Pose Estimation

In this section we present the results of two face-pose estimation experiments that were carried out to verify the ``optimal filter bank'' principle of the WNs.

For both experiments we connected a doll's head to a robot arm and let the robot move the doll's head in front of a fixed camera. With this the correct pose was always known. In the first experiment we tracked the doll's head with a color blob tracker and distributed $4\times4$ sets of 4 complex Gabor filters with the different orientations of 0, $\frac{\pi}{4}$, $\frac{\pi}{2}$ and $\frac{3}{4}\pi$ over the tracked inner face region. The resulting $128$ complex projections of these filters were then fed into an artificial neural LLM network (ANN) [Bruske and Sommer, 1995,Ritter et al., 1991]. This was done so for training as well for testing. A precise description of this experiment can be found in [Bruske et al., 1998]. The mean pan/tilt error that we reached was $\approx 0.58^{\circ}$, computed as $\sqrt{(\delta p)^2 + (\delta t)^2}$.

It is reasonable to assume that the choice of better Gabor filters would result an even lower mean pan/tilt error. In our second experiment, we therefore optimized a template WN for the doll's face with $N=52$ wavelets (see fig. 10). As mother wavelet, the odd Gabor function was used, fig. 10 shows the optimized WN.

Figure 10: The left image shows the original doll face image $I$, the right image shows its reconstruction $\hat{I}_{52}$ using formula (4) with an optimized WN ${\bf \Psi}$ of just $N=52$ odd Gabor wavelets, distributed over the inner face region.

  

As in the first experiment, the doll's head was connected to a robot arm, so that the pan/tilt ground truth was known. During the training of the ANN and testing, the doll's head was first tracked using our face tracking method of Section 3.1 and then the optimal wavelet coefficient vectors ${\bf w}$ were computed. Fig. 11 shows example images of the tracked doll's head.

Figure 11: The images show different orientations of the doll's head. The head is connected to a robot arm so that the ground truth is known. The white square indicates the detected position, scale and orientation of the WN.

  

  

  

The optimal coeff. vectors ${\bf w}$ were then fed into the ANN. The employed ANN was of the same type in both experiments. In this second experiment the dimensionality of the feature vectors was smaller: instead of the 128 complex values coefficients of the first experiment, we used in the second experiment only 52 real valued coefficients. We used 400 training images in both experiments. With this, we reached a mean pan/tilt error of $\approx 0.23 ^{\circ}$ with a processing speed of $\approx 10$ fps on a 450 MHz Linux Pentium. The experiments have been repeated several times, and the variations of the estimated mean pan/tilt error over several experiments were small ( $0.02^{\circ}$ for the WN experiment). A more detailed description of our experimental results can be found in [Krüger et al., 2000].