International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
60
mma Simulated waveform
mw FE h
2 40: MUS ]
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= 20
= WH
< 0 eme
20 10 29-35
Time (NS)
Figure 3. An example of a simulated waveform
3.2 Procedure of echo detection algorithm
Figure 4 shows the algorithm of detecting echoes by the
wavelet-based detector. For comparison, the zero-crossing(ZC)
detector is also utilized. The idea of ZC is to find zero crossings
of the first derivative of waveforms as the location of echoes.
Normally a smooth filter would be applied to waveforms when
adopting the ZC method since ZC algorithm is significantly
suffered from noises. However the wavelet-based detector can
directly process the raw waveforms without smoothing.
Firstly several waveforms with variant SNR levels are generated
(a) and then are input to the detectors (b). According to the
algorithms, the detectors output the locations of detected echoes.
One can see that some redundant echoes would be detected on
both sides of the waveform due to the noises regardless of any
detectors are applied (c). A condition is made that an echo
whose intensity (amplitude) must be greater than 3 Onoise in
order to remove the fake echoes (d). Consequently the echoes
pass the condition would be considered as efficient echoes and
transformed into 3D point.
Zero-
crossing
detector
| === waveform
— tihorder itera Ree A
s ete d echoes
where
T cho <
& ; A | 30noise ¥
Wavelet
-based
detector enl
waveform |
7 wavelet coefficients |
(9) (b) (c) (d) (e)
Figure 4. Flow chart of echo detection
3.3 Weak echo detection
To evaluate the power strength of return echoes, the signal-to-
noise ratio is utilized:
(Peak of return echo)
2
SNR - 10log,, (dB) (6)
noise
531
3.3.1 Set up: To test the ability of noise resistance between
the wavelet-based detector and the ZC detector, we generated
the echoes start from 0 SNR value and then increased the SNR
values by strengthening the power of echoes. At each SNR level,
1000 waveforms are generated. Therefore the percentage of
successful detection accuracy can be calculated by:
number of detecting 1 echo
1000
number of detecting 0 echo
1000
number of detecting more than 1 echo
1000
CRI: x100% (7)
MRI: x100%
RRI: x100%
where CRI denotes the correct rate(CR) of detection, MRI
denotes the missing rate(MR) of detection, and RR1 denotes the
redundant rate(RR) of detection.
3.3.2 Results: Figure 5 shows the detection results of the
two detectors under variant SNR levels. Comparing the CR1 of
the two detectors, the wavelet-based detector can reach to 10094
more quickly than ZC detector. In addition the wavelet-based
detector also produced less number of missing echoes. The two
detectors have approximate results in producing the number of
redundant echoes. Therefore the wavelet-based detector has
better ability of noise resistance in the case of detecting single
weak echo.
Zero-crossing detector
E730 echo
BB more than 1 echo
percentage of successful detection (%)
8
s 5 8 38 3 8 8 8
8
3
percentage of successful detection (%)
Figure 5. Results of echo detection, CR1: blue, MRI: green,
RRI: red, (a) zero-crossing, (b) wavelet-based
3.4 Overlapped echo detection
In this section, we focus on the three factors (Figure 6): echo
width (EW), the range between two echoes, and the relative
intensity between two echoes (A2 / Al in Figure 6), which have
significant influences on resolving the overlapped echoes. The
noises however are not taken into consideration in this test.
From the results of section 3.3.2, an echo can be confidently
detected by both of the detectors once its SNR vale exceeds 20
dB. In this experiment, the SNR value of each echo is set as at
least greater than 32 dB so that the noises can be treat as no
influence on the detecting results.
