Face Recognition independent of Gesture

In this section we will present the results of a face recognition experiment, using two small face databases, the Yale face database with 15 individuals and eight images per person, and the Manchester database with 30 individuals and 10 images per person. In both databases, the individuals show different facial expressions on all of their images (happy, sad, surprised, etc.). The goal was to recognize each subject independent of the expression. We proceeded as follows. First, a WN $({\bf\Psi}_i, {\bf v}_i)$ was optimized for each gallery face $I_i$ which resulted in a set of template WNs (see Section 3.1). We chose the faces with the ``normal'' expressions to be our gallery faces

The recognition of a probe face was then carried out by first finding optimal deformation values for the template WNs and by then computing the optimal wavelet coefficient vectors. This resulted optimal coefficient vectors ${\bf w}_i$ for each of the template WNs $({\bf\Psi}_i, {\bf v}_i)$ in the gallery. The technique of the previous Section 3.1 was employed to accomplish this. Fig. 6 illustrates what happens when for the same individual the optimal coefficient vectors are computed with a correct (left) and with a wrong template WN (right). Eq. (4) was used to compute the two reconstructions shown, using the optimal weight vectors.

Figure 6: These images show what happens when for the same individual the optimal coeff. vector is computed with a correct (left) and with a wrong (right) template WN.

  

Having computed an optimal coeff. vectors ${\bf w}_i$ with each of the template WNs $({\bf\Psi}_i, {\bf v}_i)$ in the gallery, they are compared each with the vector ${\bf v}_i$ of the template WNs, using $\Vert{\bf v}_i - {\bf w}_i\Vert _{{\bf\Psi}_i}$. The top match identifies the probe face.

Examples can be seen in figs. 7 and 8. Fig. 7 shows reconstructions of optimal coeff. vectors of subject 01 in the Yale database, showing different expressions, but computed with the template WN optimized for that subject, whereas fig. 8 shows the reconstructions of optimal coeff. vectors of subjects in the Yale database other than subject 01, but computed with the same WN as was used in fig. 7.

Figure 7: Various images of ``subject01'' (top) and their projections into the image subspace. The applied WN was optimized on the ``normal'' expression of ``subject01''.

  

  

 

  

  

 

Figure 8: Various images of subjects other than ``subject01'' (top) and their projections into the image subspace. The applied WN was optimized on the ``normal'' expression of ``subject 01''.

  

 

 

 

 

Figure: The table shows the distance measurements $1/\Vert\cdot\Vert _{{\bf \Psi}}$ of the images of the various subjects in the face database to the gallery WN $({\bf \Psi}_{01},{\bf v}_{01})$ of subject 01. Higher values indicate a smaller difference between the two compared wavelet coefficient vectors. One sees that the values in the left part of the tables (subject 01) indicate a much smaller difference than the values in the right part of the table (different subjects).

The visual impression of figs. 7 and 8 were reflected when we computed the distance between the vectors ${\bf w}_i$ and ${\bf v}_i$, $\left\Vert{\bf v}_i-{\bf w}_i\right\Vert _{{\bf\Psi}_i}$. Table 9 show a clear difference between the probe images that show different gestures of the original subject and the probe images that show different subjects.

All gallery WNs used $N=52$ wavelets. As mother wavelet, we chose the odd Gabor function. In case of the Yale Face Database $96\%$ of the top matches were the correct matches, while in case for the Manchester Database 93.3% of the top matches were correct. For all subjects in the Yale database, the ``surprised'' expression was the expression with the lowest similarity (see table 9). Without this expression, 97.8 % of the top matches were correct.

It should be mentioned that a direct comparison with other face recognition approaches is difficult, as the employed face databases are too small [Pentland, 2000].