. 2019 Aug 8;19(16):3465. doi: 10.3390/s19163465

Table 1.

Eye activity metrics adapted from [3] includes Equations (1)–(13).

Parameter	Description	Derived Metrics	Equation	Equation Number
Fixation	The state of a gaze that is focused (fixated) on an object.	Fixation (duration, frequency, count)	$f_{n} : \sqrt{{(x_{m a x} - x_{m i n})}^{2} + {(y_{m a x} - y_{m i n})}^{2}} < D_{m a x}$ $\forall t \in [t_{0}, t_{f n}]$	(1)
Fixation	The state of a gaze that is focused (fixated) on an object.	Time to first fixation	$T_{F i r s t F i x a t i o n} = t (f_{1}) - t_{0}$	(2)
Saccade	Small, rapid, involuntary eye movements between fixations, usually lasting 30 to 80 ms.	Saccadic length/amplitude, frequency	$s_{n} : v (t_{s_{n}} \in [t_{i}, t_{j}]) \geq 30 ° / s$ with $t_{i} + 30 m s \leq t_{j} \leq t_{i} + 80 m s$ and $v = \sqrt{{(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2}}$	(3)
		Saccade velocity (mean/peak)	${\bar{v}}_{s_{n}} = v (t_{s_{n}})$ $v_{m a x, s_{n}} = \max (v (t_{s_{n}}))$	(4)
		Explore/exploit ratio (R_EE)	$R_{EE} = \frac{s a c c a d e c o u n t + f i x a t i o n c o u n t}{l o n g f i x a t i o n c o u n t}$	(5)
Dwell	Eye movements comprising a series of fixation-saccade-fixation movements, usually with reference to (or within) a given area of interest.	Dwell count	$d_{n} : (x, y) \in ([x_{M i n}, x_{M a x}], [y_{M i n}, y_{M a x}])$ $\forall t \in [t_{i}, t_{j}] w i t h t_{j} \geq t_{i} + 30 m s$	(6)
Dwell		Dispersion [17]	$D = \sqrt{{(x_{m a x} - x_{m i n})}^{2} + {(y_{m a x} - y_{m i n})}^{2}}$	(7)
Transition	The change of dwell from one area of interest to another and is usually represented in the form of a matrix.	One-/two-way transition probability Transition frequency	e.g., $T M_{O W} = \begin{matrix} R O I & \begin{matrix} 1 & 2 & 3 \end{matrix} \\ \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} & [\begin{matrix} - & p_{1, 2} & p_{1, 3} \\ p_{2, 1} & - & p_{2, 3} \\ p_{3, 1} & p_{3, 2} & - \end{matrix}] \end{matrix}$	(8)
Scan path	The series of eye movements in accomplishing a specified task. A scan path can include elements of fixations, saccades, dwells and transitions.	Visual entropy [10]	$H = - \sum_{i = 1}^{n} p (X_{i}) \sum_{j = 1}^{m} p (Y_{i j} \| X_{i}) \log_{2} p (Y_{i j} \| X_{i})$	(9)
Scan path		Nearest Neighbour Index (NNI) [12]	$NNI = \frac{{\bar{r}}_{A}}{{\bar{r}}_{E}}$ , where ${\bar{r}}_{A} = \frac{\sum^{} r}{N}$ ${\bar{r}}_{E} = \frac{K_{D}}{2 \sqrt{N / A}}$	(10)
Pupillo-metry	Measures of pupil size and reactivity.	Pupil dilation spectral power	$P_{d i l} = \int_{2 H z}^{6 H z} r (λ) d λ$	(11)
Blink	Measures of partial or full eye closure.	Blink rate (BLR)	$B L R = \frac{n_{b l i n k s}}{t_{i + n_{b l i n k s}} - t_{i}} \times 60$	(12)
Blink	Measures of partial or full eye closure.	Percentage closure [18,19,20,21]	$%_{c l o s u r e} = \frac{\sum^{} t_{c l o s u r e, i}}{t_{T o t a l}}$	(13)