Published in: Proceedings of the ASPRS Annual Conference. St. Louis, Missouri, April 2001. SURFACE ESTIMATION BASED ON LIDAR Wolfgang Schickler Anthony Thorpe Sanborn 1935 Jamboree Drive, Suite 100 Colorado Springs, CO 80920 wschickler@sanborn.com athorpe@sanborn.com Abstract In the past several years, the use of airborne laser systems or LIDAR for the rapid collection of digital terrain models (DTMs) has proliferated. Flood plain studies, contouring, road engineering projects, volumetric computations, ortho-photo production, and mapping for beach erosion are just some of the applications driving the demand for this technology. The ability of LIDAR systems to capture accurate spot heights at an extremely rapid rate is the principle reason behind LIDAR's success. Many applications, for example, contouring, require a bald-earth DTM. Unfortunately, the raw data points captured by LIDAR do not constitute a bald-earth DTM. Even though most LIDAR systems can measure "lastreturn" data points, these "last-return" points often measure ground clutter like shrubbery, cars, buildings, and even the canopy of dense foliage. Consequently, raw LIDAR points must be post-processed to remove these undesirable returns. The degree to which this post processing is successful is critical in determining whether LIDAR is cost effective for large-scale mapping applications. We present our approach to estimating bald-earth surfaces from LIDAR data. Our approach is different from typical approaches in that we estimate a surface based on the original LIDAR points while at the same time considering important supplementary information. This other information includes independently measured breaklines and surface categories. We use a least-squares adjustment with robust estimation similar to that proposed by (Kraus, Pfeifer, 1998). The surface model is represented using a triangular irregular network or TIN. We present examples from a real mapping project that demonstrate the success of this approach. Introduction LIDAR systems have become one of the prime methods for rapid collection of large-scale height data for various applications, especially in Europe where LIDAR is used for creating and updating national DTM s. Although LIDAR technology is widely used by mapping companies, the reliable, efficient creation of accurate DTM s from LIDAR measurements is problematic. (Huising, Gomes, 1998) identify two major problems: the elimination of systematic errors and the selection of ground points, i.e. the derivation of a bald-earth DTM from LIDAR measurements. The presence of systematic errors can often be observed between overlapping LIDAR strips. The modeling and elimination of these systematic errors is currently a topic of research (Burman, 2000). The second problem is the derivation of a bald-earth DTM from LIDAR measurements. LIDAR pulses measure not only on the ground but also ground clutter like shrubbery, cars, buildings, and tree canopies. Consequently, raw LIDAR points must be postprocessed to remove these undesirable returns. In this paper we paper we focus on the second problem, the derivation of a bald-earth DTM from LIDAR measurements. Previous Work Several publications deal with the problem of bald-earth DTM derivation from LIDAR measurements. Almost all of them either use one of the following two approaches or a combination of both. The first approach is a filtering
method that is either based on mathematical morphology or based on the analysis of structural information like slope. The second approach is a surface estimation method that is usually based on least squares interpolation. (Lindenberger, 1993) adopts the filtering approach and uses a morphological filter to eliminate non-ground points. He applies an opening to the LIDAR data using a horizontal structural element. This is followed by an autoregressive process to improve the results. (Kilian et al, 1996) also use a morphological filter. They then perform a weighted smoothing of the surface based on the distance of the individual LIDAR points to the opened surface. They conclude that the size of the structural element used for the opening is a critical parameter for which there is no single optimal value. They suggest the usage of multiple openings with different sizes of structural elements. (Vosselman, 2000) presents an approach for LIDAR data filtering that is closely related to a morphological filter. He estimates an optimal filter function by analyzing the height differences between ground points in training data sets. He shows that his slope-based filtering is superior to a morphological filter with a horizontal structural element. (Kraus, Pfeifer, 1998) describe an approach for DTM estimation based on a robust, finite-element estimation for data with an asymmetrical error distribution. Our approach is an extension of this work and is described in more detail later. There are several commercial packages available for the post processing of LIDAR measurements. The (Optech, 2001) LIDAR system comes with a post-processing package. The algorithm used for the filtering is not published. The parameter set for the algorithm and the artifacts observed in the processed data suggest that the algorithm is based on a morphological filter. (TerraSolid, 2001) offers a variety of LIDAR processing modules, including TerraScan for the filtering and thinning of LIDAR data. This package includes different methods for slope-based filtering and thinning of LIDAR data. (INPHO GmbH, 2001) offers a product called SCOP for the derivation of DTM s and contours from various sources, including LIDAR data. The approach for the LIDAR data processing is based on the method described in (Kraus, Pfeifer, 1998). Overview of Our Approach We call our approach FASE for Filtering And Surface Estimation. It is based on the estimation technique proposed by (Kraus, Pfeifer, 1998). We favor this approach because it yields a direct estimate of the ground surface without a prior process of filtering. In other words, vegetation and other ground-clutter measured by the LIDAR are removed implicitly during the estimation process. This provides greater control of the results because all information is available to the surface estimator, which can make a "more informed" estimate of the ground surface. Our approach differs from (Kraus, Pfeifer, 1998) in the following ways. First, our surface model is a triangulation and not a rectangular grid. Second, we include independently measured mass-points and break-lines in the estimation with appropriate weighting. Third, we add additional curvature constraints and slope constraints to control the shape of the estimated surface. Fourth, we employ the concept of surface classes to guide the estimation process. These features are described in more detail in the next section. Surface Estimation The next sub-sections give a brief introduction in the (Kraus, Pfeifer, 1998) approach for surface estimation in wooded areas. We introduce our extensions and describe our functional model in more detail. Review of the Kraus approach The (Kraus, Pfeifer, 1998) approach for surface estimation is based on a robust finite element estimation for data with an asymmetrical error distribution. A conventional robust estimation iteratively de-weights observations with large residuals according to the weight function shown as a dashed line in Figure 1. (Kraus, Pfeifer, 1998) propose a decentralized, one-sided weight function as shown as a solid line in Figure 2. This one-sided weight function only de-weights observations with large positive residuals. It favors LIDAR points that are on the ground by lowering the weights of points on trees or other vegetation.
They propose a one-sided weight function to compute the weights P as a function of normalized residuals, nr. It has the following form. P(nr) = 1 : nr < g 1 / ( 1 + ( a ( nr g ) ) 2 : nr g They suggest changing the parameters of the weight Figure 1 One-sided robust weight function function, especially the parameter defining the origin g (solid) and robust weight function (dashed). and the shape or the aggressiveness a, based on the local distribution of the LIDAR data. (Pfeifer, et.al, 1998) describe an adaptive method to accomplish this, which uses a histogram analysis. Surface Model We use a surface model based on a Delaunay triangulation and not a rectangular grid. The elevation of each node in the triangular grid is considered an unknown and is estimated by the process. The main advantage of this model over the rectangular grid is that it adapts easily to varying point densities. That is, a sparse point distribution can be used in flat areas or in areas where the LIDAR data are scarce. Conversely, where the terrain is broken or where the LIDAR data are dense, the node spacing in the triangulation can be tightened to better estimate surface detail. For mapping products like large-scale contouring, our experience shows that the LIDAR data must often be supplemented with break-lines and mass-points. LIDAR data sometimes is not dense enough to accurately model sharp surface discontinuities. In addition, dense undergrowth near small streams, for example, prevents the LIDAR pulses from penetrating to the true ground surface. Our use of a triangulated surface model allows us to elegantly include externally measured break-lines and mass-points into the estimation process. Figure 2: Surface model based on an equilateral Delaunay triangulation with added break-lines. The surface model is constructed as follows. A triangulation is constructed from any available mass-points and break-lines. Then, a regularly spaced grid of points is added to the triangulation. These grid points are generated such that equilateral triangles are produced in the triangulation. Elevations for every node in the triangulation are estimated as described in the next section. Note that elevations for the mass-points and break-lines are re-estimated too. In doing so, the estimation algorithm takes into account the relative accuracy of the LIDAR points and the externally measured break-lines and mass-points. Figure 2 shows an example of our surface model based on an equilateral triangulation of grid points plus additional break-lines. Note that although supplementary break-lines and mass-points help to define the surface, our approach does not depend on them. Typically, break-lines and masspoints are only used for high-accuracy products like large-scale contouring. In the case of contouring, break-lines can improve the appearance of contours, for example, near road edges.
Functional Model The height of each node in the triangulation is represented by an unknown in a robust estimation. The functional model for the surface estimation is based on the following four different types of observations: 1. Each LIDAR point constitutes one observation equation. The functional relation between the LIDAR point and the unknown triangulation points is based on the Hessian normal form for a planar surface. 2. Slope constraints are applied to the each edge of the triangulation. Each observation equation is based on the slope (first derivative) of the edge. The expected value of the slope is assumed to be zero. 3. Curvature constraints are applied to each edge in the triangulation that is common to two triangles. Each observation equation is based on a numerical estimate of the second derivative across the edge. The expected value of the curvature is assumed to be zero. No curvature constraints are added to edges belonging to a breakline. 4. Break-line points and mass-points are introduced in a Bayesian manner as direct observations of the unknowns. An equation system is constructed from the above observations. The least-squares solution to the system uses a weight matrix that is derived from the a-priori variances of the observations. These weights are normalized by area. In accordance with robust estimation theory, the weights for the LIDAR point observations are iteratively recomputed based on normalized residuals and the previously described weight functions. We can tune the input parameters, for example the constraint weights or the a priori variances of the LIDAR points, to achieve smooth, rugged, flat, or horizontal surfaces. This is similar to an approach for surface estimation based on matched image points implemented in MATCH-T and described in (Wild, et al, 1996). Surface Classes Motivation. Others, for example Vosselman (2000), suggest having multiple parameter settings, which are applied depending on the morphological characteristics of the terrain. This is a central concept in our approach: we make use of surface classes to assist the estimation process. Input parameters that define the functional and stochastic model of the estimation process have a profound influence on the resulting surface. We use surface classification information like forest areas, building outlines, or water bodies to select different parameter sets. We use the term "surface class" to describe the pairing of each type of surface classification with a corresponding parameter set. In addition, a LIDAR project area will also include many different surface types: different kinds of forests with leaf-on or leaf-off conditions, open grassland, rivers, lakes, and urban areas with buildings and individual trees. In dense trees, the penetration rate of the LIDAR pulses to the ground may be less than 20%. Water bodies can cause specula reflections, which can result in no water level measurements. In urban areas, the LIDAR returns will measure miscellaneous ground clutter like cars, bushes, and buildings. In other words, the distribution of recorded LIDAR points is significantly different for each of these surface areas. Consequently, using a fixed parameter set for an entire project area will yield a result that is a compromise. Parameters chosen to optimize surface estimation in trees will give an overly generalized surface in open areas. This is additional motivation for the use of surface classes. Parameter sets. We have identified four parameters, which significantly impact the shape of the estimated surface. The four parameters we use to model the different surface classes are listed below. 1. The standard deviation of the individual LIDAR points have a direct impact on how close the estimated surface fits these observations (the smaller the standard deviation, the larger the impact of the individual observation). 2. The standard deviation of the curvature constraint affects the smoothness or stiffness of the surface. Stiffer surfaces also tend to discard LIDAR points with large positive residuals, e.g., returns from trees. 3. The standard deviation of the slope constraint defines the levelness of the surface. Smaller standard deviations lead to surfaces that are closer to horizontal. This is useful for modeling water bodies. 4. The parameters of the one-sided robust estimation function control the aggressiveness of the weight function. A more aggressive weight function will favor low points more and high points less.
We call the collection of the above parameters a parameter set. Different parameter sets can be chosen to perform optimal estimation in areas of forest, buildings, or water bodies. Our task is to efficiently choose where to apply each parameter set. Surface regions. We associate different parameter sets with classified regions of the project surface, and we call the resulting association a surface class. Sources for the classified regions include existing GIS data layers, classified hyper-spectral imagery, or photogrammetrically captured polygon boundaries like building outlines. One of our goals is to use the LIDAR data directly to derive some of the surface classes. We have had some success using both the first and last returns to automatically classify tree areas. Automatic building extraction from LIDAR data is currently a research topic. Several promising approaches have been presented to automatically extract the 3-D structure of buildings. Examples are (Brunn, Weidner, 1998) and (Maas, 1999). For the surface regions, we only need the 2-D outlines of buildings. This simpler problem might be solved by creating a triangulation of LIDAR points and looking for close-to-vertical slopes. Implementation. We have implemented our surface classes using inheritance. That is, a sub-class inherits a parameter from its super-class, unless the sub-class overrides the parameter. This allows us to easily define, for example, a tree super-class with leaf-on and leaf-off sub-classes. The table below shows six examples of surface classes, each with a qualitative definition of the four parameters we use to control the surface. LIDAR point Aggressiveness of Slope Constraint Curvature Constraint weight weight function Trees leaf-off Moderate Turned off Moderate High Trees leaf-on Moderate Turned off High High Buildings Very low Turned off High Normal Lake Normal Very high High High River Normal High High High Open Space Normal Turned off Normal Normal Examples We present examples for two different small areas in Gwinnett County, Georgia. The LIDAR data were captured from a nominal elevation of 1200m AGL with a nominal point spacing of 2.5m. The data were captured as part of an update-mapping project. Example Area #1 The first area contains several large buildings in an office park. Figure 3 shows an orthophoto of the area overlaid with the planimetric data used for surface regions and for break-lines. Break-lines are shown in yellow and building outlines are shown in red. We show the results for three different DTM extraction techniques in figures 4-9. These techniques are raw data (no filtering), slope-based filtering (TerraSolid), and FASE. Figures 4-6 show the contours from the DTM extracted with each technique, and figures 7-9 show perspectives of each DTM. The same set of break lines was used to generate contours for the filtered data and FASE data. We note the following: 1. The raw data is not useful for a bald-earth DTM as it contains buildings. Notice the presence of significant surface noise caused by the overlap of two LIDAR strips (figures 4 and 7). This example was chosen for its abnormally high elevation bias between the two LIDAR strips, in this case, approximately 30cm. 2. The contours derived from the filtered data set (figure 5) have many undesirable isolations and depressions. 3. The filtering algorithm, by itself, was unable to remove the largest building. Changing the filtering parameters could help but would introduce undesirable effects elsewhere. 4. The FASE output (figures 6 and 9) shows smooth contours with all buildings removed.
Example Area #2 The second example is a residential area that contains two lakes, a forested area, and several medium-sized buildings. Figure 10 shows an orthophoto image of the area overlaid with the planimetric data used for surface regions and for break-lines. Break-lines are shown in yellow, lakes in blue, building outlines in red, and forest outlines in green. We show the results for the three different DTM extraction techniques in figures 11-16. Figures 11-13 show the contours from the DTM extracted with each technique, and figures 14-16 show perspectives of each DTM. The same set of break lines was used to generate contours for the filtered data and FASE data. We note the following: 1. The raw data is not useful for a bald-earth DTM as it contains buildings and trees. Note also the contour problems in lakes due to overhanging trees (figure 11). 2. The contours derived from the filtered data set (figure 12) have many undesirable isolations and depressions. In our opinion, they have too much character. 3. Note also in figure 12 that the drainage break-line from the lake "digs" below the LIDAR data. This causes the undesirable contour artifacts along the break-line. 4. The filtered data set does not model the lakes properly. 5. The FASE output (figures 13 and 16) shows that the lakes have been correctly modeled, buildings have been removed, vegetation is removed, and break-lines have been incorporated. Discussion The estimation technique that we employ eliminates many of the problems seen with filtering and point classification techniques. We assert that estimating a new surface has an advantage over methods that pick and choose points from an data set in which individual points have errors. Hill cut-off problems (morphological filtering) and oddly spaced point clusters (slope based filter) are not present in our results. Using surface estimation rather than filtering to extract digital terrain models (DTM) also has the benefit of smoothing noise in the LIDAR data. When two strips of LIDAR data overlap, they will not match exactly. Even if the elevation bias between the two strips is only 10cm, the combined point surface will be noisy. Contours generated from these points appear choppy and aesthetically unpleasing. When a new surface is estimated through these noisy points, the result is a smoother surface that represents the average of the points. This surface is most likely more accurate as well. Our use of surface classes provides a critical benefit. By guiding the surface estimation process with surface classes, we are able to reliably remove ground clutter like vegetation and buildings, an extremely important function. Water bodies can also be forced to be flat. When coupled with a stereo workstation, FASE is a powerful editing tool for LIDAR data. Stereo operators can concentrate on helping the estimation process with supplementary break-lines and mass-points instead of performing bulk edits on huge quantities of raw LIDAR points. Stereo operators can also look directly at contours. They need not be bothered with the performance degradation and display saturation associated with displaying 150,000 LIDAR points in a stereo model. One drawback to our approach is the computational effort. The computational time for this surface estimation exceeds that required for a morphological or slope-based filter. In our tests, the computational time required for a large-scale stereo-model was 10 minutes. This cost must be weighed against the benefits to determine whether the benefits of the surface estimation technique are justified. Certain LIDAR applications, like surface models for small-scale ortho-photography, probably don't require this technique. Our approach is not limited to the estimation of a bald earth surface. Modifying the one-sided weight function so that high points are favored over low points allows estimating a canopy surface that follows the top of trees and buildings from last-return LIDAR data. This may be useful for Telecom applications that require surfaces for lineof-sight analysis.
Conclusion We have described an approach to estimating bald-earth surfaces from LIDAR data. Our approach, called FASE, is based on a surface estimation technique supplemented with additional information in the form of breaklines, mass-points, and surface classes. The examples we show demonstrate the success of this approach and its potential to automate the extraction of high-quality digital terrain models from LIDAR data. We will concentrate future research to developing better classifiers for vegetation and buildings. In essence, our goal is to develop an automated method of detecting buildings and vegetation areas directly from the LIDAR data. Information like return intensity and first-and-last returns will be helpful in this regard. Acknowledgments The imagery and LIDAR data used in the examples are owned by Gwinnett County. We thank them for permission to use the data for this publication. We give credit to Martin Huber from Munich University who developed the first prototype of FASE during an Internship program at ASI. References: Brunn, A., Weidner, U., (1998). Hierarchical Bayesian Nets for Building Extraction Using Dense Digital Surface Models, ISPRS Journal for Photogrammetry & Remote Sensing, Vol. 53, No.6, 1998, pp. 296-307. Burman. H., (2000). Adjustment of Laser Scanner Data for Correction of Orientation Errors, International Archives of Photogrammetry and Remote Sensing, Vol. XXXIII, Part B3, Amsterdam 2000, pp. 125-132. Huising, E. J., Gomes Pereira, L. M., (1998). Errors and accuracy estimates of laser data acquired by various laser scanning systems for topographic applications, ISPRS Journal of Photogrammetry and Remote Sensing, Vol 53, No. 5, 1998, pp. 254-261. INPHO GmbH, (2001). URL: http://www.inpho.de/ visited Jan. 2001. Kilian, J., Haala, N., Englich, M., (1996). Capture and evaluation of airborne laser scanner data, International Archives of Photogrammetry and Remote Sensing, Vol. XXXII, Part B3, Vienna pp. 383-388. Kraus, K., Pfeifer, N., (1998) Determination of terrain models in wooded areas with airborne laser scanner data, ISPRS Journal of Photogrammetry & Remote Sensing, Vol. 53, 1998. Maas, H.-G., (1999). Fast determination of parametric house models from dense airborne laser scanner data. IAPRS, Vol. 32, Part 2W1, 5W1, IC5/3W, Bangkok, Thailand, 1999. Optech, (2001). URL: http://optech.on.ca/ visited Jan. 2001. Pfeifer, N., Koestli, A., Kraus K., (1998). Interpolation of Laser Scanner Data Implementation and First Results, International Archives of Photogrammetry and Remote Sensing, Vol. XXXII, Part 3/1, Columbus, pp. 153-159. TerraSolid, (2001). URL: http://terrasolid.fi/tscan.htm visited Jan 2001. Vosselmann, G., (2000). Slope Based Filtering of Laser Altimetry Data, International Archives of Photogrammetry and Remote Sensing, Vol. XXXIII Part B3, Amsterdam 2000, pp. 935-942. Wild, D., Krzystek, P., Madani, M., (1996). Automatic Breakline Detection using an Edge Preserving Filter, International Archives of Photogrammetry and Remote Sensing, Vol. XXXII, Part B3, Vienna 1996.
Figure 3: Orthophoto image overlaid with planimetric data for example area #1. Figure 4: Contours derived from the raw LIDAR surface. Figure 5: Contours derived from filtered LIDAR surface and supplementary break-lines. Figure 6: Contours derived from the FASE surface and supplemental break-lines.
Figure 7: Perspective view of raw LIDAR surface Figure 8: Perspective view of filtered LIDAR surface and supplementary break-lines. Figure 9: Perspective view of FASE surface.
Figure 10: Orthophoto image overlaid with planimetric data for example area #2. Figure 11: Contours derived from the raw LIDAR surface. Figure 12: Contours derived from filtered LIDAR surface and supplementary break-lines. Figure 13: Contours derived from FASE surface and supplementary break-lines.
Figure 14: Perspective view of raw LIDAR surface. Figure 15: Perspective view of filtered LIDAR surface and supplementary break-lines. Figure 16: Perspective view of FASE surface.