# Module eyekit.measure

Functions for calculating common reading measures, such as gaze duration or initial landing position.

## Functions

 def number_of_fixations(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the number of fixations on that interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def initial_fixation_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the duration of the initial fixation on that interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def first_of_many_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the duration of the initial fixation on that interest area, but only if there was more than one fixation on the interest area (otherwise return None). This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def total_fixation_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the sum duration of all fixations on that interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def gaze_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the gaze duration on that interest area. Gaze duration is the sum duration of all fixations inside an interest area until the area is exited for the first time. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def go_past_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the go-past time on that interest area. Go-past time is the sum duration of all fixations from when the interest area is first entered until when it is first exited to the right, including any regressions to the left that occur during that time period (and vice versa in the case of right-to-left text). This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def second_pass_duration(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the second pass duration on that interest area. Second pass duration is the sum duration of all fixations inside an interest area during the second pass over that interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def initial_landing_position(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the initial landing position (expressed in character positions) on that interest area. Counting is from 1. If the interest area represents right-to-left text, the first character is the rightmost one. Returns None if no fixation landed on the interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def initial_landing_distance(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the initial landing distance on that interest area. The initial landing distance is the pixel distance between the first fixation to land in an interest area and the left edge of that interest area (or, in the case of right-to-left text, the right edge). Technically, the distance is measured from the text onset without including any padding. Returns None if no fixation landed on the interest area. This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def number_of_regressions_in(interest_area, fixation_sequence) 

Given an interest area and fixation sequence, return the number of regressions back to that interest area after the interest area was read for the first time. In other words, find the first fixation to exit the interest area and then count how many times the reader returns to the interest area from the right (or from the left in the case of right-to-left text). This function may also be applied to a collection of interest areas, in which case a dictionary of results is returned.

 def duration_mass(text_block, fixation_sequence, ngram_width=1, gamma=30) 

Given a TextBlock and FixationSequence, distribute the durations of the fixations probabilistically across the TextBlock. Specifically, the duration of fixation f is distributed over all characters C in its line according to the probability that the reader is "seeing" each character (see p_characters_fixation()), and this is summed over all fixations:

Returns a 2D Numpy array, the sum of which is equal to the total duration of all fixations. This can be passed to Image.draw_heatmap() for visualization. Duration mass reveals the parts of the text that received the most attention. Optionally, this can be performed over higher-level ngrams by setting ngram_width > 1.

 def p_characters_fixation(text_block, fixation, ngram_width=1, gamma=30) 

Given a TextBlock and Fixation, calculate the probability that the reader is "seeing" each character in the text. We assume that the closer a character is to the fixation point, the greater the probability that the participant is "seeing" (i.e., processing) that character. Specifically, for a given fixation f, we compute a Gaussian distribution over all characters in the line according to:

where γ (gamma) is a free parameter controlling the rate at which probability decays with the Euclidean distance (ED) between the position of fixation f and the position of character c.

Returns a 2D Numpy array representing a probability distribution over all characters, with all its mass confined to the line that the fixation occurred inside, and with greater mass closer to fixation points. This array can be passed to Image.draw_heatmap() for visualization. Optionally, this calculation can be performed over higher-level ngrams by setting ngram_width > 1.