11.4. Reconstructing probed points

In section Reconstructing removed markers, we learned how to reconstructed “virtual” markers that are not physically attached to a bony landmark, but that were during a static calibration acquisition. Sometimes, it is completely impossible to affix a marker on a landmark, for example if the landmark is obstructed with clothes or other objects. In these situation, it may be possible to use a digitizing probe (Fig. 11.1) to point landmarks during short acquisitions of a few seconds, and use these probed points to reconstruct the landmarks trajectory during other acquisitions.

Fig. 11.1 A digitizing probe (Optitrack).

The whole process is a bit more complex than in the previous tutorials, but the tools provided by Kinetics Toolkit will help. The following example represents such a situation, where the following acquisitions were performed:

• With a rigid body of three markers affixed to the right arm, an acquisition of a few seconds was recorded while another person touched the medial elbow epicondyle with the tip of the probe. Both were barely moving.

• A task acquisition was then recorded.

• We want to reconstruct the trajectory of the right medial elbow epicondyle during the task, even if it was not present during the task.

11.4.1. Loading sample data

We will create two TimeSeries, one that represents the markers during the probing acquisition, and the other representing the markers during the task acquisition.

import kineticstoolkit.lab as ktk
import matplotlib.pyplot as plt
import numpy as np

# Probing acquisition
markers_probing = ktk.read_c3d(
    ktk.doc.download("kinematics_racing_probing_medial_epicondyle_R.c3d")
)["Points"]
markers_probing = markers_probing.get_subset(
    ["ArmR1", "ArmR2", "ArmR3", "Probe1", "Probe2", "Probe3", "Probe4"]
)

markers_probing.data

{
     'ArmR1': <array of shape (140, 4)>
     'ArmR2': <array of shape (140, 4)>
     'ArmR3': <array of shape (140, 4)>
    'Probe1': <array of shape (140, 4)>
    'Probe2': <array of shape (140, 4)>
    'Probe3': <array of shape (140, 4)>
    'Probe4': <array of shape (140, 4)>
}

# Propulsion acquisition
markers_task = ktk.read_c3d(
    ktk.doc.download("kinematics_racing_propulsion.c3d")
)["Points"]
markers_task = markers_task.get_subset(["ArmR1", "ArmR2", "ArmR3"])

markers_task.data

{
    'ArmR1': <array of shape (700, 4)>
    'ArmR2': <array of shape (700, 4)>
    'ArmR3': <array of shape (700, 4)>
}

11.4.2. Defining the probe calibration

We must know the configuration of the probe. What we need is the position of the probe markers in the probe’s local coordinate system, assuming that this coordinate system’s origin is at the probe tip. These positions are generally found in rigid body configuration files or in calibration certificates. In this tutorial, our probe has four markers with the following local coordinates:

• Probe1: (0.0021213, -0.0158328, 0.0864285) m

• Probe2: (0.0021213, 0.0158508, 0.0864285) m

• Probe3: (0.0020575, 0.0160096, 0.1309445) m

• Probe4: (0.0021213, 0.0161204, 0.1754395) m

We will use these known coordinates to create a cluster as in the previous tutorials, but here we do it manually since we already know the coordinates.

probe = {
    "ProbeTip": np.array([[0.0, 0.0, 0.0, 1.0]]),
    "Probe1": np.array([[0.0021213, -0.0158328, 0.0864285, 1.0]]),
    "Probe2": np.array([[0.0021213, 0.0158508, 0.0864285, 1.0]]),
    "Probe3": np.array([[0.0020575, 0.0160096, 0.1309445, 1.0]]),
    "Probe4": np.array([[0.0021213, 0.0161204, 0.1754395, 1.0]]),
}

11.4.3. Tracking the probe during the probing acquisition

In the probing acquisition, since the probe tip points on the medial epicondyle, we can consider the probe tip as if it was a real marker affixed on the medial epicondyle. The first step is therefore to track the probe tip using the four markers of the probe.

reconstructed_probe_markers_during_probing = ktk.kinematics.track_cluster(
    markers_probing,
    probe,
)

reconstructed_probe_markers_during_probing.data

{
    'ProbeTip': <array of shape (140, 4)>
      'Probe1': <array of shape (140, 4)>
      'Probe2': <array of shape (140, 4)>
      'Probe3': <array of shape (140, 4)>
      'Probe4': <array of shape (140, 4)>
}

We can now consider that the trajectory of the probe tip is the same as if a real marker had been affixed on the medial epicondyle.

markers_probing.data[
    "MedialEpicondyleR"
] = reconstructed_probe_markers_during_probing.data["ProbeTip"]

markers_probing.data

{
                'ArmR1': <array of shape (140, 4)>
                'ArmR2': <array of shape (140, 4)>
                'ArmR3': <array of shape (140, 4)>
               'Probe1': <array of shape (140, 4)>
               'Probe2': <array of shape (140, 4)>
               'Probe3': <array of shape (140, 4)>
               'Probe4': <array of shape (140, 4)>
    'MedialEpicondyleR': <array of shape (140, 4)>
}

11.4.4. Creating a cluster of markers

We are now in the same situation as the beginning of section Reconstructing removed markers. We can now create a cluster that includes the three rigid body markers, and the medial epicondyle.

cluster = ktk.kinematics.create_cluster(
    markers_probing, ["ArmR1", "ArmR2", "ArmR3", "MedialEpicondyleR"]
)

# Print the cluster contents
print(cluster["ArmR1"])
print(cluster["ArmR2"])
print(cluster["ArmR3"])
print(cluster["MedialEpicondyleR"])

[[-0.  0. -0.  1.]]
[[ 0.04297859 -0.         -0.          1.        ]]
[[ 0.02150487  0.03747125 -0.          1.        ]]
[[0.08345064 0.12620648 0.10931605 1.        ]]

11.4.5. Tracking the cluster

Now, we use this cluster to reconstruct the whole set of four “markers” during the task acquisitions, including the epicondyle.

reconstructed_markers_task = ktk.kinematics.track_cluster(
    markers_task,
    cluster,
)

# Plot the results
plt.subplot(2, 2, 1)
reconstructed_markers_task.plot("ArmR1")
plt.subplot(2, 2, 2)
reconstructed_markers_task.plot("ArmR2")
plt.subplot(2, 2, 3)
reconstructed_markers_task.plot("ArmR3")
plt.subplot(2, 2, 4)
reconstructed_markers_task.plot("MedialEpicondyleR")
plt.tight_layout()