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Table 4 Kinematic variables

From: A low-cost virtual coach for 2D video-based compensation assessment of upper extremity rehabilitation exercises

Scenario Variable Description
Trunk forward/backward
 S1 \(\Delta H^t\) Observed changes in patient’s head position, detect through patient’s head area, \(H^t\) (\(t>1\))
 S2 and S3 \(a^t(p_8^1,p_1^1,p_1^t)\) \(\wedge\) \(\Delta x^t(p_1^t,p_1^1)\) Spine angular and linear displacements
Trunk rotation
 S1 \(a^t(p^1_{2},p^1_{1},p^t_{2})\) \(\wedge\) \(a^t(p^1_{5},p^1_{1},p^t_{5})\) Simultaneous angular displacements of both shoulders
 S2 \(\Delta x^t(p^t_{2/5},p^t_{1})\) Shoulder displacement regarding joint 1 in \({}^BX\)
 S3 \(| \Delta d^t(p^t_{2},p^t_{5})|\) Absolute changes in the observed chest length
Shoulder elevation
 S1 \(a^t(p^1_{2/5},p^1_{1},p^t_{2/5})\) Shoulder elevation angle
 S2 and S3 \(\Delta y^t(p^t_{2/5},p^t_{1})\) Shoulder displacement regarding joint 1 in Y
Trunk tilt
 S1 \(a^t(p^1_{8},p^1_{1},p^t_{1})\) Spine angular displacement
 S2 and S3 \(| \Delta H^t|\) Absolute changes in patient’s head size