CHAPTER 5 EXPERIMENTAL RESULTS. 5.1 Boresight Calibration

Transcription

1 CHAPTER 5 EXPERIMENTAL RESULTS 5. Boresight Caibration To compare the accuracy of determined boresight misaignment parameters, both the manua tie point seections and the tie points detected with image matching are appied in this research. 5.. Manua tie point seection Figure 5.: Manua seected tie point distribution 77

2 In this test a tota of 58 points were seected as tie points. The tie point distribution is shown in Figure 5.. Tie point that have arge residuas are identified as outiers. The procedure aows for a quick identification and remova of points that have arge residuas. The soution was repeated unti no outiers remained. Among the 58 tie points, three outiers were rejected. The tie point differences and reguar point eevation differences are affected by the arge panimetric shifts between the uncaibrated strips. Thus, a grid point in one strip wi generay not correspond to the same point in the second strip. The initia tie point differences are presented in Tabe 5.. Tabe 5.: Initia tie point differences X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev The most teing indication of caibration errors can be seen in the graphica profie pot. As shown in Figure 5.2a, discrepancies are painy visibe by potting aong structures such as buidings with peaked roofs. Figure 5.2a shows cear anguar differences between the four overapping strips, eevation offsets and panimetric shifts. What is not pain to see, however, is that the strips are not simpy shifted from each other, but are distorted across a 3 dimensions. The significant discrepancies between caibration strips are caused by incorrect boresight anges (used 0, 0 and 0 as initia approximation in this test) on purpose, as was discussed. a. Before caibrated b. After caibrated Figure 5.2: Profies for uncaibrated and caibrated ALS strips 78

3 The caibrated tie point difference presented in Tabe 5.2 is now shown with the boresight caibration parameters in Tabe 5.3. In contrast to Tabe 5.2, the tie points show a much better aignment with an average panimetric difference of 0.60 m and an average eevation difference of 0.04 m. The panimetric error of the tie points of 0.60 m is a itte higher than the expected vaue of 0.5 m, which is equivaent to the set weight whie appying adjustment. Tabe 5.2: Tie point differences after caibrated X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Tabe 5.3: Boresight parameters from manua tie point seection Parameters Vaue Standard deviation Standard deviation Ro Error rad rad degrees Pitch Error rad rad degrees Heading Error rad rad degrees Torsion units As presented in Tabe 5.3, the standard deviation of the ro error shows that the ro is the best-caibrated parameter. As the ro induces the argest eevation differences in the seected tie points, it has the argest chance to adjust resuting in a more precise soution. Next, the standard deviation of pitch is a itte arger than the ro, but much better than the IMU (Appanix POS 50) pitch error of degrees. This suggests that ALS strip coected at a different atitude is successfu in separating out the infuence of pitch error. Lasty, Tabe 5.3 aso demonstrates that the heading error is the weakest component of the soution. The standard deviation of heading errors is amost five times arger than both the ro and the pitch. This can be expained by the dependency of the heading on the panimetric quaity of the tie points (Figure 4.3). It can be concuded that the heading error woud be the 79

4 poorest-determined parameter. The standard deviation of heading errors, however, is a itte smaer than the IMU heading error of degrees. This impies that the soution can achieve a reasonabe precision, no matter what the tie point seection is. For ease of communication, the computed boresight caibration parameters (Tabe 5.3) wi be henceforth named as Manua_ca in the remaining parts of this research. By re-cacuating the point couds in the mapping frame with the computed boresight caibration parameters in Tabe 5.3, the point couds shoud fit the surface to which they beong. As shown in Figure 5.2b, the profie generated from four caibrated strips shows much better agreement. Basicay, the accuracy of manua tie point measurement shoud reach ps/3 (ps = pixe size) in digita photogrammetry. The intensity images used in the Attune program and the height/intensity images used in this dissertation are based on interpoated reguar grid. Therefore, these images are much different from traditiona photogrammetric images. Furthermore, the size of aser footprints varies with the strength of refectance and the factors of terrain. If the interpoated grid size is set as.0 m and is assumed as the pixe size of images, the accuracy of tie point measurement shoud be ess than 33 cm. Tabe 5.4: The caibrated tie points difference from 3 operators Operators A B C X//Z X (m) (m) Z (m) X (m) (m) Z (m) X (m) (m) Z (m) Mean Median Min Max Std Dev In a practica test, 3 operators are assigned to measure the tie points on the same data sets to compute the boresight caibration parameters. As shown in Tabe 5.4, this eve of accuracy is very difficut to reach whie appying manua tie point seection. With the innate imitation of horizonta accuracy of ALS data, how to set up the standard of accuracy on the tie point measurement for ALS interpoated data wi be another issue that requires further research. 80

5 Next, the grid size shoud aso be taken into account whie measuring the tie points in the Attune program. Two kinds of grid size are appied to measure the tie points. The caibrated tie point difference is shown in Tabe 5.5, and the boresight caibration parameters are shown in Tabe 5.6. Both Tabes 5.5 and 5.6 show that the accuracy of tie point differences as we as the computed boresight anges with 0.5 m grid size is better than the accuracy with.0 m grid size. Tabe 5.5: Tie point differences after caibrated with two kinds of grid size Grid size.0 m 0.5 m X//Z X (m) (m) Z (m) X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Tabe 5.6: Boresight parameters from manua tie point seection with two kinds of grid size Grid size Parameters Vaue Standard deviation Standard deviation Ro Error rad rad degrees.0 m Pitch Error rad rad degrees Heading Error rad rad degrees Torsion units units units Ro Error rad rad degrees 0.5 m Pitch Error rad rad degrees Heading Error rad rad degrees Torsion units units units The interpoation with a smaer grid size resuts in a higher boresight accuracy based on the parameters considered. However, the aser points are not eveny distributed. The constructed image can sometimes make tie point seection difficut when a grid size that is smaer than the average density of aser points is appied (Figure 5.3). Behan (2000) concuded that an interpoation method based on a TIN of the origina points with a grid size that reates as cosey as possibe to the point density at acquisition is found to give the best resuts. 8

6 Figure 5.3: Intensity image with grid size smaer than average point density It is cear that extreme care must be taken with the use of rasterized data for matching and the derivation of discrepancies between strips of aser data, particuary in terms of grid size and interpoation method Tie point detection with image matching Figure 5.4: The ocation and extent of each patch Both the height and intensity of uncaibrated ALS data, which were tested in Section 5.., are used to examine the improvement on tie point seection, foowing the work fow (Figure 4.8). After preprocessing the strips data, each strip is spit into six patches (Figure 5.4) 82

7 in overapping areas. Each patch is then interpoated to a grid with triange-based inear interpoation (Figure 5.5). a. height b. intensity Figure 5.5: The detected interest points for the 4th patch in two strips The trianguation with inear interpoation uses the optima Deaunay trianguation (Watson, 992; MATHWORKS, 2004). Trianguation with inear interpoation works best 83

8 when the data are eveny distributed over the grid area. Therefore, the triange-based inear interpoation is used for interpoating aser points since most of them are eveny distributed. The size of the grid was chosen to approximatey correspond to the resoution of the aser points on the ground. The automatic measurement of tie points generay requires two major steps. The first concerns the detection and the ocaization of interest points in images. Points of interest can be cacuated individuay from the images. Then these points are used to match the actua tie points. As was discussed in Section 4..4, Harris operator is used to detect the interest points for matching. The detected interest points are shown in Figure 5.5a and 5.5b for height and intensity data of the corresponding patches in two strips respectivey. Figure 5.5 immediatey presents the significant difference of quantity on the detected interest points. This proves that the refectance intensity of ALS can suppy much more features as interest points than height data can. This is one of the critica factors for image matching. As presented in Figure 5.5a, the detected interest points from height data basicay distribute on the corners of the buidings, the edges of the sidewak and on the vegetation. It suggests that these areas have high variance of vaue (i.e. height vaue). Nevertheess, the detected interest points are eveny distributed throughout the whoe image, as shown in Figure 5.5b. Figure 5.6: The detected interest points for the 4th patch in two strips 84

9 First, the intensity image is used for tie point detection. The matched tie points for the first patch are shown in Figure 5.6 based on an area-based matching technique. There are some incorrecty-matched points. For instance, one of the points in each circuar zone (right image of Figure 5.6) doesn t appear on the image on the eft hand side of Figure 5.6. These errors are mosty induced by the areas which are ocay simiar between two images (Figure 5.7). Two exampes of correct points are shown in Figure 5.8. Figure 5.7: Exampes of incorrect matching 85

10 Figure 5.8: Exampes of correct matching The mentioned agorithm is appied to remove the incorrecty-matched points. A the correcty-matched points from the two overapping ALS caibration strips after merging the six patches are shown in Figure 5.9. As expected, most of the successfuy-matched points ocate on the ground or on ocay fat areas. This resut is in accordance with one of the criteria for seecting tie points (section 4..3). 86

11 a. eft b. right Figure 5.9: The matched points in two overapping strips from intensity image 87

12 In addition to removing incorrecty-matched points, a visua assessment of the quaity of tie points permits one to note that the percentage of erroneous tie points decreases appreciaby with the order of the point (Kasser and Eges, 2002). The order of the point is defined as the number of images for which the point is visibe. For exampe, the order of the point wi reach four since there are four overapping ALS strips used for boresight caibration in this research. There are severa ways to expoit this observation with mutipe points of order. A reiabe method is to consider mutipe point as vaid if a associated measures are in tota interconnection with regard to the simiarity function, i.e. if each pair of measures is vaidated by image matching. As shown in Figure 5.0, every coupe of points of this mutipe ink has been detected as pairs of homoogous points by image matching. Figure 5.0: Mutipe point of 4th order in tota interconnection (Kasser and Eges, 2002) Foowing the mechanism in Figure 5.0, there are six combinations of matching. To decrease the number of tie points that may be seected erroneousy, a point has to appear on at east three images that are seected as fina tie points to be empoyed in the adjustment procedure. The matched points with the third order (red cross in Figure 5.9a, green cross in Figure 5.9b) and the forth order (cyan circe in Figure 5.9a, bue circe in Figure 5.9b) are aso shown in Figure 5.9. The initia tie point differences and the caibrated tie point differences are depicted in Tabes 5.7 and 5.8, respectivey. Compared to Tabe 5.2, the tie point residuas in Tabe 5.7 show a significant improvement from this soution (with an average panimetric vaue of 0.28 m and an average eevation vaue of 4.5 cm). Moreover, the accuracy of tie points is much better than the previous soution (Tabe 5.2) (with a standard deviation of X vaue dropping from 0.40 m to 0.5 m and Z vaue dropping from 4. cm to 2.3 cm). 88

13 Tabe 5.7: Initia tie point differences by using intensity images X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Tabe 5.8: Tie point differences after caibrated by using intensity images X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev The question is thus whether the higher accuracy of tie point seection eads to a higher accuracy of soution on caibration parameters. The computed caibration parameters from tie point detection by using intensity image matching are shown in Tabe 5.9. Simiarity, the caibration parameters (Tabe 5.9), wi be henceforth named as Auto_ca in the remaining parts of this document. In addition, the torsion parameter, which is the difference of computed parameters between Manua_ca and Auto_ca, is negigibe. The standard deviation of ro and pitch in Auto_ca is very cose to the soution in Manua_ca. The heading error is sti the weakest component of the soution. Tabe 5.9: Boresight parameters from image matching with intensity images Parameters Vaue Standard Standard deviation deviation Ro Error rad rad degrees Pitch Error rad rad degrees Heading Error rad rad degrees Torsion units

14 a. eft b. right Figure 5.: The matched points in two overapping strips from height image 90

15 Higher accuracy of tie point seection did not ead to a higher accuracy soution of caibration parameters. In the end, it is up to the user to judge whether the boresight parameters cacuated are good enough. It is difficut to determine what is good enough, nevertheess. In the next section, a popuar measure by comparing aser points against ground check points wi be appied to four vaidation strips to evauate the boresight parameters. For the sake of comparison, the height images derived from four quadrants of overapping strips are aso appied to image matching foowing the proposed workfow. An exampe of matched points from height image is shown in Figure 5.. Tabe 5.0: Initia tie point differences by using height images X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Tabe 5.: Tie point differences after caibrated by using height images X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev The initia tie point difference in height images is shown in Tabe 5.0, and the adjusted tie point residuas are presented in Tabe 5.. The soution is in Tabe 5.2. Compared to the soution in Manua_ca, the tie point residuas in Tabe 5. aso demonstrate a significant improvement on panimetry (with an average panimetric difference of 0.29 m and a standard deviation of panimetric vaue of 0.5 m). However, both the average and the standard deviation of the height vaue are much worse than the soution in Manua_ca and Auto_ca. It suggests that most of the matched tie points 9

16 from height images (distributed on bounds of roofs, the edges of sidewak and on vegetation) wi induce high eevation differences. Finay, the accuracy of ro and pitch is worse than the soution in Manua_ca and Auto_ca resuting from arger height residuas of tie points. However, the accuracy is much better than the IMU ro/pitch error of degrees. On the other hand, the accuracy of the heading error did not increase as expected and was arger than the IMU heading error of degrees. Tabe 5.2: Boresight parameters from image matching with height images Parameters Vaue Standard Standard deviation deviation Ro Error rad rad degrees Pitch Error rad rad degrees Heading Error rad rad degrees Torsion units* Check by GCPs There is no so-caed correct boresight caibration parameter. To compare the accuracy of caibrated parameters between manua seection (Manua_ca ) and seection with image matching (Auto_ca), 520 ground check points are used to estimate the height discrepancies. The evauation of caibrated boresight parameters wi not incude the parameters which are used to derive the tie point with height image matching, (i.e. the parameter in Tabe 5.2), since the accuracy is much worse than the others. The statistics of height differences between aser scanning points and known ground contro are presented in Tabes 5.3 and 5.4 for Manua_ca and Auto_ca, respectivey. The computed height of point couds by using Manua_ca is higher than check points with an average offsets from.7 cm to 5.2 cm. On the contrary, the computed eevation of points by appying Auto_ca is ower that check points with an average discrepancy from -4.6 cm to -.3 cm. The standard deviation for both caibration parameters is in accordance with the vertica accuracy specifications of most commercia ALS systems (Leica, 2004a; Optech, 2004). 92

17 Tabe 5.3: Height differences from aser points against GCPs by appying Manua_ca Strip No. Average(m) Std dev(m) Minimum(m) Maximum(m) Points Tabe 5.4: Height differences from aser points against GCPs by appying Auto_ca Strip No. Average(m) Std dev(m) Minimum(m) Maximum(m) Points Significanty, the potted profies (Figure 5.2) generated from four ALS verifiabe strips with the caibration parameters Manua_ca (Figure 5.2a) and Auto_ca (Figure 5.2b) appied show good aignments on a buiding roof. If the aignment of each of the fight ine aser points does not appear to ine up, it is necessary to repeat the adjustment by adding more tie points and/or refining the existing points. b. Tie point detection from intensity image a. Manua tie point seection matching Figure 5.2: Profies generated from caibrated ALS data Once the average height differences have been taken from the four ALS strips, the ast boresight misaignment parameter, i.e. the z (eevation) offset, can be derived. The ALS system eevation offset wi aways be the opposite of the determined vaue (Optech, 2003; 93

18 Leica, 2003a). This offset wi shift the data in the opposite eevation direction to correct the aser point data to the known vaues. To deveop further understanding on the reationship between boresight parameters, correation coefficients are cacuated. A correation coefficient is a numeric measure of the strength of a inear reationship between two random variabes. The correation matrix can be compied from the adjustment report of the Attune program. A correation matrix for each of Manua_ca and Auto_ca is shown in Tabes 5.5 and 5.6, respectivey. The correation matrix based on tie point detection in height images is shown in Tabe 5.7 for the sake of comparison. Tabe 5.5. The correation matrix for Manua_ca Ro Pitch Heading Torsion Ro Pitch Heading Torsion Tabe 5.6. The correation matrix for Auto_ca Ro Pitch Heading Torsion Ro Pitch Heading Torsion Tabe 5.7. The correation matrix based on tie point detection by using height images Ro Pitch Heading Torsion Ro Pitch Heading Torsion The resuts presented in Tabes 5.5, 5.6 and 5.7 show that the correation between torsion/ro and torsion/pitch are much arger than the others. 94

19 Next, except the correation of pitch/heading, the correation of each parameter in Manua_ca (Tabe 5.5) is smaer than the correation in Auto_ca (Tabe 5.6). It impies that the distribution of tie points correate with the soution of misaignment parameter. To concude, the improvement on tie point seection in image-matching techniques for caibration presents a comparabe accuracy against the techniques empoyed in manua measurements. The manua measurement of tie points is a time-consuming task, however. Previous experimenta resut reveas that any error in the tie point observation wi degrade the caibration soution. The proposed automated method of extracting tie points can significanty upgrade the accuracy in tie point seection. Furthermore, an increased number of points woud aso provide more redundancy and improve the quaity of the caibration parameters. However, the automated method has a disadvantage, compared to the manua one. In the manua case, the operator can notaby be assured of their geometric distribution a priori. In the automatic case, by contrast, the ack of inteigence of any computer method may be party compensated by the abundance of data. Considering the distribution of points, it is difficut to force the machine to find a soution in a given zone, and it is therefore probaby preferabe to et it find another soution in the neighborhood of the desired area Boresight Caibration for the Optech ALTM Figure 5.3: Boresight caibration data derived from the Optech ALTM

20 Foowing the schemes described in Section 4..5, a practica boresight caibration data set derived from the Optech ALTM is used in this section. Like the Attune used by the Leica system, the Auto Caibrator (ACaib) software is currenty used for boresight caibration by the Optech system. Next, the caibration test data (Figure 5.3) derived from the Optech ALTM 3070 are used in processing the boresight caibration aong with ACaib. The fight parameters are specified in Tabe 5.8. Tabe 5.8: Fight parameters of boresight caibration for the Optech ALTM Parameter Vaue Puse rate 70 khz Scan rate 0/20/50 Hz Returns/intensities 2/2 Operating atitude (AGL) 800 m FOV 0/25/25 degree Aircraft speed 25 knots The computed boresight caibration parameters are presented in Tabe 5.9. The initia vaue in the Tabe 5.9 is the caibrated vaue performed in the aboratory. The computed boresight caibration parameters, i.e. the finia iterated vaue in Tabe 5.9, are very cose to the vaue that was reported in a survey (CHSurvey, 2005). Tabe 5.9: Boresight parameters from the Optech ALTM Parameters Initia vaue The st iterated The fina iterated vaue vaue Pitch degrees degrees degrees Ro degrees degrees 0.4 degrees Heading* degrees degrees degrees Scae TIMs m m m * The heading vaue is not incuded for boresight caibration in the Optech ALTM. The next step in processing the caibration data set is to anayze how we aser strips match each other. One way is to use different coors in the strips to differentiate between eevations. As shown in Figure 5.4, the coor of each point shows how much the point exceeds or fas short of the average eevation of the overapping strips at that ocation. 96

21 eow and green coors are ess than 0.08 m from the average surface. Most of the points dispayed in yeow or green indicate that the strips match each other pretty we. Additionay, the Figure 5.4b aso suggests that the caibrated aser points of the overapping strips match we with the profie of the roof of a buiding. a. distance cooring b. buiding profie Figure 5.4: Eevation differences cooring and buiding profie for Optech test data Tabe 5.20: Height differences from caibrated aser points against GCPs for Optech data Average(m) Std dev(m) Minimum(m) Maximum(m) Points For Optech Correspondingy, 004 ground check points are used to estimate the height discrepancy to evauate the accuracy of the computed boresight parameters for Optech data. As depicted in Tabe 5.20, the standard deviation of the computed parameters meets the vertica accuracy requirement of the Optech ALTM. The eevation offset is therefore derived with m from Tabe The schemes on boresight caibration for both the Leica ALS and the Optech ALTM are presented in this research. Because the current schemes on the boresight caibration are different for Leica and Optech, it is not possibe to appy the Leica boresight caibration data to Optech boresight caibration scheme, and vice versa. 97

22 5..5 TerraMatch To evauate the accuracy of the misaignment parameters derived from the Attune program in Section 5..2, the TerraMatch program is aso used to sove the misaignment parameters. Unike the Attune program, the TerraMatch program needs an initia approximation of misaignment anges to access the aser point couds. The computed misaignment parameters are shown in Tabe 5.3. The initia misaignment anges are given in Tabe 5.2. These anges are appied to the same ALS caibration fights data (Figure 4.4). Tabe 5.2: The initia misaignment anges for TerraMatch Parameters Ro Error Pitch Error Heading Error Vaue rad rad rad Tabe 5.22: Boresight misaignment anges from TerraMatch Parameters Vaue Standard deviation Ro Error rad degrees Pitch Error rad degrees Heading Error rad degrees As shown in Figure 5.5a, the height and panimetric discrepancies are present when the initia misaignment anges are appied. The computed misaignment anges and the corresponding standard deviation are depicted in Tabe The standard deviation of the ro parameter shows that ro is the best-caibrated parameter, once again. The accuracy of the misaignment parameters is much better than the IMU error (with degrees for ro/pitch, degrees for heading). This impies that the soution is acceptabe. Re-cacuating the point couds with the updated boresight caibration parameters eads to the profie shown in Figure 5.5b. The one that is generated from four caibrated strips shows much better agreement. 98

23 a. before caibrated b. after caibrated Figure 5.5: Profies of the buiding before and after caibrated of misaignment parameters Tabe 5.23: Height differences from aser points against GCPs Average(m) Std dev(m) Minimum(m) Maximum(m) Points Before correction After correction Correspondingy, 520 ground check points are used to estimate the height discrepancy in evauating the accuracy of the computed misaignment parameters. The statistics of the height differences between aser scanning points and known ground contro are presented in Tabe The standard deviation for the computed parameters is aso in accordance with the vertica accuracy specifications of most commercia ALS systems. The eevation offset is therefore derived with m from Tabe Compared to Attune, TerraMatch is more sensitive with respect to the initia approximation of misaignment parameters. The process of adjustment is sometimes unabe to converge or in need of a arger number of iterations to converge. It is empiricay determined that the initia approximation for TerraMatch is a reasonabe vaue provided by system vendors. 5.2 Systematic error vaidation Next, the surface registration technique, that is, the ICP agorithm, is appied to measure the quantity of systematic errors. The goa of this experiment is to quantify the panimetry and the height offsets from the overapping strip data. The transformed data surface (P) is the 99

24 output fie when the registration is carried out. Then the offsets in X-, -, and Z- directions between the overapping strips can be derived after cacuating the differences between the origina and the transformed data surfaces. A MATLAB code is used to impement the iterative cosest point agorithm in this research. This program registers two data sets which are derived from airborne LiDAR. It is assumed that these two data sets are in approximation registration. These two data sets can be regarded as in approximation registration since they are extracted from two overapping aser strips and are spread in the nadir zones in rough. Based on the equations and the computing steps presented in section 4.2, the code iterates unti no more correspondence can be found. Two times the average distance between two aser points is used as the initia distance to estabish correspondences. For instance,.0 m is used for test I and II. Finay, the threshod (τ) for iteration convergence is set as (the average point distance/0000) Test Site I (SI) The data sets with naturay existing systematic errors, ike test data I (SI), are suitabe for anayzing the performance of the proposed accuracy assessment procedure. To verify the systematic errors in strips 9 and 0, these two strips and their neighboring strips (strips 8 and ) are seected as test data in this study (Figure 5.6). The eight patches are shown in Figure 5.6. The size of a patches is arger than 300 m 300 m. Figure 5.6: Four overapping aser scanning strips in test site I (SI) Due to the different width of aser scanning swath and irreguar strip shape of ground coverage, the number of points faing into each patch varies between strips. The average height and its corresponding standard deviation for each patch are presented in Tabe Larger average height differences are reated to smaer overapping percentage, and the 00

25 presence of vegetation, or buidings (resuted in higher standard deviation). Patch-6 between strips 0 and and patch-8 between strips 8 and 9 shown in Tabe 5.24 are two exampes. Because the overapping percentage between strips 8 and is reativey sma, the amount of common points of these two strips in these patches is smaer. Tabe 5.24: The average height (μ, meters) and its standard deviation (σ, meters) in SI Patches Strip 8 Strip 9 Strip 0 Strip No. μ σ μ σ Μ σ μ σ N/A* N/A* N/A* * There is no point faing into the overapping area. In order to examine the infuence of surface type on the parameter of ICP agorithm, 8 experimenta patches are seected based on various and use/and cover (LU/LC) categories. As discussed, some researchers (Crombaghs et a, 2000; Maas, 2003) use fat areas to estimate the height discrepancies to avoid the interpoating errors or to reduce the effect of terrain sope. It is found that the toerance of iteration convergence of the ICP agorithm wi need to be adjusted based on surface types, especiay on fat areas. The resuts of the anaysis on 4 overapping strips are summarized in Tabe The ampitude of the height offsets is from -.53 m to -.80m with an average height offsets on the order of -.67m for strips 9 and 0. Nevertheess, the height offsets are from m to 0.9 m for strips 8 & 9 and strips 0 & with an average difference on the order of 0.3 m. Based on Figure 4. and Tabe 5.25, it can be concuded that the significant height offsets exist among strips 0 to 9. The average panimetric strip shifts range from m to m, as Tabe 5.25 shows, accompanying the panimetric shifts up to 0.60 m. Compared to the detected height offsets, 0

26 the panimetric shifts are reasonabe within the accuracy specifications defined in main commercia systems (Leica 2002; Optech 2002). Tabe 5.25: Panimetry/height offset, appied to 8 patches of strip-8, 9, 0, and for SI Strips 8_9 9_0 0_ No. of patches Panimetry/Height X Z X Z X Z Average (m) Std dev (m) Min. (m) Max. (m) Comparabe transect eevations based on a buiding were potted from the DSMs that are generated from 3 overapping strips (strips 9, 0, and ), as shown in Figures 5.7 and 5.8. The coordinates of x-axis in Figures 5.7 and 5.8 are the direction of the fight and the direction perpendicuar to the fight, respectivey. That is, Figure 5.7 has the x-axis in the aong-track direction and Figure 5.8 has the x-axis in the across-track direction. a. Profie from origina data b. Profie from data with the ICP matching Figure 5.7: Aong-track profie comparison from 3 overapping strips for SI Figures 5.7a and 5.8a show significant height offsets both between strips 9 and 0, and between strips 9 and. The profies produced from the data of registering a strips to strip 9 by the ICP dispay much better aignment (Figures 5.7b and 5.8b). Based on Tabe 5.25, 02

27 Figure 5.7, and Figure 5.8, it can be concuded that the surface registration with the ICP can sufficienty estimate the height offsets and panimetric shifts from overapping aser scanning strips. a. Profie from origina data b. Profie from data with the ICP matching Figure 5.8: Across-track profie comparison from 3 overapping strips for SI Figures 5.7 and 5.8 aso revea the aong-track and across-track discrepancies among 3 adjacent strips. Furthermore, the recovery of systematic biases does not seem to be good enough based on the ICP agorithm, especiay on the was of this buiding which introduced occusions. A severe probem when appying surface matching to patches containing roofs/was is caused by occusions typicay occurring at one side of a buiding in one strip as a consequence of the quasi centra perspective geometry of aser scanning in the across-fight direction (Maas, 2002). These occusions become visibe as gaps in one of the patches. Due to the composition of aser scanning data bocks of parae strips, these occusions wi often occur in ony one of the patches to be matched. For instance, the profie of strip- shows the occusion effect in the circuar zone in Figure 5.7. The anaysis of the height data and the strip geometry suggests that the areas that were occuded in one strip are excuded from the matching (Kiian et a., 996; Maas, 2002). Figure 5.9 shows the trend of the panimetry shifts and height offsets for the first patch of 4 adjacent strips. The first row of Figure 5.9 shows that the x-shift (pitch induced) varies with the aser scanning patterns. The second row of Figure 5.9 reveas that the y-shift (ro induced) increases aong the direction of fight for a strips. The ast row of Figures 5.9a and 03

28 5.9c depicts the height offsets increasing toward the rim of the scanning extent in the acrosstrack direction. The effects are induced by an osciating scanner. X coordinates vs. X-shift (m) X coordinates vs. X-shift (m) X coordinates vs. X-shift (m) X coordinates vs. -shift (m) Fight direction: E. W. X coordinates vs. -shift (m) Fight direction: E. W. X coordinates vs. -shift (m) Fight direction: E. W. X coordinates vs. Z-offset (m) X coordinates vs. Z-offset (m) X coordinates vs. Z-offset (m) a. Strip 8/9 b. Strip 9/0 c. Strip 0/ Figure 5.9: Trend of panimetry/height shifts for patch- in SI Due to the imitation of the aser scanner s anguar resoution, the eevation accuracy is usuay much higher than the horizonta accuracy for ALS systems (Leica 2002; Optech 2002). With the height offsets much arger than the panimetry shifts, it impies that the systematic errors may be introduced by range biases or may come from an incompete caibration between GPS and IMU frames. Regarding the height offsets between strips to 9 and strips 0 to 9, the fact that the data are acquired in different dates may aso pay a roe. 04

29 In order to achieve a higher density of aser scanning data to create good quaity DSM, integrating a overapping strips data is necessary. As shown in Figure 5.20a, the DSM (Goden Software, 997) created from 4 origina neighboring strips deineates the rugged surface due to the height offsets in some strips. On the contrary, Figure 5.20b presents a distinct DSM that integrated the 4 adjacent strips after the ICP matching agorithm is appied to the patches from strips 8, 0, and with the patch of strip 9 fixed. a. From origina data. b. From data after the ICP matching when the patch of strip 9 is fixed. Figure 5.20: DSM of the integrating 4 overapping strips of patch in SI The texture shown in Figure 5.20 provides some usefu information about the shape, orientation, and depth of objects. The human visua system empoys texture as a visua cue for object recognition and image interpretation (Schenk, 999). It can be easiy found that the DSM in Figure 5.20b presents much more detaied texture than Figure 5.20a did, especiay the ditches between rice paddies and the roofs of buidings Test Site II (SII) Figure 5.2: Two overapping aser scanning strips in test site II (SII) 05

30 The preiminary evauation by using ground reference points reveas height systematic errors in SII (Section 4.5.2). Therefore strip- and strip-2 in SII are seected to run test fights for this phase of the research. As shown in Figure 5.2, there are thirteen patches seected inside the overapping area in SII as the test patches for the vaidation with the ICP agorithm. Tabe 5.26: Panimetry/height offset, appied to 3 patches of strip-and 2 for SII Strips _2 No. of patches 3 Panimetry/Height X Z Average (m) Std dev (m) Min. (m) Max. (m) The resuts from appying the ICP agorithm to the panimetry and height offsets in SII are presented in Tabe 5.26 where strip-2 is fixed. The size of the height discrepancy ranges from -0.5 m to m whie the average height offset is from m for a patches. The average panimetric strip shift is m in the x direction and 0.60 m in the y direction, accompanying the panimetric shifts up to 0.60 m. With the fight atitude at 500 m, the horizonta accuracy shoud be ess than 0.75 m. Thus, the detected panimetric shifts between these two neighboring strips are aso within the accuracy requirements specified in most ALS systems. However, the identifying height discrepancies suggest that this test set has to be adjusted so as to correct for systematic errors. The most teing indication of caibration errors can be seen in the graphica profie pot. Like the profies in SI, differences are painy visibe by potting aong structures such as buidings with gabe roofs. The significant height discrepancies between two strips can be easiy observed from Figure 5.22a. The difference is about 0.43 m and is very cose to the resut depicted in Tabe The profie generated from the transformed point couds registered by the ICP agorithm with the strip-2 fixed, shows a much better aignment (Figure 5.22b). 06

31 a. Profie from origina data b. Profie from data with the ICP matching Figure 5.22: Profie comparison from 2 overapping strips for SII Two corresponding, overapping strips are integrated. As shown in Figure 5.23a, the DSM generated from two origina neighboring patches reveas the inconsistency on the surface due to systematic height offsets. Next, the DSM is re-generated by using the registered data to repace the origina points for strip. Figure 5.23b shows a better agreement on the surface. a. From origina data. b. From data after the ICP matching when the patch of strip 9 is fixed. Figure 5.23: DSM of the integrating 2 overapping strips of patch in SII From the experimenta resuts presented in this section, it can be concuded that the surface registration by using the ICP agorithm can be an aternative way to estimate the 07

32 height offsets and panimetry shifts from overapping aser scanning strips. For exampe, there are not enough ground contro points to be used to verify the accuracy of aser data. Moreover, it is not necessary for the ICP agorithm to empoy the techniques of interpoation and image processing invoved in this step in order to find the corresponding points, which are used as tie points. 5.3 Remaining systematic error recovery The ICP agorithm pays a successfu roe not ony in estimating the panimetry shifts and height offsets from overapping aser scanning strips from the anaysis of experimenta resuts, but aso recovering the imperfect data set based on the assumed perfect data set. However, its convergence onto the desired goba minimum requires memory-insensitive and timeconsuming impementations. It is not possibe to appy the ICP agorithm to two adjacent strips. Next, this research aims towards presenting a strip adjustment procedure to recover data with remaining systematic errors. Two methods are appied. The 3-D simiarity transformation, i.e. the seven parameters transformation between two 3-D data sets, and the strip adjustment with three parameters, are used to adjust the aser strips when there is not enough ground reference points avaiabe. Meanwhie, the corresponding points derived from ICP matching are used to form the observations to impement the adjustment D Simiarity Transformation Test site I (SI) The data vaidation is foowed by data adjustment to fufi the procedures on handing systematic errors. A 3-D simiarity transformation is used to adjust data in this research. In addition to the initia seven parameters, i.e. scae, 3 rotation anges and transation vector, the correspondence between two surfaces have to be estabished. The correspondence is buit when the iteration of surface matching (i.e. the ICP agorithm) terminated. 08

33 Figure 5.24: Corresponding points for patch 4 of SI The pre-anaysis affirms that strip 0 has systematic errors when strip 9 is used as the reference surface. Then strip 9 and strip 0 are chosen as experimenta fight ines for SI. Again, ICP matching is appied to 4 patches with size of 800 m x 400 m to search the correspondence between strips 9 and 0. The corresponding points, which are derived from a patches, form the input to a 3-D simiarity transformation. For exampe, there are about 900 points that are used to estabish the correspondence on patch 4 (NCTU s campus) of SI, as shown in Figure A generated profie on a roof can te the position of the corresponding points. The mode curve is strip 9 (wi be fixed whie registering), and the data curve is strip 0 in Figure 5.25a. a. Test site I (SI) b. Test site II (SII) Figure 5.25: Two exampes to show the mode curve and data curve 09

34 The computed parameters are shown in Tabe It reveas that the systematic error on height is mainy contributed by the misaignment of ro error since the parameter in Tabe 5.27 is much arger than the accuracy of IMU (0.005 degree for ro & pitch). Tabe 5.27: The computed seven parameters for SI Parameters Scae ( ) (deg) (deg) (deg) t x (m) t y (m) t z (m) Vaue Next, the computed seven parameters are used to recover strip 0. The panimetric and vertica discrepancies are depicted in Tabe 5.28, and they are computed whie cacuating the differences of coordinate between the origina and the recovered data. The height offset in Tabe 5.28 is very cose to the discrepancies which are derived from surface matching (Section 5.2.). Tabe 5.28: Panimetric/height differences for strip 0 of SI Strips 0 Panimetry/Height X Z Average (m) Std dev (m) Min. (m) Max. (m) In order to find the moving direction and magnitude of strip 0 after transformation, the corresponding points are used as check points. As shown in Figure 5.26, a scaed symbo map using ange vaues derived from the transformed and origina coordinates is superimposed on DSM of patch 4 in strip 0. The scaed arrow in Figure 5.26 is based on the magnitude of the distance between the origina and the transformed coordinates. The magnitude ranges from.68 m to.83 m with an average of.73 m and a standard deviation of 0.04 m. The point is generay transformed to its new position aong the NW-SE direction. 0

35 Figure 5.26: A scaed symbo map using ange vaue (SI) Tabe Height differences before and after data adjustment with GCPs for strip-0 Statistics Mean(m) Std dev(m) Min.(m) Max.(m) Qty Before After Tabe 5.29 shows that the corresponding points derived from ICP matching that are appied to the 3-D simiarity transformation coud decrease the average height offsets from.65 m to 4.8 cm for strip 0. It suggests that the 3-D simiarity transformation provides an aternative way to recover data when there are not enough GCPs. Test site II (SII) Simiary, the correspondence from thirteen patches of SII can be regarded as the tie points when surface matching is done. The 3-D coordinate difference of between the origina and the recovered strip is shown in Tabe 5.3 by using the computed parameters in Tabe Again, the average discrepancy is very cose to the resut in Section Tabe 5.30: The computed seven parameters for SII Parameters Scae ( ) (deg) (deg) (deg) t x (m) t y (m) t z (m) Vaue

36 Tabe 5.3: Panimetric/height differences for strip of SII Strips Panimetry/Height X Z Average (m) Std dev (m) Min. (m) Max. (m) A generated profie on a roof can define the mode curve, strip 2 (wi be fixed whie registering) and the data curve, strip in Figure 5.25b. Next, the corresponding points are used as check points, in order to find the moving direction and magnitude of strip after transformation. As shown in Figure 5.27, a scaed symbo map using ange vaues derived from the transformed and the origina coordinates is superimposed on DSM of patch 2 in strip. The magnitude ranges from 0.60 m to 0.63 m with an average of 0.62 m and a standard deviation of 0.8 cm. The point is transformed to its new position aong the SE-NW direction. Figure 5.27: A scaed symbo map using ange vaue (SII) 2

37 a. Height difference vs. frequency b. Height difference vs. accumuative frequency Figure 5.28: Height difference between origina and transformed patch 2 (SII) Furthermore, the height difference versus frequency, and the height difference versus accumuative frequency are depicted in Figure 5.28a and Figure 5.28b respectivey. The average difference (0.43 m) coud be considered as the eevation bias between the two strips (strip and strip 2). The probabiity distribution of the height differences foows approximatey a norma distribution. Correspondingy, Tabe 5.32 shows that the derived corresponding points coud decrease the average height offsets from 0.33 m to -0.0 m for strip. For test II, the coordinate of strip is transformed to strip 2 based on the 3-D simiarity transformation. The height discrepancy for strip 2, checked by GCPs, reached -0.3 m (Appendix C, Tabe C.2); thus it resuts in higher average offsets. Tabe Height differences before and after data adjustment with GCPs for strip Statistics Mean(m) Std dev(m) Min.(m) Max.(m) Qty Before After Strip Adjustment with Three-Parameters In order to verify the corresponding points from ICP matching, a strip adjustment procedure concerning the heights is used in this section. The method proposed by Crombaghs et a. (2000) and used by Tung (2005) wi aso appy to two seected test sites. 3

38 The foundation of this method is the creation of height differences in overapping strips. The differences are not computed for individua points because the point noise of about 0-5 cm is high. Therefore, differences are computed as mean differences for groups of minima 00 points in areas of m 2. The tie points areas of m 2 have to be fat and smooth. Otherwise, sma panimetric errors might generate a arger impact on the mean difference for this seected area (Crombaghs et a., 2000). The corresponding points from ICP matching form the tie points in this research, instead. Height differences in overapping areas of neighboring strips and height differences of aser points and references measurements are used to determine and to correct for offsets and tits. Every individua strip is corrected for offset (a), aong-track (b), and across-track (c) tits. This method is therefore caed the strip adjustment with three parameters. The reference data (ground contro points) are aso seected from point couds since there is not enough ground reference points avaiabe. Therefore, the height differences between ground reference points and their corresponding aser points are not presented. The beforeand after- adjustment mean height difference and its RMSE from corresponding points wi be used to evauate the effect of appying the strip adjustment with three parameters to overapping strips. The three computed parameters are presented in Tabe 5.33 for SI and SII. Tabe 5.33: The computed three parameters for SI and SII Test Site offset (a) aong-track (b) across-track (c) strip SI strip strip SII strip The inspection of the adjusting resuts is done in various ways. One of them is anayzing the spatia distribution of the height residuas after adjustment. Two exampes are shown in Figures 5.26 and 5.27 in the previous section. These areas are grouped in pairs, so that the profie of height differences in the aong-track direction can be created. Anayzing these profies of height differences before and after adjustment faciitates the interpretation of the achieved improvement and occurring systematic errors (Crombaghs et a, 2000; Tung, 2005). 4

39 Tabe 5.34: The mean height difference and RMSE for SI and SII Test Site Before adjustment After adjustment No. of tie Mean (m) RMSE(m) Mean (m) RMSE(m) points SI SII The mean height differences of corresponding points before adjustment are -.69 m and m for SI and SII, respectivey. These two vaues are cose to the computed parameters of height offset (a) which is shown in Tabe It is reveaed that the height offset (a) is the most significant parameter of systematic errors on height for SI and SII. Next, the RMSE of the residuas after adjustment decreases to m from.65 m for SI and to 0.73 m from m for SII, respectivey. The effectiveness of the strip adjustment can aso be examined by anayzing the distribution of residuas before and after adjustment for whoe aser strips. In Figures 5.29 and 5.30, two exampes are given. The figure reates to a arge bock of strips for SI and SII, respectivey. The coordinates of x-axis in Figures 5.29 and 5.30 are the direction of fight, that is, the aong-track direction. The residuas are significanty smaer after strip adjustment, eading to the concusion that the strip adjustment with three parameters increased the quaity of dataset consideraby. a. Before adjustment b. After adjustment Figure 5.29: Residuas before and after strip adjustment for SI 5

40 a. Before adjustment b. After adjustment Figure 5.30: Residuas before and after strip adjustment for SII The decrease of RMSE is mainy caused by removing systematic strip errors, such as offset (a) and tits (b, c). Judged from the resuts from both test sites, a more sophisticated approach is required. This appies to the deformations, such as cross strip paraboic deformation, aong-track periodic effects and strip torsions (Crombaghs et a., 2000). Appying a 3-D simiarity transformation and the strip adjustment with three parameters to a aser scanning data with correspondence derived from surface matching determines the strip discrepancies. It aso demonstrates that the accuracy of height can be upgraded if a proper procedure is appied. Nevertheess, the experimenta resuts present a reative accuracy since there is not enough ground reference invoved. Therefore, the scheme based on surface matching technique as we as the remaining systematic error recovery can be used as a quaity contro too of ALS. For some digita eevation data, the reative (i.e. point-to-point) accuracy is more important than the absoute accuracy. For exampe, the reative vertica accuracy of a dataset is especiay important for derivative products that make use of the oca differences among adjacent eevation vaues, such as sope and aspect cacuations. Correspondences between overapping strips of airborne LiDAR serve as the input for strip adjustment procedures that estimate and eiminate systematic errors. In this dissertation, two methodoogies are used to estabish the correspondence between patches of aser points. First, image matching is used to find the corresponding points (tie points) for boresight 6

41 caibration. Next, the ICP registration is used for accuracy verification and buit the correspondences between overapping strips. The estabished correspondences are then used as input data for strip adjustment. Can the matched tie points from overapping strips via image matching techniques be used as corresponding points for strip adjustment? Or, is it possibe that the correspondences from ICP registration can be used as tie points for boresight caibration? The cross-experiments on these issues are presented in Appendix D. From Appendix D, it can be concuded that the interpoation of aser points to a reguar grid introduced errors on the parameters of the 3-D simiarity transformation. In addition, it reveaed that the interpoation shoud be avoided whie verifying the accuracy of the aser point couds. Next, with the intentiona boresight anges given for caibration, the tie point differences and reguar point eevation differences are affected by the arge panimetric shifts between the uncaibrated strips. Thus, a grid point in one strip wi generay not correspond to the same point in the second strip. To improve the tie point seections by using ICP registration for boresight caibration, it is necessary to address the disadvantages of ICP agorithm. Finay, the research presented an intensive work on systematic errors for system caibration, systematic error vaidation and remaining systematic error recovery. The proposed scheme (Figure 5.3) successfuy pays a roe on data correction as we as on the quaity contro mechanism for ALS data. 7

42 Figure 5.3: Work fows for accuracy assessment on ALS data 8

43 CHAPTER 6 CONCLUSION AND FUTURE WORK This dissertation presents a compete framework on handing systematic errors of ALS data for system caibration, systematic error vaidation and remaining systematic error recovery. First, for system caibration, each boresight misaignment parameter is discussed to assess its impact on data accuracy and methodoogy of recovery. A caibration soution used by a commercia system is introduced with a design of optima caibration fights. The improvement to this approach is then proposed. An in-situ data set from a caibration fight is used to evauate the improvement on the accuracy of misaignment parameters. The proposed automated method of extracting tie points to improve the current method on ALS system caibration can significanty upgrade the accuracy in tie point seection. The TerraMatch program is then used to re-verify the computed boresight parameters. Therefore, the accuracy of misaignment parameters is expected whie appying a practica caibration fight. There is sti no standardized procedure on an important issue: how often shoud the boresight misaignment caibration be checked for an ALS system? With a fast and reiabe caibration method, caibration parameters can be checked more frequenty. Furthermore, by interpoating intensity refectance into a reguar grid, a grayscae image very simiar to photogrammetric images is formed. The simiarity was expoited by using an image matching technique to search for the corresponding points. Thus, the intensity information was shown to have high potentia for further research. Next, the ICP agorithm, which is one of the surface registration methods, is adopted in this study to verify the quaity of the overapping aser scanning data. The ICP agorithm 9

44 provides the benefit of avoiding interpoating raw aser points, and evauating the height as we as the panimetry offsets from overapping aser strips. The observed systematic errors in these two data sets aso revea that the accuracy of boresight misaignment parameters pays a critica factor on the quaity of point couds. The correspondence is estabished, and it is predictabe in soving the correspondence probem between two overapping aser strips. Next, a strip adjustment procedure is proposed to recover data that have remaining systematic errors. Two methods are appied. The 3-D simiarity transformation and the strip adjustment with three parameters are used to recover the aser strips when not enough ground reference points are avaiabe. Meanwhie, the corresponding points derived from ICP matching are used to form the observations to impement the adjustment. The two proposed methods of strip adjustment not ony confirm that the corresponding points from ICP matching are good enough observations, but aso demonstrate that the two easiy impemented methods can improve the quaity of ALS data, especiay on vertica accuracy. A suggested scheme on the accuracy assessment as we as the strip adjustment for ALS data is therefore proposed. Furthermore, there are some minor findings from this research. First, the interpoation with a smaer grid size has a higher accuracy of boresight parameters, when the tie points are manuay measured with the Attune program. However, the aser points are not eveny distributed. The constructed image can sometimes introduce the difficuty for tie point seection when a grid size smaer than the average density of aser points is appied. It is concuded that an interpoation method based on a TIN of the origina points with a grid size that reates as cosey as possibe to the point density at acquisition yieds the best resuts. The findings based on the correation matrix of boresight caibration aso revea that the correations between torsion/ro and torsion/pitch that are generated with an automated tie point seection are much arger than the correations generated with a manua seection. It impies that the distribution of tie points is correated with the misaignment parameter s soution. 20

45 In this dissertation, the corresponding points that are extracted from the surface registration between two overapping strips were used as the tie points for data adjustment with the 3-D simiarity transformation and the strip adjustment with three-parameters. Before this research goes further to appy more sophisticated approaches to rectify systematic errors, the extracted corresponding points need to be fitered, since some of the pairs are incorrecty matched. The exampes incude points on moving vehices, points on trees, or points faing into occuded zones. The appropriate soution coud (i) appy image matching to fiter out points ocating on a distinctive feature such as road marking or intersections, and (ii) use the cassified ground aser points for ICP matching to avoid seecting points on vegetation or inside of occuded zones. The present work recommends future research with respective to the foowing topics: Traditionay, the accuracy of manua tie point measurement shoud reach ps/3 (ps = pixe size) in digita photogrammetry. The intensity images used in the Attune program and the height/intensity images used in this dissertation are based on interpoated reguar grid. Therefore, these images are much different from traditiona photogrammetric images. Furthermore, the size of aser footprint varies with the strength of refectance and the factors of terrain. In practica test, this eve (ps/3) of accuracy is very difficut to reach whie appying manua tie point seection. With the innate imitation of horizonta accuracy of ALS data, how to set up the standard of accuracy on the tie point measurement for ALS interpoated data wi be an issue that requires further research. Regarding the distribution of points, it is difficut to force the computer to find a soution in a desired zone whie impementing image matching to find the corresponding points. On the contrary, an operator can easiy seect the points with a priori knowedge on geometric distribution. Xu (2004) proposed a mechanism to spit the matching areas into nine (or more) rectanges to make sure that each rectange has at east one successfuymatched point. Considering the characteristics of induced errors, the soution of boresight misaignment parameters might be sensitive to the geometry of the seected tie points. It suggests that geometric distribution of corresponding points on the effects upon soution of parameters is one of the critica issues for future investigation. 2

46 For the ICP agorithm as we as other registration methodoogies, refinement of the agorithm is necessary. Firsty, a more functiona agorithm to remove the effects that are introduced by occusions shoud be appied before matching. Next, as a consequence of the characteristics of aser puse penetration as we as samping pattern and viewing direction, data points on vegetation or other objects with an irreguar shape may show rather different heights in neighbouring strips, eading to unpredictabe outiers in matching. It suggests that the cassified ground points shoud be appied for matching. Incuding the proposed surface matching agorithm in this study, some of the strip adjustment methods work ony with tie points without using GCPs. However, the use of some type of ground contro is desirabe, since eiminating the reative discrepancies between overapping strips does not provide an absoute check of the data sets. An efficient and reaizabe method to find the correspondence between aser points and ground is essentia. Specificay-designed ALS targets simiar to Csanyi et a. (2005) shoud be considered for future research on ALS strip adjustment. 22

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56 Appendix A: Observation equation of proposed methodoogy for ALS boresight caibration as: For each ground or tie point from an ALS data can be described as a parametric equation X Z ground contro X = Z aircraft position + R body frame to ground rotation R misaignment x y z aser range components (A-) where: ( X, Z ) groundcontro, : the derived terrain point ( X, Z ) aircraftposition, : the aircraft position at the observation epoch R body to ground rotation ( x y, z ) aserrange : the rotation cosine matrix from the aircraft body frame to the ground frame, : the aser range components derived from the aser range and scanner ange It has been observed empiricay that the misaignment anges are often ess than 3 degrees. The misaignment matrix R misaignment is therefore repaced by the sma-ange approximation: κ φ R misaignment = κ ω (A-2) φ ω where:,, : the ro, pitch, and heading misaignment anges From Equations (A-) and (A-2), it can be derived: X Z = κ φ κ ω φ ω X Z aser range components (A-3) 32

57 33 where: = position aircraft contro ground T rotation ground to frame body Z X Z X R Z X For simpicity, the subscript aser range components is omitted in the foowing derivation. Therefore, equation (A-3) can be represented as: + = = Z X X X Z Z Z X Z X κ φ ω ω φ ω κ φ κ (A-4) Finay the observation equation becomes: = κ φ ω X X Z Z Z X (A-5) where: = Z X Z X Z X For one contro point, the observation equation can be estabished as Equation A-5. For n contro points, the observation equation wi be: 3,,3 3, 3 X A B n n = (A-6) The east squares soution is: ( ) ) ( B A A A X T T = = κ φ ω (A-7)

58 Since the observation is inear, no iteration and initia approximation are needed for the east-squares adjustment. However, if the average positions of tie points are used as contro points, iteration is needed to update the average positions of the tie points (Morin and Esheimy, 2002). X Z average tiepoint X = Z aircraft position + R body frame to ground rotation R misaignment x y z aser range components (A-8) where: X Z average tiepoint = ( ) n X Z tiepoint tiepoint tiepoint where: n : the number of points used to parameterize the tie point The mode must be iterated so that the average constraints are updated for each correction of the caibration parameters. The proposed mode addresses the need for true observations by incorporating the tie point interpoation within the adjustment mode. The methodoogy begins by searching for the nearest true observations of the coected tie point within the ALS dataset (Morin and E-sheimy, 2002; Leica, 2003a). The tie point is then parameterized as a function of distances from the nearest true points, i.e.: X Z tiepoint = ( ) n X Z observed observed observed + dx + dy + dz (A-9) where: dx,dy,dz : the initia distances between the measured tie point and the uncorrected, observed ALS ground point. (X,,Z) observed : the updated ALS ground points using Equation (A-8) The averages can be simpe averages or weighted by the inverse of distances. The observation equation for the adjustment is then derived as: 34

59 35 ) ( ) ( tan int 0 int ce dis tiepo components range aser z y x misaignment rotation ground to frame body position aircraft n i tiepo average dz dy dx R R Z X n Z X + + = = (A-0) Athough a singe tie point observation equation now contains severa ALS observations, they are a inear combination and the partia derivates for the design matrices which are just the weighted average of the partia derivatives for each observation. Correspondingy, from Equation (A-0), it can be derived: = n components range aser Z X n Z X 0 ω φ ω κ φ κ (A-) where: = n ces dis tiepo n position aircraft tiepo average T rotation ground to frame body dz d dx n Z X n Z X R Z X 0 tan int 0 int Further derivation gives the observation equation: = κ φ ω n X n n X n Z n n Z n n n n n n Z X (A-2) where: = n Z X n Z X Z X

60 The Equation A-2 is then be used as the observation equation for taking the average of the matched tie points as contro points. After getting ( 0, 0, 0 ) for each strip from the first iteration, it is necessary to update the 3-D position of tie points and average them to obtain new contro points for next iterating computation unti a soution has converged. 36

61 Appendix B: Height statistics for two test sites Tabe B.: Height statistics for SI Strip No Z_mean(m) Z_std(m) Z_min(m) Z_max(m) Avg. Density (pts/m 2 ) Tabe B.2: Height statistics for SII Strip No Z_mean(m) Z_std(m) Z_min(m) Z_max(m) Avg. Density (pts/m 2 )

62 Appendix C: Height differences between aser scanning data and GCPs Tabe C.: Height difference for SI Strips_no Mean(m) (m) Min.(m) Max.(m) Points No N/A* Min Max *Ony one GCP fas in the extent of the 9 th aser strip data. Tabe C.2: Height difference for SII Strips_no Mean(m) (m) Min.(m) Max.(m) Points No * *The tota number of GCPs in test site II is

63 Appendix D: Correspondences from image matching vs. ICP Registration Correspondences between overapping strips of airborne LiDAR serve as the input data for strip adjustment computation which estimates and recovers systematic errors. In this dissertation, two methodoogies are used to create the correspondence between patches of aser points: (i) image matching for boresight caibration; and (ii) ICP registration for systematic error vaidation. Can the matched tie points from overapping strips via image matching techniques be used as corresponding points for systematic error vaidation? Or, is it possibe that the correspondences from ICP registration used as tie points for boresight caibration? The experimenta resuts of these two issues wi be presented in next two sections. D. Appying the matched tie points using image matching as the corresponding points for 3-D simiarity transformation Foowing the procedures on boresight caibration presented in Section 5., the tie points from thirteen patches of SII can form the correspondence as the input data for the 3-D simiarity transformation by using image matching from overapping patches. The grid size is 0.6 m for interpoation since the average point density is about 2.2 pts/m 2. Tabe D.: The computed seven parameters for SII from image matching (height) Parameters Scae ( ) (deg) (deg) (deg) t x (m) t y (m) t z (m) Vaue Tabe D.2: The computed seven parameters for SII from ICP registration Parameters Scae ( ) (deg) (deg) (deg) t x (m) t y (m) t z (m) Vaue Tabe D.3: Comparison of panimetric/height differences for strip of SII height Method ICP registration Image matching (height) Panimetry/Height X Z X Z Average (m) Std dev (m) Min. (m) Max. (m)

64 Both of the height and intensity images are aso used in is section. The resuts (i.e. described in section and presented as Tabe D.2) from ICP registration are used as reference data. For height images, the panimetric and height difference between origina and recovered strip are shown in Tabe D.3 by appying the computed parameters in Tabe D.. The difference between two methodoogies is significant for both of average panimetric and height differences (Tabe D.3). For intensity images, the panimetric and height difference between origina and recovered strip are shown in Tabe D.5 by using the computed parameters in Tabe D.4. Once again, the differences on the average height/panimetric discrepancy are aso significant as Tabe D.5 shows. Tabe D.4: The computed seven parameters for SII from image matching (intensity) Parameters Scae ( ) (deg) (deg) (deg) t x (m) t y (m) t z (m) - - Vaue Tabe D.5: Comparison of panimetric/height differences for strip of SII intensity Method ICP matching Image matching (intensity) Panimetry/Height X Z X Z Average (m) Std dev (m) Min. (m) Max. (m) It is concuded that the interpoation of aser points to a reguar grid wi reduce the accuracy of the parameters from the 3-D simiarity transformation. In addition, it reveas that the interpoation shoud be avoided whie vaidating the systematic errors for aser point couds. D.2. Appying the corresponding points using ICP registration as the tie points for boresight caibration The four boresight test strips used in the section 5. are aso used in this section. Correspondingy, the first strip is fixed whie appying the ICP registration. The difference between the initia and caibrated tie point are depicted in Tabes D.6 and D.7, respectivey. 40

65 Tabe D.6: Initia tie point differences X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Tabe D.7: Tie point differences after caibrated X (m) (m) Z (m) Mean Median Minimum Maximum Std Dev Figure D.: Mismatched tie point from ICP registration One of the interesting things in Tabes D.6 and D.7 is that the caibrated tie point difference is much arger than the initia tie point difference. The principe of the ICP agorithm estabishes correspondences between data sets by matching points in one data set to the cosest points in the other data set. Therefore, the Eucidean distance between data sets 4