Table
1 lists the features extracted in this study. We extracted some facial features from the acquired facial landmarks following the same method as described in [
7]. In addition, we defined and calculated the following features that form the facial expressions of a subject, including eyebrow movement and tilt, eye movement and its area, mouth area, size of the corners of the mouth, and blink rate. Eye movement is expressed by the amount of time variation in the coordinates of the center of the eye (iris). To consider changes in the time series over the entire dataset, we also used the variance for 3 s before and after each time step, that is, for a total of 6 s.
For the features of biometric information, we used the pulse rate obtained from a smartwatch. In particular, we used the variance of the pulse rate for 10 s before and after for a total of 20 s. The range used to compute the variation in pulse rates differs from that of facial features, because pulse rate does not change as rapidly, according to the experience of our preliminary experiment.
Table 1
Extracted features
Eyebrow tilt (right and left) | Distance between eyebrows and eyes (right and left) |
Area between eyebrows | Area of the eyes (right and left) |
Eye aspect ratio (left to right) | Blink rate |
Eye movement (right, left, horizontal and vertical) | |
Mouth area (inside/outside) | Mouth aspect ratio (inside/outside) |
Degree of raise for mouth corners | Angle of mouth |
Number of times the mouth is closed | |
In the following section, we describe the outline of the calculation for each feature shown in Table
1, where we denote the coordinates from 0 to 67 in Fig.
2 and
3 by points
P0 to
P67. To avoid confusion, we explicitly designate the figure name at the beginning of the exposition of features if we refer to the points in Fig.
3; otherwise, they are implicitly designated in Fig.
2.
Eyebrow tilt (left and right) The slope of the right eyebrow (left eyebrow) was calculated from points \(\{P17, P18, P19, P20, P21\}\) (\(\{P22, P23, P24, P25, P26\}\)) using the least squares method.
Distance between eyebrows and eyes(right and left) The distance between the eyebrows and the eyes is the average length of the eight line segments between them. For example, we created the set \(\{(P18, P36),\) \((P19, P37), (P20, P38), (P21, P39)\}\) of pairs of points on the right eyebrow and upper eyelid and then calculated the average length of these pairs as the distance between the right eyebrow and right eye. Similarly, we also calculated the distance between the left eyebrow and the left eye using the set \(\{(P22, P42),\) \((P23, P43), (P24, P44), (P25, P45)\}\) of points. To ensure that the features were unaffected by the actual size of the face image, they were re-scaled using normalization, that is, the distance is divided by the length L of the nasal bridge, which is the distance the four points \(\{P21, P22, P39, P42\}\) at the base of both eyebrows and the top of both eyes, where it is normalized by dividing by the square of L.
Area between eyebrows The area between the eyebrows is that of the rectangle formed by connecting the four points \(\{P21, P22, P39, P42\}\) at the base of the both eyebrows and the top of the both eyes, where it is normalized by dividing by the square of L.
Area of eyes (right and left) This is the area of the hexagon formed by connecting six points around the perimeter of the right eye (left eye). To compute this area, we use the set
\(\{P36, P37, P38, P39, P40, P41 \}\) of points for the right eye (
\(\{P42, P43, P44, P45, P46, P47 \}\) for the left eye). The formula for calculating the area of the right eye consisting of these coordinates is defined by:
$$\begin{aligned} S=\frac{1}{2}\left| \sum _{j=36}^{41}\left( x_{j}-x_{j+1}\right) \times \left( y_{j}+y_{j+1}\right) \right| \end{aligned}$$
(1)
Finally, the area is normalised by dividing by the square of
L.
Eye aspect ratio (left to right) To calculate the feature of eye aspect ratio, we refer to the points in Fig.
3. Let
\(L_v\) be the vertical length of the right (left) eye which is the length of the line segment connecting the top
P11 (
P39) and bottom
P17 (
P45) points on the right (left) eye, and
\(L_h\) the horizontal length of the right (left) eye which is the length of the line segment connecting the leftmost
P8 (
P36) and rightmost
P14 (
P42) points to the horizontal length of the right eye. The eye aspect ratio was then calculated using
\(L_v / L_h\).
Blink rate The number of times the eyes were closed during the 3 s immediately before classifying deception was measured. We considered that the eyes were closed if the area of the eyes was less than the first quartile in the entire data set of such areas.
Eye movement (right and left) To calculate the feature of eye movement, we refer to the points in Fig.
3. Horizontal eye movement is calculated as the distance from the inner corner
P14 (
P36) of the right (left) eye to the centre of iris of the eye, which is the average of points
P23 and
P27 (
P51 and
P55). Similarly, vertical eye movement is calculated as the distance from the top
P11 (
P39) of the right (left) eye to the centre of the iris of the eye which is the average of points
P23 and
P27 (
P51 and
P55).
Mouth area (inside) This is the area of the octagon formed by connecting the points \(\{P60, P61, P62, P63,\) \(P64, P65, P66, P67 \}\) on the inner perimeter of the mouth, where it is normalised by dividing by the square of L.
Mouth area (outside) This is the area of the dodecagon formed by connecting the points \(\{P48, P49,\) \(P50, P51, P52, P53, P54, P55, P56, P57, P58, P59\}\) on the outer perimeter of the mouth, which is normalized by dividing by the square of L.
Mouth aspect ratio (inside) Let \(L_v\) be the vertical length of the mouth, which is the length of the line segment connecting the top P62 and bottom P66 points on the inner circumference of the mouth, and \(L_h\) the horizontal length of the mouth, which is the length of the line segment connecting the leftmost P60 and rightmost P64 points of the mouse. Then, the inside mouth aspect ratio was calculated as \(L_v / L_h\).
Mouth aspect ratio (outside) Similar to the inside mouth aspect ratio, the outside mouth ratio can be calculated using the points \(\{P51, P57, P48, P54\}\).
Degree of raise for mouth corners This was calculated by subtracting the sum \(y_v\) of the y-coordinates of the uppermost P51 and lowermost P57 points of the mouth from the sum \(y_h\) of the y-coordinates of the rightmost P48 and the leftmost P54 points, where it was normalized by dividing by \(y_v\). If the resultant value was positive, then the angle of the mouth
increases.
Angle of mouth This was calculated by taking the average of the angles between the two line segments formed by connecting the set \(\{P48, P49, P59\}\) (\(\{P53, P54, P55\}\)) of points around the rightmost (leftmost) on the periphery of the mouth.
Number of times the mouth is closed This is the number of times the mouth was closed within 3 s immediately before classifying deception. We treated the mouth as closed if the inner area of the mouth was less than the first quartile in the entire dataset of such areas.
Gaze and head tilt For both features, we used the values obtained from the OpenFace library as is.
Pulse rate We obtained the value of the pulse rate per second from a smartwatch. These values were written to a CSV file, and we adjusted the number of values to that of the frames in the recorded videos (30 frames per second) when we created the dataset.