) 0.2

(d) 0.3 (e) 0.4 (f) 0.5

Figure 6.7: An example of the curvedness thresholding by different parameters using the capture selected from the Bosphorus database

Figure 6.8: R1RRs against the number of curves selected by FSFS using the capture selected from the

Bosphorus database. It is a comparison of the recognition performance using the SI maps denoised by the median filter and curvedness thresholding.

6.4.3 Gabor Filtering the SI Map

The Gabor filter, a Gaussian kernel function modulated by a sinusoidal plane wave, is one of widely used image denoising filters and has been introduced to smooth the depth map for robust feature extraction [143]. The recognition performances after introducing the Gabor filters with different parameters on the SI map are shown in Figure 6.9 and Figure 6.10.

Figure 6.9: R1RRs against the number of nasal curves selected for face recognition using the Gabor

filters with different variances. For example, in Gabor (2,4), “2” and “4” are the variances along x and y axis, respectively. The frequency is set to “16”. 360 captures of 20 subjects from the Bosphorus database are used.

Figure 6.10: R1RRs against the number of nasal curves selected for face recognition using the Gabor

The denoised SI map, G (x, y), can be obtained by 𝐺 𝑥, 𝑦 = _-{|, j|}∗ 𝑒 ~• €[( j lj)€‚( } l})€]_{∗ cos[2𝜋𝑓 𝑥}-_{+ 𝑦}-_{] (1)}

where Sx and Sy are the variances along x and y axes, respectively. f is the frequency of the

sinusoidal function. As can be seen from Figure 6.9, the R1RRs have been significantly

improved when the Gabor filters were applied to the denoised SI map by the median filter. The Gabor filters with different variances and frequencies are explored in Figure 6.9 and Figure 6.10, respectively, which demonstrate similar contribution to the recognition performances improvement.