Adjusting Highway Mileage in 3-D Using LIDAR By Hubo Cai August 4 th, 2004

Organization  Introduction  Research Objectives  3-D Models and 3-D Distance Prediction  Computational Implementations  Case Study  Accuracy Evaluation and Sensitivity Analysis  Significant Factors  Conclusions and Recommendations

Introduction  Why adjust highway mileage?  Location is Critical in Transportation  Events Are Located via Distances along Roads to Reference Points  Errors and Inconsistencies in Distance Measures in Transportation Spatial Databases  Why use GIS?  Other methods  Design Drawings  Ground Surveying  GPS  Distance Measurement Instrument (DMI)  Time-consuming and labor intensive  GIS-based approach is efficient

Introduction (Continued)  Why in 3-D?  Real World Objects ---- Three Dimensional  Using 2-D Length  Why LIDAR?  3-D approach (the introduction of elevation)  Highly accurate  Availability  Main concerns  How?  Accuracy and error propagation

Research Objectives  Adjust highway mileage in 3-D using LIDAR  Evaluate its accuracy via a case study  Evaluate its sensitivity to the use of LIDAR versus NED  Identify significant factors

3-D Models  3-D Point Model and Its Variants  3-D Distance Prediction

3-D Point Model A B C D E F G X A B C D E F G Specified by Z = f1 (X, Y) and Y = f1(X) Specified by Y = f1 (X) Y Z Specified by Z = f2 (X, Y) and Y = f2(X) Specified by Z = f31 (X, Y) and Y = f3(X) Specified by Y = f2 (X) Specified by Y = f3 (X)

3-D Point Model – Variant 1, LRS-Based Distance X Y LRS Z/Elevation 2-D Line A B CE G F D A B C D E G F Specified by Z = f1 (Distance) Specified by Z = f2 (Distance) Specified by Z = f3 (Distance)

3-D Point Model – Variant 2, LRS-Based Distance X Y LRS Z/Elevation 2-D Line A B CE G F D A B C D E G F Straight Line Segments

3-D Distance Prediction Horizon Vertical Profile Horizontal Projection Difference in Elevation--d Planimetric Length--pl Surface Length = sqrt (d*d + pl*pl)

Required Source Data  Elevation Dataset  LIDAR  USGS NED  Planimetric Line Dataset

LIDAR  General Information  A LIDAR operates in the Ultraviolet, Visible, and Infrared Region of the Electromagnetic Spectrum  A LIDAR consists of GPS, INS/IMU, and Laser Range Finder  Last “return” for Bare Earth Data  Raw Data – Mass Point Data  End Products Generation  Post Processing  Comma-Delimited ASCII File in X/Y/Z Format  DEMs  Accuracy  A Typical 6-Inch Error Budget in Elevations and Positions  The Guaranteed Best Vertical Accuracy -- ± 6 Inches (± 15 Centimeters)  No Better than 4 Inches  Market Models – Range from 10 – 30 cm (Vertical RMSE)

DEMs  A DEM is a digital file consisting of terrain elevations for ground positions at regularly spaced horizontal intervals  Grid Surface X, Y coordinates are (4, 3) Row Column

NED  Future Direction of USGS DEM Data  Merge the Highest-Resolution, Best-Quality Elevation Data Available across the US into a Seamless Raster Format  Source Data Selected According to the Following Criteria (Ordered from First to Last): 10-Meter DEM, 30-Meter Level-2 DEM, 30- Meter Level-1 DEM, 2-Arc-Second DEM, 3-Arc- Second DEM  Accuracy  Varies with Source Data  Systematic Evaluation under Processing  “Inherits” the Accuracy of the Source Data  Level 1 DEMs (Max RMSE 15 m, Desired RMSE 7 m)  Level 2 DEMs (Max RMSE One-half Contour Interval)  Level 3 DEMs (Max RMSE One-third Contour Interval)

Computational Implementations  Development Environments  ArcGIS 8.2  ArcObjects  Visual Basic for Applications  Key ---- Obtaining 3-D Points  Obtaining Planimetric Positions (Depending on the Format of Input Elevation Data)  Obtaining Elevations

Obtaining 3-D Points ---- Working with LIDAR Points  Working with LIDAR Point Data  Depending on the Point Elevation Data  Interpolation Approach  Approximation Approach  Discussions

Interpolation Approach Apply A Buffer Identify All Points in the Buffer Group Points into 3 Groups Use Group C Points Directly Identify Point Pairs for Group A and Group B Points Create Points from Each Point Pair by Linear Interpolation Deal with Start and End Points Group A points Group B points Group C points P Q O Elevation for point O is linearly interpolated from points P and Q

Approximation Approach Developed based on Road Geometry Apply A Buffer Identify All Points in the Buffer Points on Line for Direct Use Snap Points to the Line Deal with Start and End Points

Discussion Errors due to Approximation –Typical Lane Width (12 ft for Interstate and US Roads, 10 ft for NC Routes) –Typical Cross-Sectional Slope (2%) –Maximum Errors based on the typical slope (0.24 ft ( 7.31cm) and 0.2 ft (6.10 cm)) Prerequisite –Lines in Correct Positions –High-Density LIDAR Points LIDAR Point Density –18.6 ft (Average Distance between Two Neighboring LIDAR Points) Discussion –Approximation Approach Results in Almost Double the Number of 3-D Points –Snapping Provides At Least Equal Accuracy, If Not Better Vertical error due to approximation Vertical error due to interpolation Corresponding point on road centerline C LIDAR point B A B C A B LIDAR point A Points after Snapping

Obtaining 3-D Points ---- Working with LIDAR DEMs and NED Planimetric Position (2-D Point) ---- Uniform Interval (full cell-size and half cell-size) Elevation –For A Given Point, Its Elevation Is Interpolated from Elevations of the Four Surrounding Cells –Two Steps (Intermediate Points and the Target Point) A B C D E 30m 22.4m 22.25m A B C D E G F A B C D d d d

Case Study ---- Study Scope Limited by LIDAR Availability Considered Sample Size and Variety Interstate Highways in 9 Counties and US and NC Routes in Johnston County Study Scope Legend NEUSE TAR-PAMLICO River Basin County Counties in Study Scope Interstate Highways US Routes NC Routes Map produced by Hubo Cai, August 2003

Case Study Information Sources  Digital Road Centerline Data  Elevation Data  LIDAR Point Data  LIDAR DEMs (20 and 50 ft resolutions)  NED (30 m resolution)  Reference Data (DMI Data)

Digital Road Centerline Data Digitized from DOQQs B/W and 98 CIR Data Description –Link-Node Format –County by County –Stateplane Coordinate System –Datum: NAD83 –Units: foot

Elevation Data – LIDAR Data  Data Collection and Description  Downloaded from  Tile by Tile (10,000 ft * 10, 000 ft)  Bare Earth Point Data, 20-ft DEMs, and 50-ft DEMs (ASCII Files)  Datum: NAD83 and NAVD 88  Units: Foot  Accuracy  Coastal Counties (95% RMSE, 20 cm)  Inland Counties (95% RMSE, 25 cm)  Metadata States: 2 m Horizontal, 25 cm Vertical

Elevation Data -- NED  Data Collection and Description  Downloaded from North Carolina State University Spatial Information Lab (  County by County  Interchange Files (.e00 Files)  Stateplane Coordinate System  Datums: NAD83 and NAVD88  Units: Foot (Horizontal), Meter (Vertical)  Resolution: 1-arc-second (approximately 30-Meter or Feet)  Errors and Accuracy  Inherits the Accuracy of the Source DEMs  Metadata States Source DEMs Are Level 1 DEMs  Vertical RMSE: 7-Meter (Desired), 15-Meter (Maximum)

Modeling Road Centerlines in 3-D  Using LIDAR Point Data  Intermediate Points (Buffering and Snapping)  Start and End Points (Interpolation, Extrapolation, and Weighted Average)  Using LIDAR DEMs  Uniformly Distributed Points  Intervals  20-ft and 10-ft with 20-ft DEMs  50-ft and 25-ft with 50-ft DEMs  Using NED  Same as Using LIDAR DEMs  Different Intervals (30-meter and 15-meter)

Quality Control Points do not Follow the general trend

A Typical Scenario F1 F2 F4 F3 Buffer Bridge L1 L2 L3 L4 D1D2 D3 D4 E1 E2 E3 E4 D5 D6 P1/P2

Improvement An Averaging Procedure Averaging Criteria –Based on Average Densities –3 ft for Interstate and US FTSegs (average density 9.69 ft) –4 ft for NC FTSegs (average density ft) D1 D3 D4 D2 L1 L3 L4 L2 A1 A2

Sample 3-D Point Data Attribute Table XYZD_TO_SDIST2DROUTEMERGE

Results  Each Road Segment Has 8 Distances  Predicted 3-D Distance  From the Use of LIDAR Point Data  From the Use of LIDAR 20-ft DEMs and A 10-ft Interval  From the Use of LIDAR 20-ft DEMs and A 20-ft Interval  From the Use of LIDAR 50-ft DEMs and A 25-ft Interval  From the Use of LIDAR 50-ft DEMs and A 50-ft Interval  From the Use of NED and A 15-m Interval  From the Use of NED and A 30-m Interval  Reference Distance  DMI Measured Distance

Accuracy Evaluation  Error(Difference) and Proportional Error (Proportional Difference)  Evaluation Methods  Descriptive Statistics (Describing Samples)  Distribution Histograms  Statistical Inferences  Frequency Analysis  100% and 95% RMSEs  Sensitivity Analysis  Analysis of Variance (ANOVA)  Comparison of Means, Medians, Absolute Means, Frequencies, and RMSEs

Accuracy Evaluation Results ---- Descriptive Statistics I Error FormatRoad Type LIDAR Point Data MeanMedianStandard DeviationSkew Differences All Inter US NC Proportional Differences All Inter US NC Error FormatRoad Type NED, 15-m Interval NED, 30-m Interval MeanMedianStandard DeviationSkewMeanMedianStandard DeviationSkew Differences All Inter US NC Proportional Differences All Inter US NC

Accuracy Evaluation Results ---- Distribution Histograms I

Accuracy Evaluation Results ---- Hypothesis Tests and Confidence Intervals Sample Hypothesis StatisticCritical Value(s)Reject or Accept at α = 5% Confidence Interval H0H1 D_A_LP μ ≤ 0μ > A* ± 2.94 μ ≥ 0μ < R** μ = 0μ ≠ ±1.9642R D_I_LP μ ≤ 0μ > A ± 3.58 μ ≥ 0μ < R μ = 0μ ≠ ±1.9771R D_US_LP μ ≤ 0μ > A ± 6.22 μ ≥ 0μ < R μ = 0μ ≠ ±1.9979R D_NC_LP μ ≤ 0μ > A 2.86 ± 8.19 μ ≥ 0μ < A μ = 0μ ≠ ±2.0317A PD_A_LP μ ≤ 0μ > A ± 6.06 μ ≥ 0μ < R μ = 0μ ≠ ±1.9642R PD_I_LP μ ≤ 0μ > A ± 5.05 μ ≥ 0μ < A μ = 0μ ≠ ±1.9771A PD_US_LP μ ≤ 0μ > A ± μ ≥ 0μ < R μ = 0μ ≠ ±1.9979R PD_NC_LP μ ≤ 0μ > A ± μ ≥ 0μ < A μ = 0μ ≠ ±2.0317A

Accuracy Evaluation Results ---- RMSEs (LIDAR Point Data) Error FormatRoad Type 100%95% RMSEReported Accuracy# of OutliersRMSE Reported Accuracy # of Outliers Differences All Inter US NC Proportional Differences All Inter US NC

Accuracy Evaluation Results ---- Frequency Analysis (LIDAR Point Data) Error FormatGroups All FTSegsInterstate FTSegsUS FTSegsNC FTSegs #%#%#%#% Differences [-5, 5] % % % % [-10, 10] % % % % [-20, 20] % % % % [-30, 30] % % % % [-50, 50] % % % % (-∞, -50) and (50, +∞) % % % % Proportional Differences [-1, 1] % % % % [-5, 5] % % % % [-10, 10] % % % % [-20, 20] % % % % [-30, 30] % % % % [-50, 50] % % % % [-100, 100] % % % % (-∞, -100) and (100, +∞) % % % %

Sensitivity Analysis ---- ANOVA Sample 1Sample 2FFcAccept or Reject D_A_LP D_A_L20_ Reject D_A_L20_ Reject D_A_L50_ Reject D_A_L50_ Accept D_A_N_ Reject D_A_N_ Reject D_A_L20_10 D_A_L20_ Accept D_A_L50_ Reject D_A_L50_ Reject D_A_N_ Accept D_A_N_ Accept D_A_L20_20 D_A_L50_ Reject D_A_L50_ Reject D_A_N_ Accept D_A_N_ Accept D_A_L50_25 D_A_L50_ Accept D_A_N_ Reject D_A_N_ Reject D_A_L50_50 D_A_N_ Reject D_A_N_ Reject D_A_N_15D_A_N_ Accept Difference: F > Fc, Proportional Difference: F < Fc

Sensitivity Analysis ---- Comparison of RMSEs

Comparison Based on RMSEs Elevation Dataset 100% RMSE95% RMSE RMSEImprovementRMSEImprovement Difference LIDAR Point % % LIDAR DEM (20FT)33.526%27.837% LIDAR DEM(50FT)34.035%27.718% NED Proportional Difference LIDAR Point

Conclusions ---- Accuracy Evaluation and Sensitivity Analysis  Errors of the predicted 3-D distances are not normally distributed.  The higher the accuracy of the elevation dataset being used, the higher the accuracy of the predicted 3-D distances.  Using the same elevation dataset, the accuracy of the predicted 3-D distance is not dependent on intervals, given these intervals are less than or equal to the cell size.  3-D distances predicted using LIDAR point data with the snapping approach have the best accuracy.

 From the aspect of differences using the 100% RMSE as the measure of the accuracy, the use of LIDAR point data improves the accuracy by 28% compared to the use of NED data. The use of LIDAR DEMs improves the accuracy by 6% compared to the use of NED data.  From the aspect of differences using the 95% RMSE as the measure of the accuracy, the use of LIDAR point data improves the accuracy by 25% compared to the use of NED data. The use of LIDAR DEMs improves the accuracy by 8% compared to the use of NED data.  From the aspect of proportional differences, the improvements due to the use of higher accurate elevation datasets are not significant (the majority (53%) of the road segments in this case study are longer than 5,000 ft, 73% are longer than 1,000 ft, and 43% are longer than 10,000 ft). Conclusions ---- Accuracy Evaluation and Sensitivity Analysis (Continued)

Significant Factors  Goal  Evaluate the relationship between a geometric property and the accuracy of the GIS calculated distance  Factors under Consideration  Distance  Average Slope and Weighted Slope  Average Slope Change and Weighted Slope Change  Number of 3-D Points and Average Density of 3-D Points  Evaluation Methods Applied  Sample Correlation Coefficient and Sample Coefficient of Determination  Grouping and Comparison  Benefits  Cautions to be paid to certain linear features

Calculation of Factors Distance = D1 + D2 (DMI measured) Average Slope = (Abs(S1) + Abs(S2))/2 Weighted Slope = (Abs(S1) * D1 + Abs(S2) * D2)/(D1 + D2) Average Slope Change = (Abs(S1 – 0) + Abs(S2 – S1))/2 Weighted Slope Change = (Abs(S1 – 0) * D1 + Abs(S2 – S1) * D2)/(D1 + D2) Number of 3-D Points = 3 Average Density = (D1 + D2)/2 PD1 PD2 E1 E2 D1 D2 S1 S2

Evaluation Result I: Distance vs. Difference and Absolute Difference FTSeg Type LIDAR Point Data LIDAR 20-ft DEMLIDAR 50-ft DEMNED 10-ft Interval20-ft Interval25-ft Interval50-ft Interval15-m Interval30-m Interval rxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xy All Inter US NC FTSeg Type LIDAR Point Data LIDAR 20-ft DEMLIDAR 50-ft DEMNED 10-ft Interval20-ft Interval25-ft Interval50-ft Interval15-m Interval30-m Interval rxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xyrxyr2xy All Inter US NC Distance vs. Difference Distance vs. Absolute Difference

Grouping and Analysis I: Difference, Groups Based on Distance GroupDistance Range (ft) Number of FTSegs Percentage Group 1(0, 100] % Group 2(100, 1,000]269.81% Group 3(1,000, 5,000] % Group 4(5,000, 10,000] % Group 5(10,000, 20,000] % Group 6(20,000, 30,000] % Group 7(30,000, +∞) % Total % Group LIDAR Point Data LIDAR 20-ft DEMLIDAR 50-ft DEMNED 10-ft Interval20-ft Interval25-ft Interval50-ft Interval15-m Interval30-m Interval Group Group Group Group Group Group Group

Group LIDAR Point Data LIDAR 20-ft DEMLIDAR 50-ft DEMNED 10-ft Interval20-ft Interval25-ft Interval50-ft Interval15-m Interval30-m Interval Group Group Group Group Group Group Group Grouping and Analysis II: Proportional Difference, Groups Based on Distance

Significant Factor ---- Conclusions  Conclusions Based on Sample Correlation Coefficients  The Factors under Consideration are all significant to the accuracy of the predicted 3-D Distance when compared to the DMI measured distance.  Positive Linear Association between the error of the predicted 3-D distance and a factor under consideration.  Negative Linear Association between the proportional error of the predicted 3-D distance and a factor under consideration  Conclusions Based on Grouping and Analysis  Confirms the significance of these factors  Confirms the general linear associations  Reveals the existence of thresholds

 It is technically feasible to model linear objects in a 3-D space with existing datasets.  The buffering and snapping approach is a creative way in using LIDAR point data.  Two datasets (elevation and line) are required to adopt the model developed.  The prerequisite to adopt the developed 3-D model is that lines are in correct positions.  Using the proposed 3-D approach, geometric properties other than 3-D distance could be calculated.  Conclusions regarding accuracy and sensitivity.  Conclusions regarding significant factors. Conclusions

Recommendations  Adopt the 3-D approach developed in this research to calculate 3-D distance and other geometric properties.  Linear objects other than road centerlines could also adopt the 3-D model developed in this research.  Spatially correct all line (road) data.  The buffering and snapping approach developed in this research is based on road characteristics. If to be used for other linear objects, the appropriateness needs to be evaluated.  Extra caution should be paid to certain linear objects (significant factors).

Key Benefits  3-D Road Centerline  Computed 3-D Geometries  No more need for field work  Savings on time, labor, and cost  Readily Customizable Programs  Useful to Other Applications

Use of the Model to Assess Highway Flooding Objective ---- Test the Usefulness of Developed 3-D Model in Assessing Highway Flooding Flooding Scenario Two Tasks –Flood Extent and Depth Determination –Flooded Road Segment Identification Normal Water Level Flooded Water Level Area A Area B Surface Line Road Profile Segments Flooded Segments Not Flooded Flooded Water Level

Flood Extent and Depth Determination  Traditional Approach  Water Level Surface  Terrain Surface  Approach Taken in This Study  Assumption 1: Water Bodies Are Represented As Polylines  Assumption 2: Elevations along Water Lines Are Water Surface Levels  Assumption 3: Given Flood Level  Business Rule 1: Elevations along Water Lines Are Lower Than Surrounding Areas  Business Rule 2: Water flows from Higher Water Levels to Lower Water Levels

S E Water Surface after Flood Water Surface before Flood Planimetric View Cross-Sectional View Flood Extent and Depth Determination (Continued) Flood Depth

Flooded Road Segment Identification Flooded Water Level Road Segments Not Flooded Road Segments Flooded Road Segment outside Flood Extent S1 S2 T1 T2 P2 T3 T4 T5 T6

Test Area

Test Results ---- Flood Extent and Depth

Test Results ---- Flooded Road Segment Identification Legend Flood Extent Flooded Road Segment Interstate Highway Legend Flood Extent Flooded Road Segment Interstate Highway

Test Results ---- Flooded Road Segment Identification (Continued) Legend Interstate Highway Flooded Road Segment Flood Extent