Localized DLT
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Localized DLT
Application
References & Related Literature

Localized DLT

Due to the non-linear nature of refraction, it is advantageous to section the control volume into smaller sub-volumes. Sectioning of the control volume and confining the camera calibration & reconstruction to the sub-volumes decreases the non-linearity among the refracted coordinates of the control points (Kwon, 1999). For example, as shown in Figure 1, one can use the calibration parameters (L1 - L11) of the sub-volume (solid lines) instead of those of the whole volume (broken lines) in reconstructing the object-space (real-life) coordinates of marker M that belongs to the sub-volume. This intentional confining of the camera calibration & reconstruction to the sub-volume the marker belongs to is called "localization" or "localized-calibration & reconstruction". This localization strategy can be easily incorporated into any camera calibration & reconstruction program that is based on the DLT algorithm.

wpe15.jpg (5595 bytes)     Figure 1

Starting from version 3.0, Kwon3D supports the localized-calibration & reconstruction approach. Localization can be easily done through control point grouping. Both the localized 3D-DLT method and the localized double-plane method are supported.

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Application

Kwon & Lindley (2000) performed a series of camera calibrations based on a simulated underwater calibration trial. Both the 3-D DLT method and the double-plane method were combined with two different localization strategies: with overlap and without overlap. Figure 2 shows the calibration frame (28 control points) and the sub-volumes & sub-areas defined by the control point groups.

    Figure 2

The following 4 localization methods were used in this study:

Method Algorithm Overlapping Sub-Volumes/Areas Used (Figure 2)

O3
NO3
O2
NO2

3-D DLT
3-D DLT
Double-Plane
Double-Plane
Yes
No
Yes
No
1, 2, 3, 4 & 5
1, 3 & 5
1-1, 1-2, 1-3, 1-4, 1-5, 2-1, 2-2, 2-3, 2-4 & 2-5
1-1, 1-3, 1-5, 2-1, 2-3 & 2-5

Comparing with the regular 3-D DLT method, the localization methods resulted in substantive decreases in the reconstruction error:

  RMS Error (cm) Maximum Error (cm) Max-to-RMS Ratio (%)
3-D DLT
O3
NO3
O2
NO2
1.74
0.65
0.56
0.72
0.63
3.93
0.97
0.97
0.93
0.93
225.9
149.2
173.2
129.2
147.6

The double-plane method-based methods (O2 & NO2) resulted in smaller maximum calibration errors and max-to-RMS ratios than their 3-D DLT-based counterparts (O3 & NO3). The O methods (O3 & O2) provided smaller maximum errors and max-to-RMS ratios than their NO counterparts (NO3 & NO2).

The localized-calibration/reconstruction methods also showed less object space deformation throughout the control volume and at the water surface than the regular 3-D DLT method. Again the double-plane method-based methods showed less object space deformation than the 3-D DLT-based methods while the O methods showed less deformation than the NO methods. Method O2 was identified as the best localization method among the 4 methods used. See Kwon & Lindley (2000) for the details.

One potential problem observed in the localized-calibration methods is the space discontinuity due to switching of the sub-volume/area from one to another. This is common to any calibration methods dealing with distinct control volumes/areas, including the panning methods. The discontinuity problem must be treated properly to maximize the applicability of the localized-calibration approach. Although data filtering will ease the discontinuity problem to some extent, one may take additional measures such as (1) developing a strategy to temporarily tag the marker as missing at the discontinuity region so that the program later generates interpolated coordinates, and (2) using more complex control point grouping and overlapping schemes with smaller control volumes. A more fundamental approach to tackle the discontinuity problem is to develop a panning method that is based on a continuous control volume/area. Use of a continuous control volume in the panning method can eliminate switching of the control volumes/areas.

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References & Related Literature

Kwon, Y.-H., & Lindley, S.L. (2000). Applicability of the localized-calibration methods in underwater motion analysis. Submitted to the XVIII International Symposium on Biomechanics in Sports.

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Young-Hoo Kwon, 1998-