Wavelet-Based filtering the cloud points derived from airborne laser scanner
Test Result
Figure 4 shows the interpolated image of 1-meter resolution. With the low point density, the better-interpolated
resolution could not be achieved
Figure 4. The interpolated elevation image (1 meter resolution)
The wavelet analysis was carried out with 4 employed resolutions. The purpose of the wavelet analysis is to find
out the pattern of clustered laser points, and the details existing at different resolutions. The smooth images at three
consecutive resolutions are depicted in Figure 5. It is illustrated clearly the idea of multi-resolution approach, i.e.
the small objects disappears in the coarse resolutions. This is a great advantage to assist the segmentation task.
Figure 5. The smoothed images across three consecutive resolutions
Consequently, the boundaries of clusters across different resolutions were distinguished as illustrated in Figure 6.
Figure 6a shows the detected boundaries at the finest resolution, which appears very noisy. Two other resolutions,.shown in Figure 6b and Figure 6c, were selected as the appropriate resolutions to construct the boundaries of
objects. The wavelet-based algorithm proposed in this study avoids that difficulty in selection of the right size of
kernel for filtering by analyzing the data in a multi-resolution space. Simultaneously, the boundaries of clusters are
detected and the multi-resolution domain is formed to allow the selection of the appropriate resolutions.
Figure 6. The detected boundaries of clusters across three consecutive resolutions
To distinguish the laser points belonging to the objects, a spatial relation of fall-into-boundary was applied, both in
the detected boundaries and on the raw laser points. The effect of interpolation could be adjusted at this step by the
combined analysis in both mentioned formats. Subsequently, the fuzzy edge points were also identified with the
threshold value of 7 meters, as observed in the testing area. Figure 7 illustrates the histograms of the original point
set, the point set after removing the object points, and the fuzzy edge points. There are three peaks in the histogram
of the original point set (Figure 7a) where two of them were successfully removed because they belong to the
objects (Figure 7b).
Figure 7. The illustration of histogram of the original laser points (a) and the remnants after removal of the object
points and the fuzzy edge points (b)
Prior to the application of the local operator, to remove the laser points belonging to the small objects, a threshold
value of 80% was applied in cumulative histogram. This was to discard some laser points with very high elevation
and dissimilar from the remnants.
The final stage of segmentation was based on local operator. Figure 8 depicts the results of segmentation into
ground and object points, in which the green and red points are symbolized for the bare earth points and the
overlying object points, respectively. Figure 9 shows both bare earth surface and original digital surface model to
visually compare the result of segmentation.
Figure 8. The detected point classes: the object points (red), and the bare earth points (green)
Figure 9. Perspective view of the digital surface model (a) and the detected digital terrain model (b)
