AN ADAPTIVE METHOD FOR THE CONSTRUCTION OF DIGITAL TERRAIN MODEL FROM LIDAR DATA Xiaohui Yuan† , Liangmei Hu† , Bill P. Buckles† , Laura Steinberg , Vaibhav Sarma† †
Dept. of Computer Science and Engineering, University of North Texas 3940 N. Elm, Denton, TX 76207, {xyuan, lhu, bbuckles}@cse.unt.edu Dept. of Environmental and Civil Engineering, Southern Methodist University 6425 Boaz Lane, Dallas TX 75205,
[email protected] 1. INTRODUCTION LiDAR (Light Detection And Ranging) is an active sensor now approved by FEMA for construction of digital terrain models (DTMs). A LiDAR acquisition device measures the distance to the target by calculating the time spent in signal reflection. Together with a Global Positioning System and a Inertial Navigation System, a three-dimensional (3-D) land surface topology is obtained via an airborne LiDAR. The applications of LiDAR began slowly but are gaining momentum as the instruments and support for them improve [1, 2]. Given elevations, urban landscapes can be accurately visualized in 3-D, damage from natural disasters can be assessed (based on pre- and post-disaster data) or predicted (given the water level), line-of-sight analysis for proposed transportation corridors can be performed, and fine-scale air contaminant models which rely on accurate depictions of the cityscape can be improved. An important step in many of these applications is to separate bare earth measurements and construct a DTM [3, 4]. In this paper, we present an adaptive method to remove above-ground LiDAR measurements and generate DTMs. LiDAR measurement of New Orleans are used to test our algorithms. 2. METHODOLOGY The histogram of the elevation of a bare terrain tends to have a symmetric distribution in a well-selected window with slowchanging terrain [5]. In the presence of buildings and other manmade structures, such a histogram is usually skewed to one side. Minimizing the magnitude of skewness is hence providing us a clue to remove the above-ground structures. Skewness is defined as the third standardized moment about the mean: μ3 (1) λ= 3 σw where μ3 is the third moment and σw is the standard deviation of LiDAR data in a window w. μ3 can then be computed as follows: N (li − μw )3 (2) μ3 = i=1 N −1 where li is the LiDAR sample, μw is the mean of the LiDAR data points in the window w, and N is the number of samples. The skewness for any symmetric distribution is near zero. Negative values for the skewness indicate that the distribution has a relative longer tail to the left; and positive values for the skewness indicate that the distribution has a relative longer tail to the right. Selecting an appropriate window is critical to ensure the validity of the histogram distribution. In a flat region, such a window can be fixed and selected a priori. In the hilly region, imbalanced terrain elevation could affect the histogram distribution and makes it skewed even without manmade structures. Hence, a smaller window shall be used for distribution analysis. Assume gradients at every point is calculated, i.e., δx and δy (gradients in X-direction and Y-direction, respectively). The window, centered at (x, y), has sides inversely proportional to the X- and Y- gradients: a a and Δy = (3) Δx = 1 + |δx | 1 + |δy | The algorithm is summarized as follows:
1. 2. 3. 4. 5. 6. 7. 8.
Grid LiDAR data into 2-D matrix L Generate coarse-scale view La by applying an average filter Compute the sliding window w based on the gradient in La for every window w (i.e., Δx and Δy ) Compute the skewness λ while λ > 0 Select the highest points and their connected neighbors Interpolate the selected points using their neighboring measurements
An example result is illustrated in Figure 1. Fig 1(a) shows the gridded LiDAR points that contains high-rise buildings, residential buildings, superdome, and an elevated highway bridge. Fig 1(b) shows the regions that were removed and interpolated to reveal the bare terrain.
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(b)
Fig. 1. Experimental results. (a) gridded Lidar data points. (b) regions showing removed manmade structures.
3. CONCLUSIONS In this paper, we have presented a method to extract DTM from LiDAR data clouds automatically. This method is based on a valid theory of elevation distribution and requires very few manually selected parameters. Experiments were performed with LiDAR data from the city of New Orleans and we demonstrated good results with respect to human perception. Further studies will be conducted in quantitative evaluation and a comparison with existing methods. Also, fusion with images in different modalities will be explored in our future work. 4. REFERENCES [1] P. Gamba and B. Houshmand, “Digital surface models and building extraction: A comparison of IFSAR and LIDAR data,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 4, pp. 1959–1968, July 2000. [2] G. Sithole and G. Vosselman, “Experimental comparison of filter algorithms for bare-earth extraction from airborne laser scanning points clouds,” ISPRS Journal of Photogrammertry and Remote Sensing, vol. 59, pp. 85–101, 2004. [3] H. S. Lee and N. H. Younan, “DTM extraction of LiDAR returns via adaptive processing,” IEEE Transactions on Geoscience and Remote Sensing, vol. 41, no. 9, pp. 2063–2069, Sept. 2003. [4] G. Sohn and I. Dowman, “Data fusion of high-resolution satellite imagery and LiDAR data for automatic building extraction,” ISPRS Journal of Photogrammertry and Remote Sensing, vol. 62, pp. 43–63, 2007. [5] M. Bartels, H. Wei, and David C. Mason, “DTM generation from LIDAR data using skewness balancing,” in Proceedings of the 18th International Conference on Pattern Recognition, Hong Kong, China, Aug. 2006, pp. 566–569.
