IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013
1459
Geometric Errors of Remote Sensing Images Over Forest and Their Propagation to Bidirectional Studies P. Kempeneers, L. Bertels, K. Vreys, and J. Biesemans
Abstract—This study focused on the need of accurate digital surface models rather than existing digital terrain models for the geometric correction of high spatial resolution images over forests. Based on both theoretical and experimental results, it was shown here that even for close to nadir observations (view angles less than 7◦ ), the geometric error increased from within to beyond the pixel level when not taking into account the canopy height. This is particularly relevant for forest studies on bidirectional effects, data fusion and change detection techniques. The propagation of geometric errors for studies on bidirectional effects was quantified as a case study here, showing that geometric errors can easily mask such effects. Index Terms—Bidirectional effects, digital surface model, direct georeferencing, error propagation, forestry, geometric correction.
I. I NTRODUCTION
A
common technique used for geometric processing of airborne imagery is direct georeferencing, a physical model which requires knowledge of the position and look direction of the sensor [1]. This information is typically obtained from a global positioning system (GPS) and an inertial measurement unit (IMU), respectively. A digital elevation model (DEM) is also needed to adjust for the topographic relief, also known as orthorectification. Errors in the DEM will have a direct impact on the accuracy of the estimated pixel location. The geometric error is small for near nadir viewing acquisitions and increases for larger (off-nadir) viewing angles. Reflectance signals over forest are merely obtained from the upper canopy layer. Such images contain trees with heights that can range from 5 m to 40 m and thus should be processed with a digital surface model (DSM) rather than a digital terrain model (DTM). This process of orthoimage production removing object relief displacement is referred to as true orthorectification. Due to the relatively coarse spatial resolution of traditional satellite images, the effect was minor and has been generally neglected. However, with increasing spatial resolutions of mod-
Manuscript received December 21, 2012; revised March 11, 2013; accepted April 11, 2013. Date of publication July 9, 2013; date of current version October 10, 2013. The authors are with the Centre for Remote Sensing and Earth Observation Processes (TAP), Flemish Institute for Technological Research (VITO), 2400 Mol, Belgium (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2013.2260129
ern sensors on-board off-nadir viewing satellite platforms, the errors become more important. A number of studies have already dealt with true orthorectification for forestry applications [2], [3]. LiDAR sensors are now frequently used in combination with passive remote sensing sensors, in particular for forestry applications. One of the advantages of having a LiDAR sensor as one of the sources in data fusion is that it has the potential to provide a highly accurate model for both terrain (DTM) and above-ground targets (DSM). A relatively new type of data fusion is that of LiDAR and hyperspectral data. Hyperspectral sensors with their relatively large number of contiguous spectral bands can characterize different tree species based on their spectral signatures. However, they are merely sensitive to the reflectance of the upper canopy layer. Provided the pulse density is sufficiently large, LiDAR sensors have the ability to characterize canopy structure, including height, crown shape, leaf area, biomass, and volume. This complementarity of hyperspectral and LiDAR data makes them ideal candidates for sensor fusion and can explain the increasing popularity of this technique in forestry. The objective in this study was to demonstrate and quantify the effect of the DEM on the geometric correction of (airborne) hyperspectral imagery for forestry. An experiment was conducted using real airborne images, acquired with both a LiDAR and hyperspectral sensor. Hyperspectral images were obtained from multiple flight lines with different headings. The co-registration of the images for an above-ground target was shown to be within the range of a pixel when processed with a DSM, derived from the LiDAR data. This was not the case for the DTM processed images, even for close to nadir observations (view angles less than 7◦ ). Next, the propagation of such geometric errors on bidirectional studies was quantified. II. S TUDY A REA AND M ATERIAL The study area was the Aelmoeseneie forest near Gontrode (Belgium, 50◦ 58 30 N, 3◦ 48 16 E). Tree heights ranged from 20 to 39 m. LiDAR data was obtained from a TopoSys sensor Harrier 56 at full waveform. The study area was acquired in four different flight lines. The resulting point density was 13.81 m−2 with a point spacing of 0.27 m (using all returns). A DTM and DSM were derived at a spatial grid of 0.5 m × 0.5 m. The DSM was obtained by selecting the maximum of all pulse returns in each grid, followed by a morphological closing filter
1545-598X © 2013 IEEE
1460
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013
(circular kernel of size 3 × 3 pixels). For the DTM, non-ground features (e.g., trees) were removed from the LiDAR point cloud using a progressive morphological filter. As proposed in [4], the window size of the filter was gradually increased, using elevation difference thresholds to remove non-ground measurements. Due to the unique combination of the thresholds and window size in each step, ground data could be preserved in this process. Some holes (non-filled grid cells) remained in the filtered output, which were interpolated in the final DTM raster grid using an inverse distance weighting to the filled grid cells. A four direction conic search was performed to find the respective filled grid cells for each hole. Hyperspectral data was acquired with the Airborne Prism Experiment (APEX). The optical system is optimized for minimum angular distortion. Each pixel will see the same solid angle and, as consequence, will receive the same energy. Conform to the whiskbroom sensor model, geometric corrections can be based on platform position and view angles only, irrespective of sensor interior parameters such as focal length and principal point. The APEX instrument covers a wide spectral range, including the short wave infrared (372– 2498 nm) in over 300 spectral bands. The spatial resolution was 1.5 m. Hyperspectral data were acquired in four different flight lines with different headings according to a relative sunview azimuth of 0◦ , 45◦ , 90◦ and 135◦ . The four flight lines, referred to as lines a02, a03, a04 and a05, had a full overlap for the study area. This allowed an inter-comparison of the different images. Absolute location data of top of canopy targets are particularly difficult to obtain. Moreover, processing each image individually allowed us to check the reproducibility of the experimental results. Hyperspectral images were atmospherically corrected to top of canopy reflectance, based on the radiative transfer model MODTRAN4 [5]. Geometric correction was based on direct georeferencing according to [6]. III. M ETHODS A. Theoretical Approach A difficulty when assessing the absolute accuracy of geometric correction from an experiment exp is that there are different sources of error. Other than the uncertainty of the target height, there is the inaccuracy of the ground reference (ref ), measurement error of instruments ins ) such as IMU and GPS on the platform and the uncertainty of boresight angles (the offset between the sensor and the IMU coordinate system). Therefore, the error of using a DTM (dtm ) instead of a DSM for geometric correction of targets above ground was first analyzed theoretically. The approach was similar to the case of a non-accurate DEM as described in [7], using the well known formulas of direct georeferencing [1]. This theoretical geometric error (dtm ) was calculated in function of the view angle for different tree heights. The same figure can be obtained using the simple formula for relief displacement dtm = h × tan(θ) with h the tree height and θ the view (zenith) angle.
(1)
B. Tree Crown Extraction Hyperspectral and LiDAR image data were acquired over the forest area as described in Section II. The center positions of 15 individual tree crowns in the area under study were extracted. The trees were spatially distributed over the test area, which allowed to check the consistency of the results. Automatic delineation of individual tree crowns in a dense broadleaved forest is difficult and prone to errors. Therefore, it was decided to extract the center locations manually from the images (image interpretation). The trees were observed with different view angles for each flight line (a02–a05). In case of a perfect true orthorectification, the locations for crown c should be identical for each flight line = pa03 = pa04 = pa05 (pa02 c c c c ). In practice, errors of different sources are introduced, as explained in Section III-A. The manual extraction of the tree crowns produced an uncertainty in the reference location, ref . However, as the manual extraction method was identical for both the DSM and DTM processed images, ref was of the same order. For the true orthorectified (DSM processed) images, this error was expected to be the major contributor to the total geometric error. Images processed with a DTM were expected to have an important contribution of the error due to the tree heights (dtm ), especially for larger view angles.
C. Propagation of Location Error to Bidirectional Studies A correct co-registration of multiple flight lines is relevant for many applications, including studies on bidirectional effects, data fusion and change detection. Bidirectional reflectance distribution functions (BRDF) describe how reflectance changes for different view angles. Errors in geometric accuracy hamper such studies as the same target must be observed. For this reason, dedicated satellite missions have been set up where multiple sensors with different view angles are mounted on the same platform. Similar studies can be performed with airborne hyperspectral imagery, only if relative geometric accuracy can be assured. The propagation of geolocation error on the canopy reflectance with respect to bidirectional effects was studied here. The wavelength-dependent effect of Sun and viewing angles on the canopy reflectance can be described by anisotropy factors (ANIF) [8]. They are calculated as the ratio of the hemispherical-directional reflectance factor by the spectral albedo. Because such reflectances are merely measured in laboratory conditions, hemispherical and spectral albedo were replaced with reflectance factors. The spectral albedo serves as a standard target spectrum, for which we used the crown reflectance measured in the principal plane. This plane corresponds to a flight path in (and measurements perpendicular to) the solar plane. When observations are acquired in this plane, the reflectance of targets both in the left and right viewing directions are symmetric with respect to the Sun and therefore expected to show the least variation. This condition is considered as optimal and was obtained for flight line a02. For the hemispherical-directional reflectance factor, we used the crown reflectance observed from the (suboptimal) lines a03–a05. The
KEMPENEERS et al.: GEOMETRIC ERRORS OF REMOTE SENSING IMAGES OVER FOREST
1461
expected value of (directional reflectance) ANIFdr for line a0j was then estimated as C 1 Ra0j pa0j c ,λ a0j , j = 3, 4, 5 (2) ANIFdr (λ) = C c=1 Ra02 (pa02 c , λ) where Ra0j (pa0j c , λ) represents the canopy reflectance at the at wavelength λ. The reflectance correct crown center pa0j c was calculated for line a0j, processed with true orthorectification. The ANIF was expected to show the largest variance for line a04, which was perpendicular to the principal plane a02 (least optimal condition). These measurements were either acquired toward the Sun (forward scatter) or away from the Sun (backcatter mode). Making a distinction between those measurements, resulted in the respective factors ANIFfdr (λ) and ANIFbdr (λ). Geolocation errors also influence the spectral behavior of the canopy reflectance and thus can hamper studies that concentrate only on the BRDF. To quantify the effect of the geolocation errors, a geolocation error dtm was introduced for each crown center. The estimated geolocation error dtm was calculated for each crown according to Section III-B, based on the respective view angles and tree heights. Due to the closed canopy forest and relatively small geolocation errors, points pa0i c + dtm were dislocated from the crown center, but still within the tree canopy. Moreover, the forest stand was homogeneous with respect to age and tree species. It is clear that for heterogeneous and open forests with little crown cover the effect of geolocation errors on the reflectance will be more important. Our aim was to study the effect even in most optimal conditions, hereby showing the importance of true orthorectification in forest applications. The effect of the geolocation error on the reflectance was quantified by calculating a new factor ANIFloc . Similar to (2) this new factor was based on a ratio of two reflectances. The ratio was now based on the reflectance at the wrong location a0i for the respective pa0i c + dtm and the correct location pc flight lines a0i Ra0i pa0i c + dtm , λ , i = 2, 3, 4, 5. ANIFloc pc , λ = Ra0i (pa0i c , λ) (3) Unlike (2), only reflectances between the same flight lines were compared in (3), hereby minimizing the view angle effects. As a consequence, the effect of geolocation errors was expected to show little wavelength dependence. In fact, when averaged over the sample of points pa0i c , most of the effect on the reflectance can be expected to cancel out. More important for this study was the sample variation due to the location error. The standard deviation σloc (λ) of the ratio in (3) was therefore calculated and compared to ANIFa0j dr (λ) for the different flight lines a0j. IV. R ESULTS AND D ISCUSSION A. Theoretical Results Results from the theoretical approach are shown in Fig. 1. As expected, the geometric error is small for either small
Fig. 1. Geometric error in function of viewing angle and tree heights of 5 m, 15 m, 25 m, 35 m and 45 m.
heights or near nadir views. For off-nadir view angles the error dramatically increases for above-ground targets. These results explain why many studies on forestry using Landsat imagery have rarely questioned the effect of DTM on the geometric accuracy. Landsat images have a small field of view (15.2◦ ) and a spatial resolution of 30 m. This means that even for trees of 45 m high, the worst geometric error due to neglecting the tree height is less than half a pixel. However, new technology high spatial resolution sensors that can be tilted have large off-nadir view angles and geometric errors get more important. Nevertheless, few forest studies dealing with off-nadir data consider tree heights into the orthorectification process. The same is true for studies dealing with very fine spatial resolution airborne imagery, where even small off-nadir view angles can result in geometric errors of a few meters, corresponding to several pixels. In these cases, images should be geometrically corrected with a DSM. In absence of LiDAR data, a DSM can be derived from airborne or spaceborne stereo (e.g., SPOT or IKONOS) data that can be acquired from almost any location on Earth and at reasonable cost. As a drawback, the image matching needed to extract 3-D information in these stereo techniques can be problematic over forest areas due to repetitive and similar texture patterns. B. Experimental Results The heights and view angles for the corresponding pixels were used to calculate the theoretical geometric errors dtm . The experimental error for each crown c was expressed by the sample standard deviation of the extracted locations for the different flight lines 5 1 ˆ = pa0i − pc 2 (4) 3 i=2 c where pc is the center location of crown c, averaged over the flight lines a02–a05. In case of the orthorectified (DTM processed) image, the experimental error ˆ was expected to be correlated to the theoretical error dtm . This was found to be consistent over the test area. As shown in Fig. 2, there
1462
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013
Fig. 2. Experimental error plot against theoretical error (expressed in pixels) for center locations of tree crowns, after orthorectified (solid dots) and trueorthorectified (empty dots) processing.
was a strong correlation (R2 = 0.83) between the experimental error (vertical axis) and the theoretical error (horizontal axis). The mean experimental error over all crowns was calculated as 1.129 pixels. For the true orthorectified (DSM processed) images, the mean geometric error was calculated as 0.6 pixel. In this case, the standard deviation for the crown locations (ˆ ) showed no correlation with the theoretical error (R2 = 0.06). This was expected, as tree heights and view angle were already taken into account in the true orthorectification process. Extraction of individual trees is important for a number of studies, including tree species classification and the retrieval of biophysical parameters at the tree level and BRDF studies, which is discussed in Section IV-C. In particular, for open forests, the accuracy of the location will not only be determined by the vertical accuracy of the DSM used, but also by the spatial resolution in x and y. Similarly for heterogeneous forest, the spatial resolution of the DSM should represent the varying heights of the trees. C. Propagation to Bidirectional Studies The view angles for which the tree crowns were observed for the respective flight lines are shown in the form of a polar plot in Fig. 3. The acquisition time was at 11:00 with the Sun almost located South. Dots correspond to the view conditions (angles) for the respective tree crowns in each flight line. Optimal conditions for observing tree crowns were obtained for flight line a02, which corresponded to the principal plane. Observations were perpendicular to the plane of the Sun, avoiding backscatter or forward scatter. Worst case conditions were obtained for flight line a04, which was perpendicular to line a02. Results for the anisotropy factors for line a04 are shown in Fig. 4. As expected, the ANIF for the location errors, averaged over all crowns (ANIFloc ) shows little wavelength dependence. It is slightly less than 1, which can be explained by the mutual shadow effect of the crown canopy. Less shadow is expected at the center of the crown (no dislocation) where the height of the tree canopy is mostly at its maximum. On average, the mutual shadow effect is therefore larger in case of a location error, resulting in a decreased reflectance Ra0i (pa0i c + dtm , λ).
Fig. 3. View angles for which tree crowns were observed in respective lines a02–a05.
Fig. 4. Anisotropy factors for line a04, showing backscatter (ANIFbdr (λ)) and forward scatter (ANIFfdr (λ)) anisotropy. The propagation of geolocation errors is shown as a range ANIFloc ± σloc (λ).
The range ANIFloc ± σloc (λ) is also shown in Fig. 4. The anisotropy due to directional reflectance is wavelength dependent and is more expressed for backscatter (ANIFbdr (λ)) than forward scatter (ANIFfdr (λ)). It is shown that the propagation effect of the geolocation error is important for this type of study. The anisotropy due to directional reflectance is masked by the location error in almost the entire wavelength range. The situation is even worse for the lines a03 and a05 where the anisotropy is less important, as shown in Fig. 5 for line a05. V. C ONCLUSION This study has shown the importance of using an accurate DSM when processing remote sensing data for forestry applications. Both theoretical and experimental results have demonstrated that canopy heights need to be taken into account in the process of geometric correction. This is particularly true
KEMPENEERS et al.: GEOMETRIC ERRORS OF REMOTE SENSING IMAGES OVER FOREST
1463
Subpixel accuracy is particularly relevant for forest studies dealing with bidirectional effects, which was selected as a case study. It was shown that geolocation errors less than two pixels can completely mask bidirectional effects, even when forest canopy was closed. It can be expected that for heterogeneous and open forest canopies the effect of geolocation errors is even more important. R EFERENCES
Fig. 5. Anisotropy factors for line a05, showing backscatter (ANIFbdr (λ)) and forward scatter (ANIFfdr (λ)) anisotropy. The propagation of geolocation errors is shown as a range ANIFloc ± σloc (λ).
for (sub) meter spatial resolution images obtained at larger view angles, such as provided by new generation satellite sensors that can be tilted. However, even for near nadir view angles it was shown that a DTM, describing the terrain rather than canopy surface, introduce geometric errors beyond the pixel size of currently available sensors. An experiment has been conducted where imagery was acquired over a forest from multiple flight lines with different headings. Using a DSM derived from LiDAR, images were coregistered consistently with a subpixel relative accuracy. This accuracy decreased when images were processed with DTM. Errors larger than the pixel size (1.5 m) were obtained even for close to nadir views. Results were confirmed by our theoretical approach, applying the equations of direct georeferencing in function of target height and view geometry.
[1] M. Cramer, D. Stallmann, and N. Haala, “Direct georeferencing using GPS/inertial exterior orientations for photogrammetric applications,” Int. Arch. Photogramm. Remote Sens., vol. 33, pt. 3, no. B3/1, pp. 198–205, 2000. [2] R. Valbuena, T. Fernández de Sevilla, F. Mauro, C. Pascual, A. García-Abril, S. Martín, J. A. Manzanera, R. Hill, J. Rosette, J. Suárez et al., “Lidar and true-orthorectification of infrared aerial imagery of high pinus sylvestris forest in mountainous relief,” in Proc. 8th Int. Conf. LiDAR Appl. Forest Assess. Inventory SilviLaser, Edinburgh, U.K., Sep. 17–19, 2008, pp. 596–605. [3] B. St-Onge, “Methods for improving the quality of a true orthomosaic of vexcel ultracam images created using a lidar digital surface model,” in Proc. SilviLaser, 2008. [4] K. Zhang, S. Chen, D. Whitman, M. Shyu, J. Yan, and C. Zhang, “A progressive morphological filter for removing nonground measurements from airborne lidar data,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 4, pp. 872–882, Apr. 2003. [5] A. Berk, G. Anderson, P. Acharya, J. Chetwynd, L. Bernstein, E. Shettle, M. Matthew, and S. Adler-Golden, Modtran4 Users Manual. WrightPatterson Air Force Base, OH, USA: Air Force Res. Lab., Space Vehicles Directorate, 1999. [6] Q. A. Abdullah, “Photogrammetric platforms,” in Manual of Photogrammetry, 5th ed. Bethesda, MD, USA: American Society for Photogrammetry and Remote Sensing, Bethesda, 2004, pp. 677–730. [7] R. Valbuena, F. Mauro, F. J. Arjonilla, and J. A. Manzanera, “Comparing airborne laser scanning-imagery fusion methods based on geometric accuracy in forested areas,” Remote Sens. Environ., vol. 115, no. 8, pp. 1942– 1954, Aug. 2011. [8] S. R. Sandmeier, E. M. Middleton, D. W. Deering, and W. Qin, “The potential of hyperspectral bidirectional reflectance distribution function data for grass canopy characterization,” J. Geophys. Res., vol. 104, no. D8, pp. 9547–9560, Apr. 1999.
