## 4 Methodologies and Results Analysis
### Secondary Phase  
After initial face detection is complete, an intelligent secondary stage algorithm was designed to eliminate false positives which capture half-hidden human faces, based on the brightest features of the face [26; 27; 33; 34; 35; 36; 37; 38]. For each positive sample, a dynamic threshold (range from 0.5 to 0.7) was set to capture the brightest part of the intruders partially or fully covered faces. After conducting numerous experiments, it has been identified that the proposed system does not require different dynamic threshold values for day-time or night-time intrusions. For detecting the retinal point and other bright facial features, a modified Gabor filter was used [38]. The Gabor filter is a powerful tool for heterogeneous image feature extraction. The Gabor filter can extract common features from diverse face images. Gabor filters make the use of Gabor wavelets which are very powerful in detecting and discriminating image feature extraction. Gabor filters also possess similar characteristics as those of a human visual system [19].  
The nearby power range of the picture was inspected at every retinal point by the vector of Gabor channels that constituted the responsive field connected with that point. Gabor channels are ideal as they minimize the joint picture and frequency plane spread. At the point when only a small number of frequency channels are utilized, the Gaussian range of the channels results in over-dense coverage near the starting point of the frequency plane, while the high-frequency regions are poorly covered. This is because each Gaussian weights high and also low frequencies in a symmetric way, while the disintegration is coarser at high frequencies. To counter this effect, a set of changed Gabor channels were employed, which are characterized as Gaussians in the log-polar frequency plane [20]. Figure 11a,b shows the modified Gabor filter in the Fourier domain and a 2D plot of cross-sectional coordinates. Thus, a channel tuned to angular frequency can be defined as follows  
\[\omega_{0}=\exp(\delta_{0})\] \[G(\omega,\delta)=\left(\frac{A\exp\Bigl{\{}(\delta-\delta_{0})^{2} \Bigr{\}}}{2\sigma_{\theta}{}^{2}}\right)\times\exp\left(\frac{-\Bigl{\{}( \varphi-\varphi_{0})^{2}\Bigr{\}}}{2\sigma_{\varphi}{}^{2}}\right) \tag{5}\]  
where \(A\) is a normalization constant and \((\delta,\phi)\) are polar frequency coordinates.  
Figure 10: (**a**) Face detection rate analysis of the proposed system with 10,000 face samples in an ordinary scenario where an intruder has not occluded their faces (**b**) Heat map representation of face detection rate analysis of the proposed system with 10,000 face samples in an ordinary scenario where an intruder has not occluded their face.  
Figure 12: Intermediate stage classifier samples where an intruder has worn plain/black glasses, partially covered face with some type of transparent, solid, plastic, leather material, including the following, tinted glasses, plain-rimmed glasses, face covered with a white cloth, facial overlap with plastic, and face covered in a transparent cloth (copyright permission for images obtained on 21 May 2017).  
Figure 13: **(a)** Face detection rate analysis of the proposed system with 10,000 face samples in scenarios where an intruder has partially covered their face with some type of transparent, solid, plastic, or leather material. **(b)** Heat map representation of face detection rate analysis of the proposed system with 10,000 face samples in scenarios where an intruder has partially covered their face with some type of transparent, solid, plastic, or leather materials.