THE IDENTIFICATION OF IMPULSES IN 3-D RECONSTRUCTED DATA USING RECURSIVE FILTERS ON THE ORIGINALLY DIGITIZED 2-D IMAGE DATA
Keywords: impulse, recursive, 2-D filter, Kalman, 3-D reconstruction
AbstractINTRODUCTION: Reconstructed three-dimensional (3-D) data is usually processed using either a low-pass Butterworth filter or quintic spline, though neither gives an implicit indication that the processed data is more accurate than the original data. This study investigated the effect of processing the original twodimensional (2-D) data before reconstruction, a technique commonly applied in the communications industry (e.g., the removal of noise prior to amplification). Reconstruction of the 3-D data can be considered successful when the condition of coplanarity is met (i.e., the lines from each centre of projection pass through their respective image points and intersect at the object point). The 3-D data is considered to be more accurate if the lines converge after processing (i.e. the residual error of the reconstructed points was reduced) and less accurate if the lines diverge. The independent application of a recursive filter in both forward and backward directions to the 2-D data enables the detection of a discontinuity. Each original 2- D data set can then be considered as two different data sets whose paths intersect at the discontinuity caused by an impulse. The timing of the impulse can be calculated from the extrapolated curves even if it was not explicitly captured on film. METHOD: Two cameras were located so that their optical axes were approximately orthogonal to each other and a 3-D volume was calibrated to generate the linear transformation parameters. A bouncing ball was then filmed within the calibrated volume, digitized and then passed through a Kalman filter in both the forward and backward directions to determine the timing of the impulse, (i.e., when the ball hit the ground). RESULTS: Two cameras provide four image co-ordinates and thus four equations with three unknowns so the 3-D object space co-ordinates were calculated using least squares estimation. To ensure only random noise was removed, the processed 2-D signal must have the same total energy as the original 2-D signal, even if the energy density spectrum has altered and the filter was deemed to be effective if the residual error of the reconstruction was reduced. Using this method, it was possible to identify when the impulse forces occurred, for both image sets, independently. CONCLUSIONS: This technique breaks a signal down into a series of discontinuous signals, each discontinuity indicating the application of an impulse to the original measured data. With proper camera placement any impulse can be observed independently in both the 2-D images so the impulses can also be used to synchronize previously unsynchronized data.
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