Fig 1.
A diagram of camera placement for acquisition. The cameras used for DLT were placed at a 45° angle from the center point, while the DMS camera was placed frontal to the working area (in red). Also, placement of the calibration markers for the DMS method are shown.
Fig 2.
A diagram of the placement of calibration markers for the DLT method. A static structure formed by two fixed orthogonal frames was built to delineate the working area, to which markers were fixed at known positions. For each marker, global coordinates in cm are shown in the parenthesis as XYZ.
Fig 3.
Relationship between position and projections.
A diagram describing differences between actual positions of markers, relative to the camera, and their projections. Camera Height is considered as the measured height from the ground to the lens center. Camera Distance is considered as the distance between the marker’s center and the center of the camera’s lens. Ground Distance is considered as the distance from the marker’s center to the camera’s plane. Also shown are differences in projection height, where more distant markers are projected higher than closer ones, as well as diameter changes relative to distance, with closer markers appearing bigger than more distant ones.
Fig 4.
A diagram demonstrating that when a marker measures a certain diameter, said marker will have a specific camera distance independent from its direction. Corresponding camera distances are shown in red lines, all of which are equal to the measured camera distance. An example from our measurements is a projected diameter of 24 pixels, and a corresponding camera distance of 203.56 cm, in any direction.
Fig 5.
Relationship between diameter and distance.
A diagram describing the relationship between a marker’s camera distance and its diameter. The curve of this relationship takes the form of an inverse power function. From this function it is possible to see that the closer the marker is to the camera center, its size approaches infinity and as its diameter approaches zero, the distance grows to infinity. In the figure, we have included also some of the measurements obtained by us relative to the marker’s camera distance (in cm), and its projected diameter (in pixel).
Fig 6.
Plotted values of paired measurements of camera distances (in cm) and corresponding diameters (in pixels). The red curve represents the function that was fitted to the measurements. For the goodness of fit values, see text.
Fig 7.
A diagram describing the correction for perspective distortion. By using the measured projected diameter of a marker as well as the distance to some reference point, it is possible to calculate the ratio between projected diameter and distance to the reference. As the real marker diameter is known, it is possible to multiply the ratio by the real diameter, therefore obtaining the actual distance from the reference. This may be applied to both the X and Y axes. In the diagram we can see two markers (bold circles), that are placed at different distances from the camera (as shown at the bottom of the figure) and that in their projection (bold circles in the frame) appear to have a different diameter (with more distant marker having a smaller projected diameter), and a different localization (with the more distant marker appearing higher and more medial). As we can see the markers are effectively placed one behind the other (in the bottom of the figure) and, in fact, when calculating the ratio between projected diameter and distance to the reference, both present the same ratio meaning that in reality are placed one behind the other (i.e., having the same X and Y global coordinates).
Fig 8.
A diagram illustrating marker placement on the subject. As shown, 16 points were taken into consideration with 2 markers per joint for shoulders, elbows, wrists, and hips 3 markers per joint for the knees, and ankles, and a single marker for the head, trunk and left and right feet. Also shown are the joint angles, illustrated in the right part of the diagram; angles are named according to the joint at the vertex.
Fig 9.
A diagram demonstrating marker diameter acquisition. Each side of the marker is tracked for every frame.
Fig 10.
A reconstruction of the movement from both the DLT and DMS methods.
The actual action, as sequenced images is displayed along with the reconstruction for each method. For simplicity, only 1 every 10 frames is shown for reconstructions and image sequence. Reconstructions are shown in three different points of view: front, top, and side views. To differentiate between body segments, different colors were used for the lower extremities (black), upper extremities (red for DLT and blue for DMS) and head (cyan for DLT and green for DMS).
Fig 11.
Comparison between the DLT and DMS methods for linear displacement.
DLT results (red lines) and the DMS results (blue lines) are shown in the graphs. Graphs represent the amount of displacement for each joint (in cm, from 0 to 90 cm) over time (in seconds).
Fig 12.
Comparison between the DLT and DMS methods for angles.
DLT results (red lines) and the DMS results (blue lines) are shown in the graphs. Graphs represent the angle measured (in degrees, from 0 to 180) over time.
Table 1.
Results linear displacement.
Table 2.
Results angles.