Estimating plot-level tree heights with lidar: local filtering with a canopy-height based variable window size

Transcription

1 Computers and Electronics in Agriculture 37 (2002) 71/95 Estimating plot-level tree heights with lidar: local filtering with a canopy-height based variable window size Sorin C. Popescu a,, Randolph H. Wynne a, Ross F. Nelson b a Department of Forestry, Virginia Tech, Blacksburg, VA 24061, USA b Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD, USA Abstract In recent years, the use of airborne lidar technology to measure forest biophysical characteristics has been rapidly increasing. This paper discusses processing algorithms for deriving the terrain model and estimating tree heights by using a multiple return, high / density, small-footprint lidar data set. The lidar data were acquired over deciduous, coniferous, and mixed stands of varying age classes and settings typical of the southeastern US. The specific objectives were: (1) to develop and test algorithms to estimate plot level tree height using lidar data, and (2) to investigate how ground measurements can help in the processing phase of lidar data for tree height assessment. The study area is located in the Piedmont physiographic province of Virginia, USA and includes a portion of the Appomattox-Buckingham State Forest (37825?N, 78841?W). Two lidar processing algorithms are discussed*/the first based on single tree crown identification using a variable window size for local filtering, and the second based on the height of all laser pulses within the area covered by the ground truth data. Height estimates resulted from processing lidar data with both algorithms were compared to field measurements obtained with a plot design following the USDA Forest Service Forest Inventory and Analysis (FIA) field data layout. Linear regression was used to develop equations relating lidar-estimated parameters with field inventories for each of the FIA plots. As expected, the maximum height on each plot was predicted with the highest accuracy (R 2 values of 85 and 90%, for the first and the second algorithm, respectively). The variable window size algorithm performed better for predicting heights of dominant and co-dominant trees (R 2 values 84/85%), with a diameter at breast height (dbh) larger than 12.7 cm (5 in), when compared with the algorithm based on all laser Corresponding author. Address: Department of Forestry, 319 Cheatham Hall, Virginia Tech, Blacksburg, VA 24061, USA address: spopescu@vt.edu (S.C. Popescu) /02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S ( 0 2 )

2 72 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 heights (R 2 values 57/73%). The use of field-based height thresholds when processing lidar data did not bring significant gains in explaining the total variation associated with tree height. The technique of local filtering with a variable window size considers fundamental forest biometrics relationships and overall proved to give better results than the technique of all laser shots. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Lidar; Forest inventory and analysis; Tree height; Interpolation; Digital elevation model; Variable window size 1. Introduction Airborne laser sensors allow scientists to analyze forests in a 3-D format over large areas. In contrast to monoscopic optical remote sensing methods, which yield information on horizontal forest pattern, modern lidar systems provide georeferenced information of the vertical structure of forest canopies. Laser pulses from a sensor carried aboard an aircraft are directed toward the ground to collect ranging data to the top of the canopy, and in some instances, to subcanopy layers of vegetation and to the ground. Airborne lidars have been used to describe topographic relief (e.g., Krabill et al., 1984; Schreier et al., 1985; Bufton et al., 1991; Ritchie, 1995), and forest vegetation characteristics, such as percent canopy cover, biomass (e.g., Nelson et al., 1984, 1988a,b), and gross-merchantable timber volume (Maclean and Krabill, 1986). Previous studies that focused on estimating forest stand characteristics with scanning lasers used lidar data with either relatively large laser footprints, 5/25 m, (Harding et al., 1994; Lefsky et al., 1997, 1999; Weishampel et al., 1997; Blair et al., 1999; Means et al., 1999) or small-footprints, but with only one laser return (Næsset, 1997a,b; Magnussen and Boudewyn, 1998; Magnussen et al. 1999). A small-footprint lidar with the potential to record the entire time-varying distribution of returned pulse energy or waveform was used by Nilsson (1996) for measuring tree heights and stand volume. In recent years, the use of airborne lidar technology to measure forest biophysical characteristics has been rapidly increasing. In addition to providing a characterization of ground topography, lidar data give new information about the canopy surface and vegetation parameters, such as height, stem density, and crown dimensions, which is critical for environmental modeling activities. Airborne lidar data combine both surface elevations and accurate planimetric coordinates, and processing algorithms can identify single trees or groups of trees in order to extract various measurements on their 3-D representation. Laser scanner systems currently available are in a fairly mature state of art, while the processing of airborne scanning lidar data still is in an early phase of development (Axelsson, 1999). Airborne laser scanning represents an emerging technology that is making the transition from the proof-of-concept to reliable uses (Flood and Gutelius 1997). It is a general feature of new technologies that technical potential opens the ground for new applications. Airborne laser scanning is presently

3 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 73 in that process, spreading into other fields beyond the generation of terrain models (Ackermann, 1999). Existing processing algorithms for lidar data are implemented through proprietary software and generally try to filter vegetation to obtain the terrain elevation model. The basic processing task that needs to be accomplished before attempting to estimate forest parameters is the characterization of the terrain elevation and creation of a digital elevation model (DEM), as a subset of the digital surface model (DSM) obtained from raw laser points. It is the unique ability of laser scanning to measure ground elevation directly, most often through penetrating the tree canopy; that is one of the major advantages that lidar offers over traditional photogrammetry when operated in forested areas. However, few papers published on the subject of separating lidar data into vegetation and terrain points provide all the algorithmic details. In most of the forestry studies of lidar, the terrain elevation is computed by the lidar data providers (e.g., Næsset, 1997a,b; Means et al., 2000). Most of the algorithms for removing the vegetation laser hits are based on iterative algorithms that combine filtering and thresholding methods (Kraus and Pfeifer, 1998; Axelsson, 1999; Jaafar et al., 1999; Petzold et al., 1999). The irregularly dispersed laser points assumed to correspond to the ground are used with appropriate interpolation methods to derive the high /accuracy DEM. Lam (1983) offers a comprehensive review of spatial interpolation methods. For point interpolation, the numerous methods can be classified into exact and approximate. Exact methods include distance-weighting, Kriging, spline interpolation, triangulation, and finite-difference methods. Approximate methods include power-series trend models, Fourier models, distance-weighted least squares, and least-squares fitting with splines. Despite intense efforts in the creation of high /resolution DEMs from lidar data, driven by either commercial or scientific purposes, the characterization of terrain topography under forest conditions is still a challenge. Some lidar sensors (e.g., Optech ALTM 1020, Optech Inc.) can be toggled to record either the first or the last return, thus two flights are necessary over the same area to get the bare ground terrain model and the top of the canopy surface. Image subtraction with first- and last-return interpolated data can be used to derive tree heights (Young et al., 2000), though not all of the last-return hits penetrate to the ground. Surveys in the U.S. Pacific Northwest carried out using the Optech ALTM 1020 scanning system indicated a minimum 20/30% penetration of coniferous canopies (Flood and Gutelius, 1997). In the same region, with conifer-dominated stands and dense overstory, Means (2000) experienced a very low penetration to the ground, only 1/5%, for a small-footprint lidar. Kraus and Pfeifer (1998) estimated a penetration rate of less than 25% for their lidar study in the Vienna Woods (Wienerwald) in Austria, using an Optech ALTM 1020 lidar system. Measurement of stand height by current photogrammetric or field survey techniques is time consuming and expensive. Tree heights have been derived from scanning lidar data sets and have been compared with ground-based canopy height measurements (Næsset, 1997a,b; Magnussen and Boudewyn, 1998; Magnussen et al., 1999; Young et al., 2000). Recent studies show that, in moderate to dense forests, small-footprint lidars tend to underestimate stand height (Nilsson, 1996; Næsset,

4 74 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/ a). More frequent laser sampling of the crown shoulders than the tree apex biases canopy heights toward low values. Potential future uses of the lidar technology that have been foreseen in the literature (e.g., Means, 2000) include the assessment of forest biomass, measurement of forest structural attributes critical to understanding forest ecosystem condition, and automated processing and integration with co-registered multi- and hyperspectral digital imagery. Data from large-footprint lidar may become publicly available with the launch of the vegetation canopy lidar in the year 2004, as a result of the collaboration between NASA and the University of Maryland (Dubayah et al., 1997). Small-footprint lidars are available commercially and more research on their potential for forestry applications is needed. Applications of small-footprint lidar have not progressed too far, mainly because of the current cost of lidar data. However, with an anticipated decline of lidar data cost in the near future combined with promising current research efforts, the use of lidar in forestry is expected to extend over many aspects of forest measurements. Situated in this context, the overall objective of this study is to develop robust processing and analysis techniques to facilitate the use of airborne laser data for forest tree height assessment. The specific objectives are: (1) to develop and test algorithms to estimate plot level tree height using lidar data, and (2) to investigate how ground measurements can help in the processing phase of lidar data for tree height assessment. 2. Materials and methods 2.1. Study site The study area is located in the southeastern US, in the Piedmont physiographic province of Virginia (Fig. 1). It includes a portion of the Appomattox-Buckingham State Forest that is characterized by deciduous, coniferous, and mixed stands of varying age classes (37825?N, 78841?W). Fig. 2 provides a map of forest stand types covered by the lidar data. A mean elevation of 185 m, with a minimum of 133 m and a maximum of 225 m, and gentle slopes characterize the topography of the study area Ground reference data The ground-truth data collection took place in the leaf-off season in December 1999, while the lidar was flown at the beginning of September, with leaf-on canopy conditions. Three forest vegetation types were covered by the field sampling*/pinehardwoods, upland hardwoods and pine plantations. The leaf-off canopy condition for hardwoods allowed a more accurate measurement of tree heights from the ground. The stand age varied, being approximately 15 years for the pine plantations, 35/55 years for the pine-hardwood mixed stands, and up to 100/115 years for the upland-hardwood stands. The tree species found in the pine-hardwoods stands were white oak (Quercus alba L.), chestnut oak (Quercus prinus L.), northern red oak

5 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 75 Fig. 1. Map of eastern US indicating the location of the study area. (Quercus rubra L.), southern red oak (Quercus falcata Michx.), yellow poplar (Liriodendron tulipifera L.), red maple (Acer rubrum L.), and three species of pines*/virginia pine (Pinus virginiana Mill.), loblolly pine (Pinus taeda L.), and shortleaf pine (Pinus echinata Mill.). In addition to the hardwood species mentioned above, the following species were inventoried in the upland-hardwood stands: pignut hickory (Carya glabra (Mill.) Sweet), scarlet oak (Quercus coccinea Muenchn.), black oak (Quercus velutina Lam.), blackgum (Nyssa sylvatica Marsh.), and American beech (Fagus grandifolia Ehrh.). Of the two subplots located in pine plantations, one was in a pure loblolly pine plantation, and one in a mixed pine species plantation. The plot design followed the USDA Forest Service Forest Inventory and Analysis (FIA) field data layout. An FIA plot consists of a cluster of four subplots approximately ha (0.04 acres) each, with a radius of 7.32 m (24.0 ft) (National Forest Inventory and Monitoring CORE Field Guide, 1998). One plot is distributed over an area of approximately 0.4 ha (1 acre), thus it represents a sample of the conditions within this area. The center plot is subplot 1. Subplots 2, 3, and 4 are

6 76 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Fig. 2. Forest stand types covered by lidar data. located m (120.0 ft) at azimuths 0, 120, and 2408 from the center of subplot 1 (Fig. 3). Subplots are used to collect data on trees with a diameter at dbh of 12.7 cm (5.0 in), or greater. To allow a more detailed inventory of trees within the subplots, Fig. 3. Layout of a single FIA plot with four subplots.

7 we collected tree height and tree position data on trees with a dbh of at least 6.35 cm (2.5 in). Except for the microplot, FIA standards only require measurement of trees with a dbh larger than 12.7 cm. A microplot with a radius of 2.07 m (6.8 ft) was located at the center of each subplot, to account for seedlings and saplings with a dbh above 2.54 cm (1 in), but less than 6.35 cm (2.5 in). A total of 6 plots were measured in the study area, each with 4 subplots. Plot centers (subplot 1 centers) were located on a 200/200 m 2 grid (656/656 ft 2 ), with two rows oriented East/ West, and three columns oriented North/South (Fig. 2). The centers of subplots 1, for all plots, were laid out in the field using a navigational GPS unit. In addition, all FIA subplot locations were determined using 60 s static measurements with a 12- channel GPS receiver, HP-GPS-L4 with a PC5-L data collector (Corvallis Microtechnology, Inc.). The reported mapping accuracy for the HP-GPS-L4 unit, obtained under open sky for 60 s of static measurements is 30 cm (Corvallis Microtechnology and Inc., 2001). Under forest canopy, GPS systems tend to yield from 1.5/3 times less accurate solutions (Craig Greenwald, 2001, Corvallis Microtechnology, Inc., Technical Support, personal communication). Therefore, we estimate sub-meter accuracy for locating the plot centers. For this study, the subplots were pooled together with no reference to the full plot to which they belong, and the results were compared on a subplot basis. From the total of 24 subplots, 11 were located in upland hardwood stands, 11 in pine-hardwood stands, and 2 in pine plantations. On each subplot, the heights of all trees were measured. Trees higher than 7.62 m (25 ft) were measured using a Vertex hypsometer, while smaller trees were measured using a height pole. Several heights less than 7.62 m were measured with both methods and the height difference never exceeded 15 cm (0.5 ft). Diameter at dbh was measured on all trees within the subplots using a diameter tape. Crown width was measured on all trees with a dbh larger than 12.7 cm (5.0 in). Crown width was determined as the average of four perpendicular crown radii measured with a tape from the tree bole towards the subplot center, away from it, to the right and to the left. The location (x,y) of each tree relative to the subplot center was determined by bearing and distance using a distance tape and a compass, with an expected standard error of up to 30 cm (1 ft), depending on the distance to the subplot center. Taking into account the positional accuracy of the differential GPS unit for determining the location of the subplot centers, the maximum error of a tree s position is expected to be approximately 1.5 m. This error only refers to the position of the base of the tree, without considering the deviation of the tree top relative to the base Lidar data set S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 77 The lidar data were acquired over an area of 1012 ha, on September 2, The canopy condition at that time was leaf-on. The lidar system (AeroScan, EarthData, Inc.) utilizes advanced technology in airborne positioning and orientation, enabling the collection of high /accuracy digital surface data. The aerial platform is a Piper Navajo Chieftain aircraft capable of carrying aerial cameras, airborne GPS, inertial measuring units, and the lidar sensor. The carrier airspeed was between 110 /145 knots. The scanning system uses an oscillating mirror with a scanning rate of 10 Hz

8 78 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 and a scanning angle that can be adjusted from 1 to 758. For the Appomattox- Buckingham data set the scanning angle was 108, giving a total field of view of 208. The laser wavelength was 1064 mm and the pulse rate 15 khz. The area was flown at an average altitude of 1980 m above ground level. With a laser beam divergence of 0.33 mrad, the average footprint on the ground was 0.65 m. The laser instrument field of view and the average flying height resulted in an average ground swath width of 699 m. The entire research area was covered by 21 parallel flight lines, oriented North/South. The mission was designed with up to 70% overlap between adjacent swaths to increase the point density on the ground and to correct for the scanning pattern evident in Fig. 4(a) and (b). The sensor had a pulse time width of 12 ns. The AeroScan system is not capable of recording the intensity of the backscattered laser echo, but it is able of recording up to five returns for each laser pulse, depending on the ground cover. We used only the first and last returns. The last return could coincide with the first return where there was only one return per laser pulse, or it could be the second, the third or the fourth, depending on how many returns there were per pulse and which one of the subsequent returns was the last one. The laser point density on the ground, for one swath, was of 0.47 points/m 2 for the first return, 0.20 points/m 2 for the second return, 0.02 points/m 2 for the third return, and points/m 2 for the fourth return. None of the pulses were able to produce a fifth return for the given ground conditions. The point density for the first or last return translates into an average point distance of 1.5 m. The resulting 3-D coordinates of laser hits were compiled in an ASCII mass point file of x, y, z on the UTM projection for each of the laser returns. By pooling all the laser points from adjacent swaths into the same point file, the average interpoint distance decreased to 0.7 m. The provider performed an evaluation of the lidar data, including a comparison of the data from flight line to flight line. This comparison showed Fig. 4. Lidar scanning pattern on the ground; (a) at the center of the swath, (b) at the edge of the swath.

9 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 79 high /accuracy of overlapping lidar lines and no anomalies in the data. All ranges were post-processed by EarthData and corrected for atmospheric refraction and transmission delays. The reported accuracies for the AeroScan lidar system flying at less than 2400 m above ground, over open homogeneous flat terrain, are as follows: an elevation or vertical accuracy of 9/15 cm and an horizontal accuracy of 9/25 cm (EarthData Inc., 2001) Ground digital elevation model As previously stated, one must characterize the ground elevation before estimating the vegetation height. A high laser point density allows an adequate filtering of vegetation hits for the derivation of terrain elevation, since only a relatively low number of laser pulses are able to entirely penetrate the canopy. The separation of laser points into terrain and vegetation hits still remains a difficult task even for lidar data provided by systems that are able to record multiple returns. A 2-D black-andwhite representation of lidar data (Fig. 5) depicts higher points with lighter pixels and lower points with darker pixels. The images in Fig. 5 were created by interpolating the cloud of first-return (a) and last-return (b) lidar points to a regular grid using linear kriging. The interpolated grid cell size was 0.5 m. Both images show the same area with a deciduous stand in the upper-left part of the scene and a young pine plantation in the lower right corner. Though it is evident that Fig. 5(b) shows points of lower heights, with darker pixels, parts of the deciduous tree crowns are still apparent. Assumed ground returns are also noticeable in the young coniferous stand, as they appear as small areas of darker pixels. It is clear that the last return does not necessarily penetrate dense canopy layers to record the ground elevation Fig. 5. (a) First- and (b) last-return, lidar image of a deciduous-coniferous wooded area.

10 80 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 and most of the returns are still vegetation points. In areas with low penetration rates, filtering vegetation points proved to be a difficult task. The step-by-step approach used to construct the terrain model from the raw lidar data points, using only the last return elevation values, is shown in Fig. 6. The first step of our algorithm for constructing the terrain elevation model overlays a grid with a cell size of 5 m (Fig. 7) over the laser points and identifies the minimum laser point elevation in each cell. The terrain slopes are gentle and a smaller grid cell size is not justified, while a larger size would not adequately characterize the micro-relief. Up to this point, the raw laser heights, without interpolation, are used. By interpolating, some information in the original laser points is lost, thus it is recommended to use original laser point values for as long as possible in the processing phase (Axelsson, 1999). Some of the large hardwood crowns, like the one depicted in the rectangle outlined in Fig. 5(a) and (b), cover an area larger than one 5 m grid cell, thus, the minimum elevation laser hit in such situations would not correspond to a ground hit. Fig. 8 shows the result of the second step of the algorithm. The image in Fig. 8 was interpolated using linear kriging from the lidar points selected at the first step. The high laser points hitting vegetation above the ground, though the lowest points in some grid cells, are clearly pictured in Fig. 8 as small tops, with light colored pixels. Also evident in Fig. 8, the darker sinks correspond most probably to true ground hits. The third step of the algorithm identifies the laser points (corresponding to the dark pixels in Fig. 8) by running a local minimum filter with a window size of 3/3 pixels (i.e., 1.5 m) through the interpolated lidar grid. The final DEM (Fig. 9) is interpolated using linear kriging from the irregularly dispersed points identified in step 3. The average point distance for the presumed ground points left in step 2 is 9.8 m. The grid cell size for the interpolated DEM is 0.5 m. The linear kriging technique was chosen for interpolating from dispersed lidar points to a regular grid. Two other techniques were tried for the final DEM: distance-weighting and triangulation with linear interpolation. The inverse distance or distance-weighting gridding method is a weighted average interpolator. The weight given to a particular data point when calculating a grid node is proportional to the inverse of the distance of the observation from the grid node. Kriging is a geostatistical gridding method that uses a variogram to analyze the spatial variation Fig. 6. Flow chart of terrain finding algorithm.

11 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 81 Fig. 7. Grid overlay on the laser points. Fig. 8. Interpolated image from the lowest lidar elevations in 5 m grid cells. present within an area. Triangulation with linear interpolation is an exact interpolator that works by creating triangles by drawing lines between data points. Residuals were calculated as the difference between original laser heights for the first lidar return and interpolated elevation values at the same points in the gridded

12 82 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Fig D view of the terrain DEM (vertical exaggeration of 3). surface, for each of the interpolation methods. Residuals were analyzed and their distribution represented graphically using box-and-whiskers plots. The derivation of the DEM was only an intermediate step towards estimating the tree heights. No ground truth data with points of known elevation were collected to estimate the accuracy of the DEM itself. The accuracy of the DEM is reflected indirectly in the accuracy of estimating tree heights. The laser penetration rate was estimated by analyzing the residuals of the original last return laser points and the interpolated DEM. The penetration rate was considered the percent of original laser points that have residuals less than 15 cm (9/15 cm being the reported lidar vertical accuracy for the AeroScan system, EarthData, Inc.) Tree heights As mentioned before, the frequency of ground returns can be low and the characterization of terrain elevation might degrade the accuracy of the derived canopy heights. The tree canopy height model (CHM) was computed as the difference between tree canopy hits and the corresponding DEM values. The same method was also used by Næsset (1997a), though details on the algorithm used to compute the DEM are not provided. The tree canopy surface is the DSM obtained by interpolating the first lidar returns to a regular grid. A portion of the CHM covering 36.5 ha is presented in Fig. 10, along with the ortho-image of the entire area covered by lidar data. The ortho-image is derived from 1: color-infrared photography acquired by NASA in the fall of Fig. 11 shows a vertical profile through the CHM and a ground photo taken from the same location as the profile. The ground photo was taken in the leaf-off season, but a hardwood stand is visible

13 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 83 Fig. 10. (a) Ortho-image and (b) CHM.

14 84 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Fig. 11. Ground photo showing the location of the vertical profile through the CHM. The arrow to the left of the CHM image indicates the direction of sight for the photo. The vertical profile corresponds to a portion of the left edge of the CHM image. The vertical bar on the profile corresponds to the location of the arrow. (Illustrations in colour online in Science Direct). to the left of a fire line and a pine plantation to the right. The fire line is also clearly visible as a linear feature oriented west-east on the ortho- and CHM-images in Fig. 10(a) and (b). Two approaches were used to estimate the tree height on the same circular areas covered by the field FIA subplots. The first approach is based on the height of all laser pulses within the area covered by a subplot. The FIA subplot circumferences were used to extract all pixel values from the CHM. Pixel values represent

15 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 85 interpolated laser heights for the canopy surface. A priori information from the field data collection regarding the minimum tree height was used to threshold the laser height values in order to eliminate the effect of shrubs and understory vegetation. The minimum tree height measured on the ground in the 24 subplots, including the microplots measurements, was 2.44 m, thus all observations with height values less than that were excluded from computations. In an operational setting, a quick ground inspection and possibly a reduced forest inventory could give indications on forest condition for use in lidar processing. Statistics were extracted for each subplot, and they include mean height of all height values within the circular plot, standard deviation, and percentiles of the heights distribution for 1, 5, 10, 25 (first quartile), 50 (median), 75 (third quartile), 90, 99%, maximum and mode. The standard deviation of laser heights within a subplot was computed, since it is an additional characteristic of the vertical stand structure. Three sets of statistics were extracted from both the field data and lidar data and used with linear regression (Table 1). The first threshold, 2.44 m, was used to eliminate the effect of bushes, stumps, and low-lying vegetation. Næsset (1997b) used a threshold of 2 m to eliminate the effect of stones, shrubs, etc. Similarly, trees with a dbh larger than 6.35 cm were higher than 3.96 m on the ground. The rationale behind using this threshold is that in operational use, a forest inventory with a reduced sample size could provide information regarding the minimum height of trees in this category. It is very improbable that the lidar processing would be done without a preliminary investigation of the ground and vegetation condition. Except for the microplots, the FIA field measurements include only trees with a dbh larger than 12.7 cm. As such, lidar height values below a certain threshold, in this case 7.62 m, should be ignored, since they are probably returns from smaller trees. Linear regression with stepwise selection was used to investigate the estimation of tree heights. The dependent variables were the mean height values for all the trees in each subplot, all trees with dbh larger than 6.35 cm, all trees with dbh larger than 12.7 cm, and the maximum tree height for each subplot. The second method to estimate tree heights is based on single tree identification. A common technique used to identify tree locations on high /resolution optical images uses a local maximum (LM) filter with a static-sized, user specified, moving window, commonly 3/3, 5/5, and 7/7 pixels, depending also on the pixel size (Niemann et al., 1999; Pinz, 1999). The LM technique used with optical images is based on the fact that the reflectance of a tree crown is typically greatest at its apex. The LM technique used with lidar data operates on the assumption that the highest laser elevation value among laser hits of the same tree crown is the apex. Successful identification of the tree location using the LM technique depends on the careful selection of the filter window size. If the filter size is too small or too large, errors of commission or, respectively, omission occur. The static nature of this technique is inconsistent with the complex canopy structure of hardwood and mixed pinehardwood stands. Thus, the second method for estimating tree height uses a variable window size LM technique that operates under the assumption that there are multiple tree crown shapes and sizes and that the moving LM filter should be adjusted to an appropriate size that corresponds to the spatial structure found on the

16 86 Table 1 Variables used in linear regression Set of variables Dependent variables (measured on the ground) 1 Mean height of all trees and maximum height 2 Mean height of all trees with a dbhe/6.35 cm and maximum height 3 Mean height of all trees with a dbhe/12.7 cm and maximum height Independent variables Method based on all laser heights/ subplot: percentiles, maximum, and mode for Heights distribution of pixel values higher than 2.44 m Heights distribution of pixel values higher than 3.96 m Heights distribution of pixel values higher than 7.62 m Variable window size method: mean height, minimum and maximum height, standard deviation of height, median, 1st and 3rd quartiles, and number of trees for Lidar identified trees higher than 2.44 m Lidar identified trees higher than 3.96 m Lidar identified trees higher than 7.62 m S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95

17 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 87 lidar image and on the ground. Daley et al. (1998) used texture analysis of high/ resolution optical images (MEIS-II) with a variable window size to estimate crown position in stands of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco). The LM filter works best for trees with a single, well defined, apex, such as the conifer species. The derivation of the appropriate window size to search for tree tops is based on a relationship between the height of the trees and their crown size. Basically, the higher the trees, the larger the crown size. Thus, tree height and crown size data from the field inventory, a total of 189 trees, were used to derive a relationship between tree height and crown size. Crown size was considered the dependent variable and linear and nonlinear regression models were tested. The best prediction for crown size based on tree height, with an R-square value of 0.51, was obtained when using linear regression with a quadratic model as shown below in Eq. (1): Crown width (m)2:210:01022h 2 (1) where H is the tree height (m). For loblolly pine plantations in the same area, with ages from 1 to 10 years, Sharma (Mahadev Sharma, 2001, unpublished data) obtained higher R-square values for predicting crown width from height (0.7 with height alone and 0.76 using height and height-squared, with both variables significant). However, at early ages in plantations, when tree competition is not very strong, it is expected to find a better correlation between crown width and height. In our study, using only height as the predictor variable, the relationship is not as strong as between dbh and height, but it offers a base to continuously vary the LM filter size when moved across the grid of laser height values. By using the equation above, the window size varied between 3/3 and 25 /25 pixels, which would correspond to crown widths between 1.5 and 12.5 m. The algorithm reads the height value at each pixel and calculates the window size to search for the LM. If the current pixel corresponds to the LM, it is flagged as a tree top (Fig. 12). Each pixel has a window size associated with it, but Fig. 13 shows only the windows that identified tree tops. Once the location of each identified tree crown has been established, the canopy 3-D surface of laser heights (CHM) is sampled only at the positions of the tree apex to find out the height of each tree. The total number of local maxima within one plot is an indicator of the number of stems. Three sets of height estimates were extracted from the CHM for each subplot, with the same thresholds used for the first method of estimating heights*/2.44, 3.96, and 7.62 m (Table 1). Each set of lidar estimates included mean height, minimum and maximum heights, standard deviation of tree heights, median, first and third quartiles, and number of trees. Each set of height estimates was compared to the corresponding set of field measurements using linear regression with stepwise selection (0.15 significance level). Height estimates from both the first and the second methods were compared to the same field data values.

18 88 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Fig. 12. Ortho-image (a) and tree tops identified in the pine-hardwood mixed stand (b) and the pine plantation next to it (c). Rectangle on the ortho-image shows approximate location of zoom window (b). Window (c) is located to the right of (b). Plantation row pattern oriented SW-NE is visible in (a) and (c). (Illustrations in colour online in Science Direct). 3. Results Residuals from the three interpolation techniques, inverse distance, kriging, and triangulation, are represented graphically using box-and-whiskers plots in Fig. 14. The kriging method shows a smaller range, interquartile range, and standard error of the mean and was chosen for interpolation. Fig. 15 shows the frequency of residuals for the first and last returns from the calculated DEM. These residuals are basically canopy heights for the first and last

19 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 89 Fig. 13. A portion of the lidar derived CHM and the variable windows that identified tree tops. The dark portions of the CHM corresponds to pine plantations, with smaller and denser trees, while the lighter area covers hardwoods crowns, with larger windows. returns. They give an indication of the vertical distribution of canopy heights for the entire area. The penetration rate for the last return laser hits, when considering residuals less than 15 cm, was estimated to be 3.9%. Linear regression was used to develop equations relating lidar-estimated parameters with field inventories for each of the FIA subplots. The results for both methods are shown in Table 2. The presence of multicollinearity effects was investigated using eigenvalues and eigenvectors of the correlation matrix. The condition number of the correlation matrix (Myers, 1990, p. 369/370), that is, the ratio of the largest to the smallest eigenvalue, and ratios of eigenvalues were implied for diagnosing the impact of a dependency. No multicollinearity effects were found. 4. Discussion and conclusions The results of the current study show that the technique of estimating mean tree height by identifying the location of individual trees performed better than the first

20 90 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Fig. 14. Boxplots of residuals (m) for three interpolation techniques. technique that makes use of all laser height values within the subplots. However, only a small percent of the variation in mean tree height was explained by lidar variables (35% for the variable window size method and only 21% for the all laser heights method). These results could be attributed to the influence of intermediate and overtopped trees measured on the ground to the calculation of mean height. Such trees have crowns partially or entirely below the general level of the canopy and intercept very few of the laser hits and have very little influence on the lidar variables. The results show a rather intuitive behavior by obtaining better R 2 values (all above 80%) for estimating the height of dominant trees, in this case of trees with a dbh larger than 12.7 cm. The upper layer of dominant trees intercept most of the laser shots, and thus, estimates better correlate with their mean height. Dominant and codominant trees, with large dbh and tall height, account for a major portion of the timber volume and above-ground biomass. One crucial aspect that could strongly affect the results is the accurate co-location of lidar data and field subplots. Also, the top of the trees could be horizontally displaced from the base of the stem due to leaning caused by competition and/or defective stem structure. Assuming an accurate location of the subplot center on the lidar image, outwards-leaning marginal trees would be tallied in the field but their top would not be included in the subplot area on the lidar image. Part of the unexplained variance could also be attributed to the terrain DEM. As expected, the

21 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 91 Fig. 15. Residuals of first return (a) and last return (b) laser points from the calculated DEM. best prediction was obtained for the maximum height. The variable window size method gave consistent results for all situations (R 2 of 85%). Maximum height was best predicted with the second method, by taking into account all laser height values per plot. When using the height threshold of 3.96 m, the maximum height was predicted with an R 2 value of 90%. For the first method of estimating tree height, the variables that appeared significant in most of the regression models were mean height and maximum height estimated from the lidar data. For the method that considered all laser heights per plot, upper quartile values of the tree heights distribution proved to be significant. The 90th percentile was most significant for estimating mean height for all trees and for trees with a dbh larger than 6.35 cm. Similarly, for trees with a dbh larger than 12.7 m, the most significant for estimating mean height was the 95th percentile. Predictably, when estimating maximum height, the uppermost 99th percentile was among the significant variables in the regression models. With the exception of estimating maximum height for trees higher than 3.96 m (R 2 of 90% when using the method of all laser heights per plot), processing lidar data

22 92 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Table 2 Regression results Method Predicted variable Regression model with significant variables a (P B/0.05) R 2 (%) (a) Independent variable */estimates for all laser heights in each subplot 1 (all laser heights) Mean height 7.13/0.26 Q90 20 Maximum height 0.77/1.00 Q75/1.82 Q99 79 Mean height for 6.48/0.33 Q90 35 dbh/6.35 cm Mean height for 2.93/4.37 STDEV/1.13 Q5/1.84 Q99 73 dbh/12.7 cm 2 (individual trees) Mean height 5.45/0.32 LMAX 35 Maximum height /0.13/0.25 LMEAN/1.21 LMAX 85 Mean height for dbh/6.35 cm 4.67/0.40 LMAX 55 Mean height for dbh/12.7 cm 2.86/0.57 LMEAN/0.22 LMIN// 0.31 LMAX (b) Independent variable */estimates for laser heights/3.96 m in each subplot 1 (all laser heights) Mean height 7.14/0.26 Q90 21 Maximum height 1.63/2.35 LMEAN/1.49 Q25/ Q75/1.14 Q90/1.81 Q99 Mean height for dbh/6.35 cm 6.43/0.34 Q90 36 Mean height for dbh/12.7 cm 4.78/2.17 LMEAN /1.12 Q25 /1.27 Q99 2 (individual trees) Mean height 5.45/0.32 LMAX 35 Maximum height /0.13/0.25 LMEAN/1.21 LMAX 85 Mean height for 4.67/0.40 LMAX 55 dbh/6.35 cm Mean height for 2.86/0.57 LMEAN/0.22 LMIN/ 85 dbh/12.7 cm 0.31 LMAX (c) Independent variable */estimates for laser heights/7.62 m in each subplot 1 (all laser heights) Mean height 7.63/0.24 Q95 19 Maximum height 4.77/0.40 Q25/1.1 Q99 55 Mean height for 7.11/0.30 Q95 33 dbh/6.35 cm Mean height for 6.08/4.78 Q50/0.91 Q99 57 dbh/12.7 cm 2 (individual trees) Mean height 5.45/0.32 LMAX 35 Maximum height 0.06/0.28 LMEAN/1.22 LMAX 85 Mean height for 4.67/0.40 LMAX 55 dbh/6.35 cm Mean height for dbh/12.7 cm 1.65/0.45 LMEAN/0.35 LMAX 84 a Variables notation is as follows: LMAX, lidar estimated maximum height/subplot; LNR, lidar estimated number of trees/subplot; LMIN, lidar estimated minimum height/subplot; LMEAN, lidar estimated mean subplot height; Q5/Q99, quartiles of heights distribution

23 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 93 with a priori field information did not prove to be useful. The gain in explaining the total variation of maximum tree height was 11% in that case. Low R 2 values (below 57%) were obtained for all predicted variables with the method of all laser height values per plot, when using laser heights above 7.62 m. Thus, we conclude that the use of height thresholds when processing lidar data was not particularly useful for this study. The LM technique with a variable window size considers fundamental forest biometrics relationships. It seems more appropriate than the static LM filter or the grid approach that arbitrarily selects only the highest values in a grid with a user defined size (e.g. Næsset, 1997a). The terrain DEM lacks a field based estimation of its accuracy, but judging by the results obtained for tree heights, it is assumed to model the terrain topography fairly accurately. However, the study was based on a rather limited sample of FIA subplots, with no stratification based on tree species or age, and the lidar data were not fully exploited by neglecting secondary returns from within the tree canopy. Thus, the analysis, though very encouraging, indicates a potential for improvements in stand height determination by using scanning laser data. Further research on extracting other parameters, such as crown width, or canopy closure, could help in improving estimates of volume and biomass. Acknowledgements We gratefully acknowledge the help provided with the field data collection by Dr John Scrivani at the Virginia Department of Forestry, by Jan van Aardt, and Rebecca Musy at Virginia Tech, Neil Clark at the USDA Forest Service, Jared Wayman at Questerra, Inc., Karsten Nitsch at the University of Berlin, FIA crew members at the Virginia Department of Forestry and Wayne Bowman, David Houttekier, Donald Jamerson, and Ralph Totty at the Appomattox-Buckingham Forest Office. This research has been supported by NASA Earth System Science Fellowship Program (NGT ), NASA Laboratory for Terrestrial Physics, NCASI, McIntire-Stennis research program (VA ), Virginia Tech Department of Forestry, and USDA Fund for a Rural America ( ). References Axelsson, P., Processing of laser scanner data*/algorithms and applications. ISPRS Journal of Photogrammetry and Remote Sensing 54 (2/3), 138/147. Ackermann, F., Airborne laser scanning*/present status and future expectations. ISPRS Journal of Photogrammetry and Remote Sensing 54 (2/3), 64/67. Blair, B.J., Rabine, D.L., Hofton, M.A., The laser vegetation imaging sensor: a medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography. ISPRS Journal of Photogrammetry and Remote Sensing 54 (2/3), 115/122. Bufton, J.L., Garvin, J.B., Cavanaugh, J.F., Ramos-Izquierdo, L., Clem, T.D., Krabill, W.B., Airborne lidar for profiling of surface topography. Optical Engineering 30 (1), 72/78.

24 94 S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71/95 Corvallis Microtechnology, Inc., CMT Products*/HP-GPS-L Available from (March 1, 2001). Daley, N.M.A., Burnett, C.N., Wulder, M., Niemann, L.O., Goodenough, D.G., Comparison of fixed-size and variable-sized windows for the estimation of tree crown position. IEEE Transactions on Geoscience and Remote Sensing. Dubayah, R., Blair, J.B., Bufton, J.L., Clarke, D.B., Jaja, J., Knox, R., Luthcke, S.B., Prince, S., Weishampel, J., The vegetation canopy lidar mission. In: Land Satellite Information in the Next Decade II: Sources and Applications. ASPRS Proceedings, Washington, DC. EarthData, Inc., Technologies-Lidar Available from (March 5, 2001). Flood, M., Gutelius, B., Commercial implications of topographic terrain mapping using scanning airborne laser radar. Photogrammetric Engineering and Remote Sensing 63 (4), 327/366. Harding, D.J., Blair, J.B., Garvin, J.B., Laurence, W.T., Laser altimetry waveform measurement of vegetation canopy structure. Proceedings of the International Geoscience and Remote Sensing Symposium-IGARSS 94. ESA Scientific & Technical Pub. Noordwijk, The Netherlands, pp. 1251/ Jaafar, J., Priestnall, G., Mather, P.M., Vieira, C.A., Construction of DEM from Lidar DSM using morphological filtering, conventional statistical approaches and artificial neural networks. In: Earth Observation: From Data to Information, Proceedings of the 25th Annual Conference and Exhibition of the Remote Sensing Society, University of Wales at Cardiff and Swansea, 8/10 September, 1999, pp. 299/306. Krabill, W.B., Collins, J.G., Link, L.E., Swift, R.N., Butler, M.L., Airborne laser topographic mapping results. Photogrammetric Engineering and Remote Sensing 50 (6), 685/694. Kraus, K., Pfeifer, N., Determination of terrain models in wooded areas with airborne scanner data. ISPRS Journal of Photogrammetry and Remote Sensing 53, 193/203. Lam, N.S., Spatial interpolation methods: a review. The American Cartographer 10 (2), 129/149. Lefsky, M.A., Cohen, W.B., Acker, S.A., Spies, T.A., Parker, G.G., Harding, D., Lidar remote sensing of forest canopy structure and related biophysical parameters at the H.J. Andrews experimental forest, Oregon, USA. In: Greer, J.D. (Ed.), Natural Resources Management using Remote Sensing and GIS. ASPRS, Washington, DC, pp. 79/91. Lefsky, M.A., Harding, D., Cohen, W.B., Parker, G., Shugart, H.H., Surface lidar remote sensing of basal area biomass in deciduous forests of eastern Maryland, USA. Remote Sensing of Environment 67, 83/98. Maclean, G.A., Krabill, W.B., Gross-merchantable timber volume estimation using an airborne LIDAR system. Canadian Journal of Remote Sensing 12 (1), 7 /18. Magnussen, S., Boudewyn, P., Derivations of stand heights from airborne laser scanner data with canopy-based quartile estimators. Canadian Journal of Forest Research 28, 1016/1031. Magnussen, S., Eggermont, P., LaRiccia, V.N., Recovering tree heights from airborne laser scanner data. Forest Science 45 (3), 407/422. Means, J.E., Comparison of large-footprint and small-footprint lidar systems: design, capabilities, and uses. In: Proceedings of the Second International Conference on Geospatial Information in Agriculture and Foretry, Lake Buena Vista, Florida, 10/12 January 2000: I-185/192. Means, J.E., Acker, S.A., Fitt, B.J., Renslow, M., Emerson, L., Hendrix, C., Predicting forest stand characteristics with airborne scanning lidar. Photogrammetric Engineering and Remote Sensing 66 (11), 1367/1371. Means, J.E., Acker, S.A., Harding, D.J., Blair, J.B., Lefsky, M.A., Cohen, W.B., Harmon, M.E., McKee, W.A., Use of large-footprint scanning airborne lidar to estimate forest stand characteristics in the Western Cascades of Oregon. Remote Sensing of Environment 67, 298/308. Myers, R.H., Classical and modern regression with applications. The Duxbury advanced series in statistics and decision sciences. PWS-Kent, Boston. National Forest Inventory and Monitoring CORE Field Guide. Version 2, May Næsset, E., 1997a. Determination of mean tree height of forest stands using airborne laser scanner data. ISPRS Journal of Photogrammetry and Remote Sensing 52, 49/56.