*6.4. Computation Time*

With a training set of 541 images, the running time of the algorithm was 11 s. We now show how to improve the computation time by reducing the image size. One drawback of this method is that the performance of the algorithm can be affected by reducing the size of the correlation plane. The selection of one over two pixels was first considered, then an increase by considering 2 out of 3 was considered, then 3 out of 4 and so on, until 10 out of 11. When selecting 1 out of 2 pixels, it takes almost 0.5 s to perform the algorithm with a MSE of 4.81%. For 4 out of 5 pixels, the MSE is close to 1.5% and the running time is less than 6 s (Figure 8). In Figure 8, the top plot shows the MSE according to the number of pixels used and the bottom plot shows the corresponding running time. As the number of pixels is increased, the MSE decreases due to the loss of information in making the correlation planes. But the computation time increases with the number of pixels used. A good compromise is to use 4 out of 5 pixels. This yields to a running time less than 6 s

**Figure 8.** MSE and corresponding running times (in seconds) obtained by reducing the image size in the set of images.

#### *6.5. Simulations for a Second Series of Faces from the PHPID Database*

Consider a second series of faces from the PHPID database. These simulations differ from the previous database, since the clothes and haircuts are different and the persons can wear glasses. Here, there are 93 images of person 0 with different poses. For the training set, we use the 541 images coming from the series 1 so that we have 39 images of person 0. We find an error rate of 12.9%. For 93 images, only 12 were not detected. To illustrate the performance of our procedure, Figure 9 shows 4 images and their corresponding correlation planes. The 4 images have been well recognized by our method, where the PCE method gives an error. The first column represents the 4 images and the second column represents the corresponding correlation planes with the image of reference of person 0.

**Figure 9.** Images and correlation planes well recognized by our method (KSR) and badly recognized by PCE.

In order to compare our results with those obtained using the PCE criterion, we provide a comparison of the ROC curves in Figure 10. We conclude that our method is significantly better than the method using the PCE criterion. To make this plot, we used 93 images of two persons from the second series of faces from the PHPID database as the testing set. The training set comprised 541 images (from which, there were 39 images of person 0) from the first series of faces from the PHPID database.

**Figure 10.** Same as Figure 7 for the second series of faces from the PHPID database.
