*3.3. Experiments*

The first experiment compares the detection rates of the six face detectors, along with some of their combinations, by adjusting (1) the sensitivity values of *s*, where applicable, and (2) the detection procedure which either does or does not involved the addition of poses constructed by rotating images 20◦/−20◦.

The value for the sensitivity threshold *s* is shown in parentheses in Table 1. To reduce the number of false positives (FP), all output images having a distance of their centroid ≤30 pixels are merged as in [9].

As evident in the results in Table 2, the addition of rotated poses is of little value for the RF face detector, since this detector was originally trained on images that contained rotated faces. Thus, the addition of rotated poses increased the number of false positives.

**Table 2.** Performance of the six face detectors and the best performing ensembles (see the last seven rows) on the MERGED dataset (\* denotes the addition of the 20◦/−20◦ rotated images/poses in the dataset). As in [9], a face is considered detected in an image if the eye distance *ED* < 0.35. DR: detection rate, FL: fast localization, FP: false positives, NPD: normalized pixel difference, SFD: Single Scale-invariant Face Detector, SN: Split up sparse Network of Winnows, VJ: Viola–Jones.


Only the most interesting results are reported for the ensembles of classifiers. As can be seen in Table 2, high-performing approaches in an ensemble increase the detection rates while also generating more false negatives.

In Table 3, the performance of the face detectors presented in Table 2 are reported on the BioID dataset. As noted in [9], the addition of rotated poses is not needed when images are acquired in constrained environments. Although there is no significant difference in performance when adding the rotated poses, a difference is evident in the number of false positives that the rotated poses produce: they increase the false positives.


**Table 3.** Performance of the six face detectors and ensembles reported above on the BioID dataset (note: some values are taken from [9]).

In Table 3, we also discover that each of the face detectors identifies a different set of faces. This diversity in the individual face detectors is what enables the ensemble to improve the best standalone approaches. It is also noteworthy that the same classifier can perform differently on the MERGED versus BioID dataset. For instance, RF works well on BioID but not so well on MERGED; perhaps this is because it contains low-quality faces.

In Table 4, an experiment is reported that evaluated the seven filtering steps, as detailed in Section 2.3, along with their combinations. The first experiments showed that the best ensemble (considering the trade-off between performance and false positives) is FL + RF(−0.65) + SN(1)\* + SFD. For this reason, the filtering sets are tested only for this detector.

**Table 4.** Performance of FL + RF(−0.65) + SN(1)\* + SFD obtained combining different filtering steps on MERGED.


SIZE is clearly the best method for removing false positive candidates from a set of faces detected by FL + RF(−0.65) + SN(1)\* + SFD. The next best filter is EYE. However, because EYE is computationally expensive, it cannot be used in all applications. Although the other filters, when considered individually, are of less value because of their low computational costs, they are useful for reducing the number of false positives when applied sequentially. If real-time detection is not required (which is typically the case when tagging faces), then EYE filtering can be used to reduce the number of false positives produced by an ensemble without decreasing the number of true positives.

The results presented in the previous tables shows that the proposed approach performs better than FL and SPD, both of which are considered two of the best face detectors in the literature. It is true that the results reported here have been obtained on two rather small datasets; nonetheless, MERGED is highly realistic. Thus, it is reasonable to predict that the best ensemble proposed in this work would perform comparatively well in real-world conditions. The images contained in MERGE include those containing a single frontal face as well as those containing multiple faces acquired "in the wild".

Finally, in order to evaluate the computational cost of our approach, the processing time per 640 × 480 image on a i7-7700HQ PC system is reported in Table 5 for each detection method of "FL\* + RF(−0.65) + SN(1)\* + SFD" and each additional filter (on a candidate region of size 78 × 78 pixels). All the tests are performed without parallelizing the code. However, it should be noted that the filters and face detectors can run in parallel, resulting in a significant reduction of computation time.


**Table 5.** Average processing time per image in ms.
