Correction of Incidence Angle and Distance Effects on TLS Intensity Data Based on Reference Targets
"> Figure 1
<p>Reflected laser shots by extended Lambertian targets are uniformly scattered into a hemisphere. <math display="inline"> <semantics> <mrow> <mi mathvariant="normal">n</mi> </mrow> </semantics> </math> is the normal vector, and <math display="inline"> <semantics> <mi mathvariant="sans-serif">θ</mi> </semantics> </math> is the incidence angle. In most cases of TLS (terrestrial laser scanning), the emitter and receiver coincide.</p> "> Figure 2
<p>Geometric relationship of scan time. <math display="inline"> <semantics> <mrow> <mi mathvariant="normal">n</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi mathvariant="normal">n</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">n</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">n</mi> <mn>3</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> is the normal vector estimated by computing the best-fitting plane to a neighborhood of points surrounding the point of interest <math display="inline"> <semantics> <mrow> <mi mathvariant="normal">S</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">x</mi> <mo>,</mo> <mi mathvariant="normal">y</mi> <mo>,</mo> <mi mathvariant="normal">z</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math>. <math display="inline"> <semantics> <mrow> <mi mathvariant="normal">O</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi mathvariant="normal">x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">y</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">z</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo> </mo> </mrow> </semantics> </math> is the scanner center. <math display="inline"> <semantics> <mi mathvariant="sans-serif">θ</mi> </semantics> </math> is the incidence angle and <math display="inline"> <semantics> <mi mathvariant="normal">R</mi> </semantics> </math> is the distance.</p> "> Figure 3
<p>Instruments and equipment utilized in the experiments. Four Lambertian targets with a size of 10 cm× 10 cm and reflectance of 20%, 40%, 60%, and 80% were mounted on a board that can rotate horizontally through a goniometer. The instrument used was Faro Focus<sup>3D</sup> 120.</p> "> Figure 4
<p>(<b>a</b>) Original intensity with respect to incidence angle at a distance of 5 m for the four reference targets; (<b>b</b>) Original intensity with respect to distance at an incidence angle of 0° for the four reference targets.</p> "> Figure 5
<p>Measured and interpolated intensity values for the four reference targets at scanning geometries from A to L.</p> "> Figure 6
<p>Relative correction results for the four targets at scanning geometries from A to L. (<b>a</b>) The 80% target is used as a reference; (<b>b</b>) The 60% target is used as a reference; (<b>c</b>) The 40% target is used as a reference; (<b>d</b>) The 20% target is used as a reference.</p> "> Figure 7
<p>(<b>a</b>) Original intensity image of the white lime wall; (<b>b</b>) Original intensity image of the building facade with gray bricks; (<b>c</b>) Original intensity image of the cement road; (<b>d</b>) Original intensity values of the sampled regions of the three surfaces; (<b>e</b>) Distances of the sampled regions of the three surfaces; (<b>f</b>) Cosine of incidence angles of the sampled regions of the three surfaces.</p> "> Figure 8
<p>Relatively corrected intensity values of the sampled regions of the three surfaces. (<b>a</b>) The 80% target is used as a reference; (<b>b</b>) The 60% target is used as a reference; (<b>c</b>) The 40% target is used as a reference; (<b>d</b>) The 20% target is used as a reference.</p> "> Figure 9
<p>Absolutely corrected intensity values of the sampled regions of the three surfaces. (<b>a</b>) The 80% target is used as a reference; (<b>b</b>) The 60% target is used as a reference; (<b>c</b>) The 40% target is used as a reference; (<b>d</b>) The 20% target is used as a reference.</p> ">
Abstract
:1. Introduction
- to provide a short review of recent work on the correction of the incidence angle and distance effects of TLS;
- to introduce a new method to correct the incidence angle and distance effects on TLS intensity data based on reference targets;
- to derive relative formulas of the proposed method for linear interpolation of the intensity–incidence angle and intensity–range relationships of the reference targets. Existing correction methods for distance and incidence angle effects in TLS are reviewed in Section 2. The proposed correction model is introduced in Section 3. Section 4 outlines the dataset and experimental results. Section 5 presents and discusses the correction results of the proposed method, and the conclusions are presented in Section 6.
2. Existing Correction Methods
2.1. Radar Range Equation for Extended Lambertian Reflectors
2.2. Existing Correction Methods for Distance and Incidence Angle Effects
3. Proposed Model for Intensity Correction
4. Incidence Angle and Distance Experiments
5. Results and Discussion
5.1. Comparisons of Measured and Interpolated Intensity Values
- First, according to Equation (9) and Figure 4a, the intensity value of the 80% target at 7.6° was interpolated between the intensity values at 5° and 10°.
- Second, according to Equation (14) and Figure 4b, the intensity value of the 80% target at 1.54 m was interpolated between the intensity values at 1 m and 2 m.
- Finally, the intensity value of the 80% target at 7.6° and 1.54 m according to Equation (20) was calculated as 1794; the measured intensity value of the 80% target at 7.6° and 1.54 m was 1772. The measured and interpolated intensity values were approximately equivalent.
5.2. Correction Results of Reference Targets
5.3. Correction Results of Natural Targets
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Emitted power | 20 mW | Beam divergence | 0.009° |
Wavelength | 905 nm | Maximum range | 120 m |
Field of view | 360° × 305° | Exit beam diameter | 3.8 mm, circle |
Scanning Geometry | A | B | C | D | E | F |
Distance (m) | 1.54 | 4.23 | 6.88 | 8.49 | 10.10 | 13.96 |
Incidence angle (°) | 7.6 | 18.3 | 33.3 | 47.4 | 68.5 | 4.4 |
Scanning Geometry | G | H | I | J | K | L |
Distance (m) | 15.45 | 18.67 | 20.06 | 24.44 | 26.21 | 28.34 |
Incidence angle (°) | 23.9 | 38.6 | 56.4 | 72.6 | 25.4 | 3.5 |
A | B | C | D | E | F | G | H | I | J | K | L | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
80% | Measured | 1772 | 1797 | 1799 | 1728 | 1570 | 1639 | 1609 | 1577 | 1511 | 1424 | 1593 | 1598 |
Interpolated | 1794 | 1813 | 1792 | 1720 | 1566 | 1658 | 1630 | 1601 | 1537 | 1443 | 1619 | 1633 | |
60% | Measured | 1665 | 1679 | 1678 | 1613 | 1465 | 1513 | 1492 | 1456 | 1405 | 1315 | 1458 | 1472 |
Interpolated | 1679 | 1699 | 1680 | 1609 | 1463 | 1529 | 1507 | 1476 | 1416 | 1327 | 1499 | 1511 | |
40% | Measured | 1550 | 1553 | 1558 | 1497 | 1359 | 1390 | 1362 | 1340 | 1304 | 1221 | 1354 | 1366 |
Interpolated | 1568 | 1570 | 1547 | 1482 | 1356 | 1411 | 1374 | 1349 | 1296 | 1227 | 1368 | 1390 | |
20% | Measured | 1440 | 1428 | 1437 | 1381 | 1254 | 1282 | 1256 | 1226 | 1182 | 1102 | 1249 | 1261 |
Interpolated | 1454 | 1438 | 1438 | 1363 | 1237 | 1278 | 1242 | 1208 | 1165 | 1091 | 1234 | 1260 |
Reference Targets | ||||||
---|---|---|---|---|---|---|
80% | 60% | 40% | 20% | |||
=0.19 | =0.13 | =0.13 | =0.20 | |||
Scanned Targets | 80% | 0.87% | 0.64% | 1.01% | 2.07% | |
( =7.18%) | 0.12 | 0.09 | 0.14 | 0.29 | ||
60% | 1.43% | 0.92% | 0.91% | 1.61% | ||
( =7.68%) | 0.19 | 0.12 | 0.12 | 0.21 | ||
40% | 1.68% | 1.13% | 0.91% | 1.44% | ||
( =7.79%) | 0.22 | 0.15 | 0.12 | 0.18 | ||
20% | 2.03% | 1.36% | 1.07% | 0.88% | ||
( =8.32%) | 0.24 | 0.16 | 0.13 | 0.11 |
Reference Targets | ||||||
---|---|---|---|---|---|---|
80% | 60% | 40% | 20% | Mean | ||
Scanned Targets | 80% | 77.08% | 78.57% | 81.01% | 85.62% | 80.57% |
60% | 55.82% | 57.19% | 59.44% | 63.70% | 59.04% | |
40% | 35.35% | 36.61% | 38.69% | 42.63% | 38.32% | |
20% | 14.88% | 16.03% | 17.94% | 21.54% | 17.60% |
Reference Targets | |||||
---|---|---|---|---|---|
80% | 60% | 40% | 20% | ||
=0.19 | =0.13 | =0.13 | =0.20 | ||
Wall | 0.64% | 0.57% | 0.43% | 0.77% | |
( =2.99%) | 0.21 | 0.19 | 0.14 | 0.26 | |
Building | 1.54% | 0.91% | 0.91% | 1.76% | |
( =8.53%) | 0.18 | 0.11 | 0.11 | 0.21 | |
Road | 90.00% | 0.91% | 0.85% | 1.25% | |
( =9.78%) | 0.09 | 0.09 | 0.09 | 0.13 |
Reference Target | Mean | Standard | ||||
---|---|---|---|---|---|---|
80% | 60% | 40% | 20% | |||
Wall | 76.58% | 75.84% | 76.48% | 77.25% | 76.54% | 78% |
Building | 51.96% | 53.05% | 54.61% | 57.73% | 54.34% | 49% |
Road | 32.45% | 31.71% | 30.62% | 31.58% | 31.59% | 27% |
2.41 | 2.27 | −2.42 | 1 | ||
3.71 × 109 | −7.23 × 108 | 2.90 × 108 | −5.20 × 107 | 4.92 × 106 | |
−2.66 × 105 | 8.33 × 103 | −140.91 | 1 | ||
Reflectance | Wall: 76.82%; Building: 51.34%; Road: 26.51% |
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Tan, K.; Cheng, X. Correction of Incidence Angle and Distance Effects on TLS Intensity Data Based on Reference Targets. Remote Sens. 2016, 8, 251. https://doi.org/10.3390/rs8030251
Tan K, Cheng X. Correction of Incidence Angle and Distance Effects on TLS Intensity Data Based on Reference Targets. Remote Sensing. 2016; 8(3):251. https://doi.org/10.3390/rs8030251
Chicago/Turabian StyleTan, Kai, and Xiaojun Cheng. 2016. "Correction of Incidence Angle and Distance Effects on TLS Intensity Data Based on Reference Targets" Remote Sensing 8, no. 3: 251. https://doi.org/10.3390/rs8030251