Modeling Touch Point Distribution with Rotational Dual Gaussian Model

Abstract

Touch point distribution models are important tools for designing touchscreen interfaces. In this paper, we investigate how the finger movement direction affects the touch point distribution, and how to account for it in modeling. We propose the Rotational Dual Gaussian model, a refinement and generalization of the Dual Gaussian model, to account for the finger movement direction in predicting touch point distribution. In this model, the major axis of the prediction ellipse of the touch point distribution is along the finger movement direction, and the minor axis is perpendicular to the finger movement direction. We also propose using projected target width and height, in lieu of nominal target width and height to model touch point distribution. Evaluation on three empirical datasets shows that the new model reflects the observation that the touch point distribution is elongated along the finger movement direction, and outperforms the original Dual Gaussian Model in all prediction tests. Compared with the original Dual Gaussian model, the Rotational Dual Gaussian model reduces the RMSE of touch error rate prediction from 8.49% to 4.95%, and more accurately predicts the touch point distribution in target acquisition. Using the Rotational Dual Gaussian model can also improve the soft keyboard decoding accuracy on smartwatches.

Test-retest Reliability on Movement Times and Error Rates in Target Pointing

“…A negative 𝜌 indicates that the spread of endpoints had an ellipse diagonal along the top-right to bottom-left direction on the screen. This is obviously because we tested only such angles (0 • ≤ 𝜃 ≤ 90 • ) and is consistent with Ma et al 's report on rectangular-target pointing with known movement angles [27].…”

“…Ma et al proposed the Rotational Dual Gaussian Model to predict touch-point distributions [27]. They strictly controlled the movement angle in each trial and proposed a target-size adjustment method based on the movement angle, called projected target width and height.…”

“…shown that integrating the movement angle significantly outperformed the angle-ignored model [27], we focus only on the prediction accuracy when the movement angle is unknown, i.e., various angles appear unbiasedly and the data are analyzed after merging.…”