Next in this series on physical and behavioral biometric technologies, Ravi Das continues on the topic of facial recognition technology. In the previous article, the author described how the facial recognition process is performed. Here, he delves into the various facial recognition models and techniques—and the scientific and mathematical factors that support them.

The entire process of facial recognition starts with the location of the actual image of a face within a set frame. The presence of the actual face can be sensed or detected from various cues or triggers, such as skin color, any kind of head rotation, the presence of the face or even head shape, as well as the detection and presence of both eyes in the face.

Some of the challenges involved in locating the face in the frame include identifying the differentiation between the skin tone and the background color, and the various shapes within the face (depending of course on the angle in which the raw image is presented to the facial recognition system). When the facial recognition system is used in a covert fashion, such as in a very large crowd, it can be challenging to differentiate many images of faces captured within a single frame.

The models and techniques of Facial Recognition

To help alleviate the obstacles of facial recognition, and to provide a solution in which a single facial image can be detected in a single frame, various techniques have been developed and applied to facial recognition. These techniques fall under two categories: appearance based and model based.

  • With appearance based facial recognition techniques, a face can be represented in several object views, and it is based on one image only; 3-Dimensional models are never utilized. The specific methodologies here include Principal Component Analysis (PCA), and Linear Discriminant Analysis (LDA).
  • Model based facial recognition techniques construct and create a 3-Dimensional model of the human face, and from that point onwards, the facial variations can be captured by computer using a methodology known as Elastic Bunch Graph Mapping (EBCM).

All of the techniques that fall under these two categories will now be discussed in greater detail.

Principal Component Analysis (PCA): This linear based technique dates all the way back to 1988, when it was first used for facial recognition. This technique primarily uses what is known as “Eigenfaces.” Simply put, Eigenfaces are 2-Dimensional spectral facial images, which are composed of grayscale features.

Hundreds of Eigenfaces can be stored in the database of a facial recognition system. When facial images are collected by the system, this library of Eigenfaces is placed over the raw images and are then superimposed over one another. At this point, the level of variance between the Eigenfaces and the raw images are computed, averaged together, and different weights are assigned.

The end result is a 1-Dimensional image of the face, which is then processed by the facial recognition system. In terms of mathematics, PCA is merely a linear transformation in which the raw facial images are converted into a geometrical coordinate system. Imagine if you will, a quadrant-based system. With the PCA technique, the data set with the greatest variance lies upon the first coordinate of the quadrant system (this is also termed the first Principal Component Analysis). Next, the data set with the second largest variance falls onto the second coordinate, and so on, until the 1-Dimensional face is created.

The biggest disadvantages with this technique are that it requires a full-frontal image, and as a result, a full image of the face is required. Thus, any changes in any facial feature requires a full recalculation of the entire Eigenface process. However, a refined approach has been developed, thus greatly reducing the calculating and processing time required.

Linear Discriminant Analysis (LDA): In this linear based approach, the goal is to project the face onto a vector space, with the primary objective being to speed up the verification and identification processes by cutting down drastically on the total number of facial features which need to be matched.

The mathematics behind LDA is to calculate the variations which occur between a single raw data point from a single raw data record. Based on these calculations, the linear relationships are then extrapolated and formulated. One of the advantages of the LDA technique is that it can actually take into account the lighting differences and the various types of facial expressions which can occur, but still, a full-face image is required.

After the linear relationship is drawn from the variance calculations, the pixel values are captured and statistically plotted. This results in a computed raw image, which is simply a linear relationship of the various pixel values. This raw image is called a Fisher Face. Despite its advantages, a major drawback of the LDA technique is that it requires a large database.

Elastic Bunch Graph Matching (EBGM): This model based technique looks at the nonlinear mathematical relationships of the face, which includes such factors as lighting variations, and the differences in facial poses and expressions. This technique, known as Gabor Wavelet Mathematics, is similar to the technique used in iris recognition.

With the EBGM technique, a facial map is created. The facial image on the map is simply a sequencing of graphs, with various nodes located at the landmark features of the face, which include the eyes, edges of the lips, tip of the nose, etc. These edge features become 2-Dimensional distance vectors, and during the identification and verification processes, various Gabor mathematical filters are used to measure and calculate the variance of each node on the facial image.

Next, Gabor mathematical wavelets are used to capture up to five spatial frequencies, and up to eight different facial orientations. Although the EBGM technique does not require a full facial image, the main drawback of this technique is that the landmarks of the facial map must be marked extremely accurately, with great precision.

Up Next:  This and previous articles have provided an in-depth understanding of how facial recognition technology works, as well as the various models involved. The next article in this series will summarize the advantages and disadvantages of facial recognition. This will help you evaluate the effectiveness of each approach.

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Ravi Das is a Cybersecurity Consultant and Business Development Specialist. He also does Cybersecurity Consulting through his private practice, RaviDas Tech, Inc. He also possesses the Certified in Cybersecurity (CC) cert from the ISC2.

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