Accuracy Evaluation of a 3-D Spatial Modeling Approach to Model Linear Objects and Predict Their Lengths

Abstract

Real world objects are three-dimensional. Numerous applications in geographic information systems (GISs) require modeling spatial objects in a 3-D space, but many current GISs only represent two-dimensional information. The GIS community has been struggling with solving complex problems dealing with 3-D objects using a 2-D approach.

This research focused on modeling linear objects in a 3-D space, predicting their 3-D distances, and evaluating the accuracy. A point model was developed, which modeled a 3-D line with a group of 3-D points (with X/Y/Z-coordinates) connected by straight lines. It required two input datasets, an elevation dataset and a planimetric line dataset. With elevation datasets in different formats (point data and digital elevation models (DEMs)), two approaches were proposed, differing in how the third dimension (elevation) was introduced. With point data, a snapping approach was developed. With DEMs, elevations for points uniformly distributed along planimetric lines were obtained via bilinear interpolations. Mathematical equations were derived to predict 3-D distances.

A case study was designed in the transportation field because of the rich source of linear objects and the criticality of 3-D distances in GIS-T and LRS. Two elevation datasets were used: LIDAR and national elevation dataset (NED). LIDAR datasets were further categorized into point data and DEMs (20-ft and 50-ft resolutions). Two intervals were taken to locate points planimetrically along lines when using DEMs (full cell size and half cell size). Consequently, each line was associated with seven calculated 3-D distances (one from LIDAR point data, two from LIDAR 20-ft DEM, two from LIDAR 50-ft DEM, and two from NED).

The accuracy of predicted 3-D distances was evaluated by comparing them to distance measurement instrument (DMI) measured distances. Errors were represented in two formats: difference and proportional difference (based on DMI measured distances) between the predicted 3-D distance and the DMI measured distance, taking road types into consideration. Evaluation methods included descriptive statistics, error distribution histograms, hypothesis tests, frequency analysis, and root mean square of errors (RMSE). The effects from the use of different elevation datasets and intervals on the accuracy were evaluated via a sensitivity analysis. The effects from the geometric properties of linear objects on the accuracy were evaluated via significant factor analyses. Factors under consideration included distance, average slope and weighted slope, average slope change and weighted slope change, and the number and density of 3-D points. The usefulness of this research was proved by applying the resulting 3-D road centerlines to determine flooded road segments under flooding scenarios.

This research concluded that errors in the predicted 3-D distance varied with elevation datasets and road types, but not with the use of different intervals with the same elevation dataset, given the interval was less than or equal to the cell size. Using elevation datasets with higher vertical accuracies resulted in higher accuracies in predicted 3-D distances. In this research, using LIDAR point data improved the accuracy by 28% and using LIDAR DEMs improved the accuracy by 6%, compared to using NED data, with 100% RMSEs as the accuracy measure.

It was also concluded that there was a positive association between the error and any one of these factors from the aspect of the difference but a negative association from the aspect of the proportional difference. Each factor had a threshold, above which effects from the increase of the factor value were insignificant.