Modelling behaviour over time

In order to try to capture the direct synchronization between the teacher as the signal emitter and student as the receiver of information, we formed a hypothesis that the people with higher synchronization will also have a higher attention level. In order to test this, we modelled the interaction between the two measures (teacher’s position and student’s head orientation) with a number of measurements.

7.2. Defining behaviour measures

pled 24 times a second (every frame). Given that we are sampling attention in intervals of approximately 10 minutes, we have to aggregate the 14400 (10mins * 60sec * 24frames) samples of students behaviour into a single value comparable with attention. Periods with less than 25% of maximal number of samples were rejected as invalid.

We already proposed our function for estimating gaze uncertainty from head pose in Section 6.5. The function models the expected limits of gaze direction based on the observed head pose. In order to test the correlation between the student’s head motion and teacher’s location in the classroom, we modelled the gaze behaviour with a number of functions. In the increasing order, each model adds additional assumptions about the gaze behaviour. All models are visualized in Figure 7.13.

Step function returns 1 if the teacher lies within the gaze limits of the student and otherwise 0.

The function disregards the behaviour of eyes completely, and shows just whether the teacher is visible to the student based on the head orientation. The values collected over 10 minutes are aggregated by calculating the mean, which effectively represent the percentage of time the teacher spent in the view-field of the student.

T-H Correlation assumes that there is a linear relationship between the head orientation

(centre of the view-field) and location of the teacher. We calculated the Pearson’s r coefficient of correlation between the teacher’s location and projection of student’s head orientation on the front wall. A higher correlation coefficient indicates that the head movement follows the teacher’s movement.

T-H Distancehas a similar assumption, that the students with higher attention will more

closely follow the movement of the professor. To measure this, at every time point we calcu- lated the distance between the teacher’s location and projection of student’s head orientation on the front wall. Mean distance over the period of 10 minutes as used as the final value.

Mean pose prediction (MPP). We have shown in Section 6.4.1 that the usage of gaze within the

limits is similar to a 2D Gaussian distribution positioned in the centre of the view-field. Here, we are using this assumption only for the horizontal plane and model probability of horizontal gaze direction with a normal distribution. The probability is centred on the projection of the centre of view-field and standard deviation is equal to half of the view-field width (view-field limits account for 95% of cumulative probability). The model shows how predictive is the student’s gaze of the teacher’s location. Probability values for teacher’s locations over the whole period are averaged into a single value.

Normalized mean pose prediction (nMPP). Formulating the probability based on the view-

field angle implicitly makes the probability scores for people sitting in the back lower (the distribution is “wider” and “flatter”). In order to cancel out this bias, we normalized the probability values with the peak-value of the probability when looking at the closer edge of the projection area. This put the output values in 0.0 - 1.0 range. Mean was used to aggregate values into a single measure.

f(x) d(x) f(x) f(x) Step function T-H Correlation T-H Distance Mean position prediction (MPP) Normalized mean position prediction (nMPP) 0 1 f(x) d 1 Aggregated value: mean Practical meaning:

Percentage of time the teacher spent in the student's view-field

Aggregated value:

Pearson's R between pairs of teacher's position and student's gaze projection

Practical meaning:

The correlation level between two values.

Aggregated value:

Mean distance between teacher's position and student's gaze projection

Practical meaning:

How closely does the student's head orientation follow the teacher position.

Aggregated value:

Mean value of teacher's position probability in the student's gaze distribution.

Practical meaning:

Student's gaze predictability of teacher's location.

Aggregated value:

Mean value of normalized teacher's position probability in the student's gaze

distribution.

Practical meaning:

Student's gaze predictability of teacher's location, with effects of distance neutralized.

Figure 7.13 – Visualizations of the gaze modelling methods used. Red dot illustrates the student, with blue arrow line showing the centre of view-field and green triangle depicting the field of view. Blue dot represents the teacher’s position in the front of the classroom. We illustrate

7.2. Defining behaviour measures

a) b)

Figure 7.14 – Shape of Gaussian probabilities modelling gaze probability for the student located in the centre of “projection zone” (x=0.5) sitting in different rows. As a reference, vertical lines represent the edges of “projection zone” (0.0 - 1.0 span in the normalized positional coordinates). Models are given for a) Classroom A and b) Classroom B.