# Eye gaze mapping

#### Alexander (Sasha) Pastukhov

#### 2025-10-09

Bidimensional regression can be used to transform the eye gaze data into a the screen coordinate system using a calibration sequence. For this, we use known target coordinates as independent variables. Please note that the example below assumes that participants fixate faithfully for most of the time and that recording artifacts, such as blinks, were already removed. This example will use the example dataset.

## Plotting raw data

    ggplot(data= EyegazeData, aes(x= x, y= y, color= target, fill= target)) +
      geom_point(data= EyegazeData %>% group_by(target, target_x, target_y) %>% summarise(.groups="drop"),
                 aes(x= target_x, y= target_y), shape= 21, size= 10, fill= 'white') +
      geom_point(alpha= 0.5, shape= 21, show.legend=FALSE) +
      ggtitle('Raw eye gaze')

## Using lm2 to transform the eye gaze

    lm2aff <- fit_transformation(target_x + target_y ~ x + y,  EyegazeData, transformation = 'affine')
    #>
    #> SAMPLING FOR MODEL 'tridim_transformation' NOW (CHAIN 1).
    #> Chain 1:
    #> Chain 1: Gradient evaluation took 0.000148 seconds
    #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.48 seconds.
    #> Chain 1: Adjust your expectations accordingly!
    #> Chain 1:
    #> Chain 1:
    #> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
    #> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
    #> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
    #> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
    #> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
    #> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
    #> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
    #> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
    #> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
    #> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
    #> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
    #> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
    #> Chain 1:
    #> Chain 1:  Elapsed Time: 3.643 seconds (Warm-up)
    #> Chain 1:                2.01 seconds (Sampling)
    #> Chain 1:                5.653 seconds (Total)
    #> Chain 1:
    adjusted_gaze <- predict(lm2aff, summary=TRUE, probs=NULL)
    colnames(adjusted_gaze) <- c('adjX', 'adjY')
    adjusted_gaze <- cbind(EyegazeData, adjusted_gaze)

    ggplot(data= adjusted_gaze, aes(x= adjX, y= adjY, color= target, fill= target)) +
      geom_point(data= adjusted_gaze %>% group_by(target, target_x, target_y) %>% summarise(.groups="drop"),
                 aes(x= target_x, y= target_y), shape= 21, size= 10, fill= 'white') +
      geom_point(alpha= 0.5, shape = 21, show.legend = FALSE) +
      xlab('x')+
      ylab('y')+
      ggtitle('Adjusted eye gaze')