Smoothness of Motion

Bitbox computes common metrics of smoothness, including averge jerk and log dimensionless jerk.

Average jerk: Mean magnitude of each object’s jerk (third-order derivative of position), summarizing average abruptness of motion.

Log dimensionless jerk (LDJ): Negative natural log of the time-normalized, amplitude-normalized squared-acceleration integral, giving a dimensionless/unitless smoothness index.

$\mathrm{LDJ} = -\ln\left(\frac{T^{3}}{v_{\text{peak}}^{2}}\displaystyle\int_{0}^{T}\lVert \mathbf{a}(t) \rVert^{2},dt\right)$

Similar to kinematics measures, you can compute these variables for face bounding boxes, head pose, facial landmarks, or body joints (coming soon). When using landmarks, variables are calculated for each landmark separately.

from bitbox.biomechanics import motion_smoothness

# run the processor
rects, lands, exp_global, pose, lands_can, exp_local = processor.run_all()

# quantify abruptness of motion for face rectangles
jerk, ldj = motion_smoothness(rects)

# quantify abruptness of motion for head pose
jerk, ldj = motion_smoothness(pose)

# quantify abruptness of motion for facial landmarks
jerk, ldj = motion_smoothness(lands)

With head pose, you can either use translation coordinates or rotation angles (yaw, pitch, roll).

# using translation coordinates
jerk, ldj = motion_smoothness(pose)

# using rotation angles
jerk, ldj = motion_smoothness(pose, angular=True)