Fig. 2: Functional and algorithm flow charts for joint angle measurements and the performance of the vision system.

a Functional flow chart of the system, showing initial data collection for magnetometer response calibration and routine use with calibrated magnetometer responses. During calibration, ground truth angles (θ) are collected through the vision system. Orientation vectors (u, ν, and w) of two markers are used to estimate angles from (b) flexion/extension and (c) radial/ulnar motions. Subscripts, d, p, f, and r, denote distal, proximal, flexion/extension, and radial/ulnar, respectively. Symbols θ and ϕ represent joint angles and magnet angles, respectively. d A captured image of the screen of a smart device while marker tracking is active. The accuracy and range of measured angles with respect to four different camera angles are displayed in (e) and (f). Boxes in (f) simply denote the range (i.e., the minimum and maximum values) for each camera angle, whereas in (e), they represent the interquartile range (IQR) from the 25th to the 75th percentiles. Whiskers extend to 1.5 times the IQR. The midline within each box indicates the median of the dataset. g Algorithm flow chart for the calibration, detailing the use of extrapolation to address the limited range of measured angles resulting from camera angles. An \({{{{\boldsymbol{R}}}}}^{{{{\boldsymbol{2}}}}}\) value obtained from curve fitting indicates the goodness of fit and serves as a criterion for either passing or failing the calibration step.