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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




Trunk forward/backward


\(\Delta H^t\)

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


\(a^t(p^1_{2},p^1_{1},p^t_{2})\) \(\wedge\) \(a^t(p^1_{5},p^1_{1},p^t_{5})\)

Simultaneous angular displacements of both shoulders


\(\Delta x^t(p^t_{2/5},p^t_{1})\)

Shoulder displacement regarding joint 1 in \({}^BX\)


\(| \Delta d^t(p^t_{2},p^t_{5})|\)

Absolute changes in the observed chest length

Shoulder elevation



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



Spine angular displacement

 S2 and S3

\(| \Delta H^t|\)

Absolute changes in patient’s head size