# Empirical Radiometric Normalization of Road Points from Terrestrial Mobile Lidar System

^{*}

## Abstract

**:**

## 1. Introduction

^{2}correction cannot be directly applied to TLS. Due to internal system factors such as brightness reducer, AGC [17], or receiver optics [18,19], the radiometric correction of TLS is more complex than ALS and does not completely follow the inverse square range function (1/r

^{2}) [20,21,22,23]. Because the TLS data, particularly TLS intensity at near range, cannot simply use the lidar equation in model-driven approach, most TLS radiometric processing uses the data-driven approach [17,20,21,22,23,24,25].

^{2}) (Figure 1). In addition, the MLS obtains 3-D points in a dynamic platform and is more complicated than static TLS.

**Figure 1.**An example of range-amplitude for MLS: the behavior of near-range is different from theoretical lidar equation.

## 2. Study Area and Dataset

Case 1 (Reference Area) | Case 2 | Case 3 | Case 4 | |
---|---|---|---|---|

Road type | Crossroads | Crossroads | U-turn lane | Linear road |

Number of Strips | 4 | 4 | 1 | 2 |

Size | 100 m × 100 m | 100 m × 100 m | 100 m × 100 m | 1400 m × 50 m |

**Figure 2.**Test data colored by normalized amplitude: (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, and (

**d**) case 4.

## 3. Proposed Scheme

#### 3.1. Data Pre-Processing

_{0}and the duration time of a scan line is dt, the points within t

_{0}to t

_{0}+ dt are classified onto a scan line. As the test area in this study is relatively simple than other cases, the results of the previous method and this refined method are the same. The scan line identification can be used to calculate the length of range for a scan line. So, we select the longest scan line to observe the relationship between amplitude and range. Besides, the sequential points on a scan line can be used to determine the height jump between points. It can be used to remove the non-road points. In scan line extraction, different colors indicate different scan lines (Figure 4), illustrating that the scan lines are distributed along the MLS trajectory.

- x, y, z = coordinates of lidar point;
- A, B, C, D =coefficients of a plane; and
- n
_{x}, n_{y}, n_{z}= normal vector of a plane.

**Figure 5.**Extraction of road points for case 1: (

**a**) additional manual digitization of road marks, (

**b**) scanner 1 (colored by amplitude), and (

**c**) scanner 2 (colored by amplitude).

#### 3.2. Empirical Radiometric Normalization

^{2}in the lidar equation. The data-driven approach is usually applied to the radiometric correction of TLS. There are two possibilities to collect the reference dataset for data-driven approach. One is to collect the amplitudes from signalized Spectralon targets at different ranges [26] and then apply the collected amplitudes and ranges to estimate the amplitude-range function. An alternate method is to measure the amplitude from available natural field targets. For example, asphalt roads exhibit stability for the radiometric correction of ALS [2]. Most of the TLS used the signalized Spectralon targets at different ranges for radiometric correction. The position of TLS and target are fixed in data collection. For MLS, the laser scanning mechanism is a line scanner mounted on a moving platform. As for the dynamic lidar sampling and moving platform, the natural field target like asphalt road is more favorable for radiometric correction of MLS. We assume that the asphalt road at different ranges should have similar amplitude after radiometric normalization; therefore, this study used asphalt road as a reference target to determine the amplitude-range function.

^{2}after 10 m to 15 m distance [21,22], which means that the near range and non-near range are two different functions. In this study, a separation approach [20] was applied to estimate the amplitude-range functions, using two low-order polynomial functions rather than a high-order polynomial function. The advantage of separation approach is to avoid over-fitting in high-order polynomial functions.

**Figure 6.**Extraction of separation points: (

**a**) scanner 1 (colored by number-of-point in a cell) and (

**b**) scanner 2 (colored by number-of-point in a cell).

_{sp}), the positional continuous functions (C° continuous) and first-order differential equations (C

^{1}continuous) were added to constrain the continuity (see Equations (4) and (5)). Finally, f(r) was used as a normalized factor to convert the original recorded amplitude into normalized amplitude (Equation (6)). Because the fitting result will influence the normalization process, the optimal polynomial order is needed. The lowest root mean square error (RMSE) was chosen to be a standard function and was applied to the normalization process.

- f
_{1}(r) = polynomial function for near-range; - f
_{2}(r) = polynomial function after separation point; - r = range;
- r
_{sp}= range at separation point; - a
_{0}~a_{n}, b_{0}~b_{n}= polynomial coefficients to describe the range effect; - A
_{o}= original amplitude; and - A
_{n}= normalized amplitude.

#### 3.3. Verification

#### 3.3.1. Consistency Check

_{scanner}and maximum amplitude difference between strips ∆A

_{strip}. The idea of DeltaA (delta amplitude) is to evaluate the consistency of amplitudes between strips or scanners in a cell. We have to define the size of a cell before the evaluation. If the cell size is too large, different types of points (e.g., white-colored road mark, black-colored asphalt pavement, etc.) will be mixed in a cell. The standard deviation of amplitude will be overestimated because the amplitudes of white-colored road mark and black-colored asphalt pavement have large differences. If the cell size is too small, the problem of mixing points can be solved, but the number of points is insufficient to calculate the reliable standard deviation. Therefore, we consider a small cell size and calculate the differences between the maximum and minimum amplitudes (DeltaA) in the evaluation.

_{scanner}, assuming that a set of amplitudes from scanner 1 in a cell is A

_{scanner}

_{1}= {A

_{scanner}

_{1}(1),A

_{scanner}

_{1}(2),…A

_{scanner}

_{1}(n)}, a set of amplitudes from scanner 2 in the same cell is A

_{scanner}

_{2}= {A

_{scanner}

_{2}(1),A

_{scanner}

_{2}(2),…A

_{scanner}

_{2}(m)}. The maximum amplitude difference, ∆A

_{scanner}, can be determined from Equation (6), and the improvement after radiometric normalization is defined as Equation (8).

_{strip}, assuming that a set of amplitudes from strip id 1 to n in a cell is $B=\left\{{A}_{strip\_1},{A}_{strip\_2},\cdots ,{A}_{strip\_n}\right\}$. The maximum amplitude in

**B**is max(B)

_{j}and j is the strip id for this maximum amplitude. The minimum amplitude in

**B**is min(B)

_{k}and k is the strip id for this minimum amplitude. The maximum amplitude difference, ∆A

_{strip}, can be determined from Equation (7), and the improvement after radiometric normalization is defined as Equation (8).

- $\u2206\text{A}$ = the maximum difference of amplitudes in a cell;
- $\overline{\u2206{\text{A}}_{\text{o}}}$ = the mean of amplitude differences in overlapped areas before normalization; and
- $\overline{\u2206{\text{A}}_{\text{n}}}$ = the mean of amplitude differences in overlapped areas after normalization.

#### 3.3.2. Classification

## 4. Results

#### 4.1. Selection of Polynomial Functions

_{1}(r)) from degrees 2 to 4 were tested; far-range, the inverse-range polynomial functions (f

_{2}(r)) from degrees 1 to 3 were tested. RMSE was selected as the accuracy index. The fitting results from combinations of polynomial functions and corresponding RMSEs (Table 2) showed no significant improvement after combination 3. To avoid over fitting, we choose combination 3 as the best model. The fitting errors for scanners 1 and 2 were 0.0291 (0.0291/0.8 = 3.6%) and 0.0269 (0.0291/0.8 = 3.3%), respectively. The maximum value of amplitude was about 0.8, and therefore the fitting errors were less than 4%.

Combination | ${f}_{1}\left(r\right)$ | ${f}_{2}\left(r\right)$ | RMSE (Scanner 1) | RMSE (Scanner 2) |
---|---|---|---|---|

1 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}$ | ${b}_{0}+{b}_{1}{r}^{-1}$ | 0.0311 | 0.0292 |

2 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}$ | ${b}_{0}+{b}_{1}{r}^{-1}+{b}_{2}{r}^{-2}$ | 0.0313 | 0.0291 |

3 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}+{a}_{3}{r}^{3}$ | ${b}_{0}+{b}_{1}{r}^{-1}+{b}_{2}{r}^{-2}$ | 0.0291 | 0.0269 |

4 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}+{a}_{3}{r}^{3}$ | ${b}_{0}+{b}_{1}{r}^{-1}+{b}_{2}{r}^{-2}+{b}_{3}{r}^{-3}$ | 0.0291 | 0.0269 |

5 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}+{a}_{3}{r}^{3}+{a}_{4}{r}^{4}$ | ${b}_{0}+{b}_{1}{r}^{-1}+{b}_{2}{r}^{-2}$ | 0.0290 | 0.0269 |

6 | ${a}_{0}+{a}_{1}r+{a}_{2}{r}^{2}+{a}_{3}{r}^{3}+{a}_{4}{r}^{4}$ | ${b}_{0}+{b}_{1}{r}^{-1}+{b}_{2}{r}^{-2}+{b}_{3}{r}^{-3}$ | 0.0290 | 0.0269 |

**Figure 8.**Range-amplitude polynomial function (combination 3): (

**a**) polynomial fitting and (

**b**) amplitude normalization.

#### 4.2. Statistical Analysis

^{2}. A large number of overlapped areas were selected in the evaluation process, which included a minimum number of observations of 140,000 cells.

Number of Overlapped Cell | Original | Normalized | Improvement (%) | |||||
---|---|---|---|---|---|---|---|---|

Mean | Std. | Mean | Std. | |||||

Case 1 | Between scanners | Strip 1 | 159,869 | 0.1145 | 0.0616 | 0.0586 | 0.0340 | 48.82% |

Strip 2 | 196,738 | 0.1063 | 0.0560 | 0.0520 | 0.0315 | 51.04% | ||

Strip 3 | 198,458 | 0.1058 | 0.0590 | 0.0538 | 0.0332 | 49.15% | ||

Strip 4 | 194,938 | 0.1106 | 0.0665 | 0.0577 | 0.0370 | 47.83% | ||

Between strips | 322,272 | 0.1517 | 0.0576 | 0.0745 | 0.0328 | 50.89% | ||

Case 2 | Between scanners | Strip 1 | 145,301 | 0.1010 | 0.0602 | 0.0514 | 0.0326 | 49.11% |

Strip 2 | 150,302 | 0.1165 | 0.0611 | 0.0598 | 0.0339 | 48.67% | ||

Strip 3 | 145,162 | 0.1091 | 0.0588 | 0.0554 | 0.0331 | 49.22% | ||

Strip 4 | 150,035 | 0.1055 | 0.0581 | 0.0534 | 0.0322 | 49.38% | ||

Between strips | 284,262 | 0.1585 | 0.0533 | 0.0778 | 0.0304 | 50.91% | ||

Case 3 | Between scanners | Strip 1 | 161,140 | 0.1221 | 0.0616 | 0.0611 | 0.0347 | 49.96% |

Case 4 | Between scanners | Strip 1 | 1,487,061 | 0.1208 | 0.0648 | 0.0628 | 0.0356 | 48.01% |

Strip 2 | 1,666,863 | 0.1087 | 0.0603 | 0.0568 | 0.0325 | 47.75% | ||

Between strips | 586,934 | 0.1529 | 0.0748 | 0.0663 | 0.0354 | 56.64% |

**Figure 9.**Comparison of statical results for all cases: (

**a**) improvement, (

**b**) comparison of mean differences, and (

**c**) comparison of std. errors.

#### 4.3. Road Surface Classification

Case | Correctness (%) | Completeness (%) | Overall Accuracy (%) | Kappa | |||||
---|---|---|---|---|---|---|---|---|---|

New Pavement | Ordinary Pavement | Road Mark | New Pavement | Ordinary Pavement | Road Mark | ||||

1 | Original (ISODATA) | 75.09 | 77.84 | 66.01 | 59.27 | 84.25 | 86.53 | 76.01 | 0.5422 |

Normalized (ISODATA) | 85.36 | 82.38 | 71.95 | 67.80 | 90.03 | 86.40 | 82.29 | 0.6597 | |

Normalized (OBC) | 81.69 | 88.16 | 76.20 | 81.68 | 87.50 | 81.00 | 85.08 | 0.7200 | |

2 | Original (ISODATA) | 59.26 | 80.25 | 80.72 | 64.28 | 76.45 | 83.90 | 73.31 | 0.4985 |

Normalized (ISODATA) | 85.18 | 90.23 | 77.09 | 80.3 | 90.9 | 89.77 | 87.56 | 0.7626 | |

Normalized (OBC) | 93.43 | 91.71 | 65.46 | 80.86 | 93.08 | 91.91 | 89.24 | 0.7960 | |

3 | Original (ISODATA) | 58.58 | 68.96 | 25.13 | 44.38 | 65.74 | 84.31 | 59.47 | 0.2531 |

Normalized (ISODATA) | 69.56 | 76.99 | 37.92 | 57.18 | 77.32 | 84.12 | 70.90 | 0.4388 | |

Normalized (OBC) | 68.79 | 81.10 | 59.98 | 70.51 | 78.97 | 69.45 | 75.61 | 0.5260 | |

4 | Original (ISODATA) | 3.68 | 98.89 | 37.61 | 69.44 | 84.18 | 85.1 | 84.17 | 0.3358 |

Normalized (ISODATA) | 8.66 | 98.85 | 40.06 | 48.82 | 90.48 | 85.13 | 90.02 | 0.4521 | |

Normalized (OBC) | 61.31 | 98.70 | 52.26 | 66.69 | 95.57 | 80.64 | 94.64 | 0.6090 |

^{2}) in case 4 was relatively smaller than other cases. The commission areas for original and normalized amplitude were 231.71 m

^{2}and 65.68 m

^{2}, respectively, and the result of normalized amplitude was better than original amplitude.

#### 4.4. Visualization Check

**Figure 10.**Case 1: (

**a**) orthophoto, (

**b**) original amplitude, (

**c**) corrected amplitude, (

**d**) manual digitization, (

**e**) classified results using original amplitude, (

**f**) classified results using corrected amplitude, and (

**g**) results of object-based classification using corrected amplitude.

**Figure 11.**Case 2: (

**a**) orthophoto (reference only), (

**b**) original amplitude, (

**c**) corrected amplitude, (

**d**) manual digitization, (

**e**) classified results using original amplitude, (

**f**) classified results using corrected amplitude, and (

**g**) results of object-based classification using corrected amplitude.

**Figure 12.**Case 3 (underway lidar acquisition): (

**a**) aerial photo above the underpass, (

**b**) original amplitude, (

**c**) corrected amplitude, (

**d**) manual digitization, (

**e**) classified results using original amplitude, (

**f**) classified results using corrected amplitude, and (

**g**) results of object-based classification using corrected amplitude.

**Figure 13.**Case 4: (

**a**) original amplitude, (

**b**) original amplitude (zoom-in A), (

**c**) original amplitude (zoom-in B), (

**d**) range-corrected amplitude, (

**e**) range-corrected amplitude (zoom-in A), (

**f**) range-corrected amplitude (zoom-in B), (

**g**) manual digitization (zoom-in C), (

**h**) classified results using original amplitude (zoom-in C), (

**i**) classified results using range-corrected amplitude (zoom-in C), and (

**j**) results of object-based classification using corrected amplitude (zoom-in C).

## 5. Conclusions

## Acknowledgements

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Teo, T.-A.; Yu, H.-L. Empirical Radiometric Normalization of Road Points from Terrestrial Mobile Lidar System. *Remote Sens.* **2015**, *7*, 6336-6357.
https://doi.org/10.3390/rs70506336

**AMA Style**

Teo T-A, Yu H-L. Empirical Radiometric Normalization of Road Points from Terrestrial Mobile Lidar System. *Remote Sensing*. 2015; 7(5):6336-6357.
https://doi.org/10.3390/rs70506336

**Chicago/Turabian Style**

Teo, Tee-Ann, and Hui-Lin Yu. 2015. "Empirical Radiometric Normalization of Road Points from Terrestrial Mobile Lidar System" *Remote Sensing* 7, no. 5: 6336-6357.
https://doi.org/10.3390/rs70506336