5. A simple feature vector from face

A simple feature vector is formed for drunk person identification by simply taking the pixel values of 20 different points on the face of each person (Figure 1). Therefore, each face image corresponds to a 20-dimensional feature vector:

xi ¼ ½181 169 203 166 217 175 171 189 169 206 152 144 243 165 225 147 247 149 247 127� <sup>t</sup> (1)

a radiometric dynamic range which adjusts automatically to temperature range. This wavelength region corresponds to the maximum of the Wien curve for blackbody emission with temperature at 300K. This is exactly the behavior in emitting electromagnetic radiation from the human skin [22]. In our experiment, 41 persons participated among them 10 females. A quantity of half liter of wine which corresponds to 62.4 mL of alcohol was consumed by each subject, in an hour time duration. A first frame sequence of 50 frames was obtained for each person before alcohol consumption. Another sequence of the same number of frames was acquired half an hour after consuming the last glass of wine. The frame rate acquisition was

The resolution of the infrared images is 128 160 pixels. The camera was quite close to the face of the person so that the thermal image contains the whole face. The experimental procedure requires the availability of the thermal images of an intoxicated person as well as the thermal images of the corresponding sober person so that comparisons can be carried out. The persons that participated in the experiment were alert about the strict requirements of the procedure. Researchers working close to our research group and being sensitized on the experimental requirements took part in the experiment. All of them were healthy and willing to release their personal data to the public (http://www.physics.upatras.gr/sober/). The created database contained all relevant information for the participants (age, weight, sex, etc.). We considered the person who consumed half a liter of wine as drunk or intoxicated. In the experimental

Three glasses of wine are enough to bring a person in the intoxication situation which corresponds in exceeding 0.2 mg/L of exhaled air [15]. However, with this quantity of wine, other participants were brought in the limit of intoxication while others were deeply intoxicated. Measurements carried out by the police showed off these differences in persons' intoxication (breathalyzer 0.22–0.9 mg/L). The maximum concentration of alcohol in the exhaled air was reached half an hour after the consumption of the last glass of wine. This concentration was found at 0.22 mg/L for the heavy persons that used to drink alcohol and raised to 0.9 mg/L for the light persons that used not to drunk alcohol. Gradually, breathalyzer indication decreases.

Finally, it is worth mentioning that all participants were healthy and calm when the experiment started, and had not undergone any kind of body exercise. All participants were present at the room of experiment half an hour before its initiation. Actually, the purpose of the experiment was to reveal temperature changes caused only by alcohol consumption. No other

A simple feature vector is formed for drunk person identification by simply taking the pixel values of 20 different points on the face of each person (Figure 1). Therefore, each face image

set to 10 frames/sec.

150 Human-Robot Interaction - Theory and Application

procedure, no blood tests were contacted.

abnormality is considered.

Females were more sensitive to alcohol than the males.

5. A simple feature vector from face

corresponds to a 20-dimensional feature vector:

which corresponds to a point in the 20-dimensional space; since in each single acquisition, 50 images are grabbed and this information corresponds to a cluster of 50 points in the 20 dimensional space.

It is important to find out if the cluster which corresponds to the same person moves in the feature space as the person consumes alcohol [24]. Simultaneously, we have to examine if the cluster of each person moves toward the same direction with alcohol consumption. If the direction of movement due to alcohol consumption is different for different persons, then we would have many directions in the 20-dimensional space, toward which the clusters of the drunk persons are moving. In this case, it would be difficult to demonstrate the space in a simpler way (preferably in two dimensions).

In this paragraph, it is analytically explained that the final problem is of two dimensions since only two of the eigenvalues obtained by means of the generalized eigenvalues problem are of significant value. In these two dimensions, it is evident that the clusters are moving toward the same direction with alcohol consumption (Figure 2).

In our case, the feature space dimensionality was examined by the statistics of the clusters of eight persons. Consequently, there exist eight clusters in the feature space for the sober persons and the corresponding eight clusters for the drunk persons projecting onto this 2-D space, the suitable directions for maximum separability, has to be found.

This maximum separability in a reduced dimensionality space is achieved by a linear transformation W. The two most important directions wi of W are used for projection. This linear transformation is:

$$y\_i = w^t x\_i \tag{2}$$

Figure 1. Twenty points were obtained on each face to monitor temperature changes with the consumption of alcohol.

Figure 2. The 16 clusters of 8 persons in the 2-D space formed by the two most important directions (correspond to the first 2 largest eigenvalues). We call hereafter this space, the "drunk space".

An important criterion function that can be used for the separation of the clusters is given by

$$J = \frac{\mathbf{S}\_B}{\mathbf{S}\_W} \tag{3}$$

ð Þ¼ SB <sup>w</sup><sup>t</sup>

J wð Þ¼ <sup>w</sup><sup>t</sup>

The maximization of the function J(w) results in vectors w obtained from the solution of the

The obtained matrix W contains the eigenvectors wi which show the directions in the transformed feature space on which the original features xi are projected. From this solution, the eigenvalues which correspond to wi are also obtained. Each eigenvalue describes the amount of information that the corresponding eigenvector contains regarding each cluster separability capabilities. Actually, the Fisher Linear Discriminant (FLD) method corresponds to the solution of (10). Obviously, in this procedure, the matrices SB and SW operate with

The generalized eigenvalue problem was solved, as we mentioned previously, for 8 persons (males) of the same weight. A total of 16 clusters are available in the 20-D feature space, that is, two clusters per person (sober and drunk). The sum of these two largest eigenvalues over the sum of all eigenvalues gives the quality of cluster separability in the reduced (2D) feature space. In this experiment, this ratio was found equal to 70%. The resulting two-dimensional feature space is demonstrated in Figure 2, along with the 16 clusters. Furthermore, in Figure 2, the direction of movement of the cluster of each person is exhibited. According to Figure 2, the new 2-D feature space is separated into two regions corresponding to sober and drunk persons, respectively. Consequently, a person can be easily classified as sober or drunk depending on the position of its cluster in this new reduced space. This space is called, hereafter, the

The thermal differences between various locations on the face are examined in this section [2]. The purpose of this approach is to examine specific locations on the face and find out if the temperature difference between these regions changes with alcohol consumption. Thus we are not interested for the temperature of the eye but if its temperature changes with respect to another location of the face, for example, the lips. In order to apply this procedure, the image of the face of each person was partitioned into a matrix of 8 � 5 squared regions of 10 � 10 pixels each. The position of the regions was exactly the same for a specific person (sober and drunk). The temperature difference of all possible pairs of squared regions is monitored as the person consumes alcohol. A total of 40 values were calculated on the face of a specific person who

6. Face temperature differences after alcohol consumption

correspond to the squared regions for a specific acquisition.

SBw wt

Therefore, the function J in the transformed space is given by

generalized eigenvalue problem:

opposite effect.

"drunk space".

SBw (8)

Intoxication Identification Using Thermal Imaging http://dx.doi.org/10.5772/intechopen.72128 153

SWw (9)

SBWi ¼ λiSW Wi (10)

The clusters are moving apart as J increases. The matrices SW and SB are called within-scatter and between-scatter matrices, respectively. Eventually, SW must be small and SB must be large. The cumulative dispersion of all separate clusters (cluster scatter) can be estimated by the corresponding SW matrix, which is evaluated by summing up all individual cluster-scatter matrices Si as follows

$$\mathcal{S}\_w = \mathcal{S}\_1 + \mathcal{S}\_2 + \dots \ \ \ \ . \ \ . \ + \ \mathcal{S}\_8 \tag{4}$$

where

$$S\_i = \sum \mathbf{x}\_i \ast \mathbf{x}\_i^t \tag{5}$$

In the transformed space, the within-scatter matrix (SW) is given by

$$\mathbf{w}(S\_W) = \mathbf{w}^\dagger S\_W \mathbf{w} \tag{6}$$

The between-scatter matrix SB reveals how much the centers of the clusters are separated. The evaluation of the between-scatter matrix SB is realized as follows

$$S\_{\mathcal{B}} = \sum m\_{i} \* m\_{i\prime}^{t} \qquad i = 1, 2, \ldots 8 \tag{7}$$

where mi corresponds to each cluster center. In the transformed space, the between-scatter matrix (SB) will be given by

Intoxication Identification Using Thermal Imaging http://dx.doi.org/10.5772/intechopen.72128 153

$$\mathbf{w}(S\_B) = \mathbf{w}^t S\_B \mathbf{w} \tag{8}$$

Therefore, the function J in the transformed space is given by

An important criterion function that can be used for the separation of the clusters is given by

Figure 2. The 16 clusters of 8 persons in the 2-D space formed by the two most important directions (correspond to the

<sup>J</sup> <sup>¼</sup> SB SW

The clusters are moving apart as J increases. The matrices SW and SB are called within-scatter and between-scatter matrices, respectively. Eventually, SW must be small and SB must be large. The cumulative dispersion of all separate clusters (cluster scatter) can be estimated by the corresponding SW matrix, which is evaluated by summing up all individual cluster-scatter

Si <sup>¼</sup> <sup>X</sup>xi∗xt

ð Þ¼ SW <sup>w</sup><sup>t</sup>

The between-scatter matrix SB reveals how much the centers of the clusters are separated. The

where mi corresponds to each cluster center. In the transformed space, the between-scatter

In the transformed space, the within-scatter matrix (SW) is given by

first 2 largest eigenvalues). We call hereafter this space, the "drunk space".

152 Human-Robot Interaction - Theory and Application

evaluation of the between-scatter matrix SB is realized as follows

SB <sup>¼</sup> <sup>X</sup>mi∗m<sup>t</sup>

Sw ¼ S<sup>1</sup> þ S<sup>2</sup> þ ::: þ S<sup>8</sup> (4)

<sup>i</sup> (5)

SW w (6)

<sup>i</sup> , i ¼ 1, 2, …8 (7)

matrices Si as follows

matrix (SB) will be given by

where

(3)

$$J(w) = \frac{w^t S\_B w}{w^t S\_W w} \tag{9}$$

The maximization of the function J(w) results in vectors w obtained from the solution of the generalized eigenvalue problem:

$$
\Delta S\_B \mathbf{W}\_i = \lambda\_i \mathbf{S}\_W \mathbf{W}\_i \tag{10}
$$

The obtained matrix W contains the eigenvectors wi which show the directions in the transformed feature space on which the original features xi are projected. From this solution, the eigenvalues which correspond to wi are also obtained. Each eigenvalue describes the amount of information that the corresponding eigenvector contains regarding each cluster separability capabilities. Actually, the Fisher Linear Discriminant (FLD) method corresponds to the solution of (10). Obviously, in this procedure, the matrices SB and SW operate with opposite effect.

The generalized eigenvalue problem was solved, as we mentioned previously, for 8 persons (males) of the same weight. A total of 16 clusters are available in the 20-D feature space, that is, two clusters per person (sober and drunk). The sum of these two largest eigenvalues over the sum of all eigenvalues gives the quality of cluster separability in the reduced (2D) feature space. In this experiment, this ratio was found equal to 70%. The resulting two-dimensional feature space is demonstrated in Figure 2, along with the 16 clusters. Furthermore, in Figure 2, the direction of movement of the cluster of each person is exhibited. According to Figure 2, the new 2-D feature space is separated into two regions corresponding to sober and drunk persons, respectively. Consequently, a person can be easily classified as sober or drunk depending on the position of its cluster in this new reduced space. This space is called, hereafter, the "drunk space".
