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Journal of Terrestrial Observation Volume 2, Issue 2

Spring 2010

Article 7

Refinement of Digital Elevation Models in Urban Areas Using Breaklines Via a Multi-Photo Least Squares Matching Algorithm Ahmed F. Elaksher and James Bethel

Copyright © 2010 The Purdue University Press. All rights reserved. ISSN 1946-1143.

Refinement of Digital Elevation Models in Urban Areas Using Breaklines Via a Multi-Photo Least Squares Matching Algorithm Ahmed F. Elaksher* and James Bethel** *

Cairo University, **Purdue University

ABSTRACT High quality DEMs are necessary for several urban applications such as telecommunication, urban development, and visualization, and city planning and management. Sudden changes in surface topography weaken the capability of existing automatic terrain extraction techniques to provide high quality DEMs. Hence, these DEMs need to be refined either manually or automatically to be useful for such applications. Manual refinement is costly and time consuming, thus automatic refinement is preferred. In this research, three new DEM refinement approaches are demonstrated. In the first approach only breaklines are utilized, while the second approach incorporates image signals in a least squares matching model. In the third approach, pixels corresponding to hidden objects are detected and eliminated from the least squares matching model. Breaklines are used in the three approaches to impose surface discontinuity. The least squares matching model minimizes the differences between the image intensities by adjusting the elevations of the DEM posts. The refining approaches are tested on eight one-meter resolution DEMs. The DEMs are generated with a digital-mapping software from 1:4000 scale aerial photographs scanned at 30µm resolution. Results revealed that the accuracy of the DEMs is considerably improved using the third approach and demonstrate its benefit in refining DEMs especially for urban area applications.

1. INTRODUCTION Digital elevation models (DEMs) are an important and valuable data source for a large number of applications like cartographic analysis, air traffic navigation, mobile communication, environmental studies, and urban planning. Although DEMs can be generated from a wide range of sources such as land surveying, satellite images, and laser ranging data; aerial images are still the main source to produce highquality DEMs in either urban or rural areas (Mikhail et al., 2001). Both manual and automatic methods have been developed to create DEMs from aerial images. Although manual techniques provide high-quality elevation data, human operators need advanced photogrammetric knowledge, image understanding skills, and The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010) 67

68 | Ahmed F. Elaksher and James Bethel

technical experience to select and match image points. Hence, Automatic Terrain Extraction (ATE) techniques are preferred. The target of ATE algorithms is to establish correspondence between individual points in two or more images automatically. The elevation of ground points is then computed using projective geometry. However, these algorithms fail to provide high-quality DEMs in the presence of discontinuous surfaces due to noise, hidden points and surfaces, and sudden surface changes. As a result, blunders and spikes exist in the final products of ATE DEMs and a refinement step is essential. DEMs refinement has been addressed by several researchers in the last decade. Milledge et al. (2009b) recommended using old DEMs to remove gross errors in stereo-matching. First the new DEM was compared with the old data to locate areas where elevation differences are higher than a predefined threshold. This comparison led to identifying errors and provided means to train the stereo-matching algorithms to enhance the accuracy of the new DEMs up to 50%. Karkee et al. (2008) discussed the fusion of Shuttle Radar Topographic Mission (SRTM) DEMs and Advanced Spaceborne Thermal Emission and Reflection (ASTER) DEMs to improve the quality of DEMs. After registering both datasets vertically and horizontally, voids in both DEMs were filled through an erosion technique utilizing elevations, slopes, and aspects from the other DEMs. To eliminate errors, both DEMs were transferred to the frequency domain and an ideal low-pass filter was applied to the ASTER DEM and a high-pass filter was applied to the SRTM DEM. The filtered spectra of both DEM were summed in the frequency domain and transferred back to the spatial domain. The Root Mean Square Error (RMSE) of the final DEM was decreased to about 58%. Yang et al. (2007) illustrated improving small-scale DEMs by decreasing errors in DEM data sources, i.e., contour, spot height, and hydrologic features, and optimizing the interpolation parameters using higher accuracy independent validation data and semi-quantitative analysis of DEM derivatives. Shi and Tian (2006) proposed a hybrid interpolation method that incorporates both the bilinear and the bi-cubic interpolation methods for DEM refinement. The weight of each interpolation method was defined by the complexity of the terrain. Although both procedures achieved some progress toward reliable and high-quality DEMs, they are not suitable for areas with surface discontinuities. Georgopoulos and Skarlatos (2003) used a pair of stereo images to refine coarse DEMs. Two orthoimages were generated, one for each image. The parallax between the two orthoimages was computed by image correlation methods based on reference and search templates taken from the two orthoimages. Subsequently, the displacement of the best match point was used to compute elevation errors in the DEMs. The errors were then used to refine the DEM. A similar approach was used iteratively until the parallax fell below a certain threshold recommended by Amitabh et al. (2005). The RMSE was decreased to 50 centimeters using 1:17000 scale images. Techniques for generating and refining DEMs using descent and rover imThe Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

Refinement of Digital Elevation Models in Urban Areas |

69

agery for Mars mapping were detailed in Olson et al. (2007) and Di et al. (2007). During the descending process of a Mars spacecraft, ten descent images were taken at approximately every half of the altitude. The images were used to generate an initial DEM of the landing site. The DEM was then refined in both accuracy and resolution to form a five-layer hierarchical DEM, with resolutions ranging from one centimeter to one meter. Area-based matching, epipolar constraints, and least squares matching were used in the refinement process of the DEM. The proposed technique works fine when no surface discontinuity exists, but it is inapplicable in urban areas. DEM refining using filtering techniques has been widely investigated. Milledge et al. (2009a) addressed the possibility of filtering Interferometric Synthetic Aperture Radar (InSAR) and image-based DEMs with three different techniques. First they convolved the DEM with a Gaussian noise removal filter (Walker and Willgoose, 2006). In addition, they considered integrating a geostatistical filter (Felicísimo, 1994) with a hierarchical surface fitting technique (Wang et al., 2001). Finally, they adopted a threshold slope-based filter (Vosselman, 2000) to enhance the DEM quality. For the image-based DEM, the mean error of the original DEM was reduced from 1.71 meters to 1.17, 1.55 for the first and second filters, respectively, while the third filter did not improve the DEM quality. Filtering techniques usually smooth DEMs and in the vicinity of urban buildings this deteriorates the DEM quality. Dragos et al. (2004) used breaklines in the filtering process of laser-based Digital Surface Model (DSM). A moving plane interpolation method was used to generate the DSM from a point cloud in a hierarchical approach. First, a rough approximation of the surface was computed. Then, the oriented distances from the surface to the original cloud of points were computed. Each measured elevation was given a weight according to its distance value. The surface was then recomputed using the moving plane under the consideration of weights. The moving plane was trimmed when a breakline was crossed. The proposed filtering technique is ideal for laser-based elevation models. However, these models are expensive to collect and insufficient to provide surface texture. Refinement and filtering techniques from the literature are adequate for either small-scale DEMs or DEMs with no discontinuities. Hence, there is a need to develop a refinement procedure that can handle discontinuities in high-resolution DEMs. This paper introduces three different algorithms that utilize breaklines and image intensities to improve the quality of high-resolution DEMs. The first algorithm is based on only smoothing the elevations except in the vicinity of breaklines, while image intensities are added in the second algorithm via a least squares matching model. In the third algorithm, image intensities of obscured posts are removed from the least squares matching model. The outputs of the algorithms are the adjusted elevations of the DEM posts. Results cut down the RMSE of eight ATE DEMs to about 50%. The reminder of the paper is organized as follows: the algorithms are summarized in the 2. Methodology section, followed by 3. Experimental Results and Analysis and 4. Conclusions. The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

by 3. Experimental Results and Analysis and 4. Conclusions. 70 | Ahmed F. Elaksher and James Bethel 2. Methodology

Three different DEM refinement algorithms, based on the least squ 2. Methodology

in this In the first algorithm, four equations are Three different DEMpaper. refinement algorithms, based on the leastcontinuity squares adjustment, are proposed in this paper. In the first algorithm, four continuity equations post and its eight neighboring posts. However, if a breakline are imposed equation, between each DEM post and is its eight neighboring However,algorithm, the equation eliminated. In posts. the second if a breaklinematching intersects with a continuity the equation isIneliminated. model is addedequation, to the adjustment. this model, observ In the secondquantify algorithm,the a multi-photo squares the matching model isof added to differenceleast between intensities corresponding p the adjustment. In this model, observation equations are formed to quantify the observation equations are formulated as functions of the elevati difference between the intensities of corresponding in allmatching image pairs. The is to min objective of the multi-photo leastpixels squares model observation equations are formulated as functions of the elevations of the DEM the intensities of corresponding pixels via changing the elevations o posts. The objective of the multi-photo least squares matching model is to minialgorithm, observation equations of obscured posts are removed fr mize the differences between the intensities of corresponding pixels via changing three subsections discuss the details of each algorithm. the elevations of the DEM posts. In the third algorithm, observation equations of obscured posts are removed from the adjustment. The next three subsections discuss the details of each algorithm.

2.1. Refinement using linear features only 2.1. Refinement using linear features only In this method, adjusted elevations of DEM posts are considere In this method, adjusted elevations of DEM posts are considered whilepost, an ob elevations are taken as observations. For unknowns each DEM measured elevations are taken as observations. For each DEM post, an observation between the observed and the adjusted values (Eq. 1). equation is formed between the observed and the adjusted values (Eq. 1).

− (lijij + vijij ) = 0 Fij , 0 = Z ijij

(1)

Where: observation equation, Fij,0 is the realWhere: Fi Zij is the adjusted elevation for post (i,j), Fij,0 is the real observation equation, lij is the observed elevation for post (i,j), i.e., measured from the DEM, and Zij is the adjusted elevation for post (i,j), vij is the residual of the elevation for post (i,j). lij is the observed elevation for post (i,j), i.e. measured from the DEM Additionally, for each DEM post and its eight neighboring posts, four contivij is the residual of the elevation for post (i,j). nuity equations are enforced in the North-South, Northeast-Southwest, East-West, Fij and Southeast-Northwest directions (Figure 1). All possible continuity equations for eachDEM DEM postHowever, and its’if eight posts, Fij are generatedAdditionally, between all neighboring posts. the lineneighboring segment enforced inintersects the North-South, Northeast-Southwest, connecting two DEM posts with a breakline, the continuity equation be- East-Wes F directions (Figure 1). All possible continuity equations are generij tween these two posts is ignored. The continuity equations in the four directions Figure 1. Neighboring posts forifpost (i,j) segment and the directions for the four con Fi DEM However, theequations line are characterized byposts. four pseudo observation (Eq. 2). connecting two DEM pos

the continuity equation between these two posts is ignored. The co Fijij ,1 = Z i −1,directions Z icharacterized vijij ,1 = 0 − 2Z i , j +are − (li −1, j −1 −by2lfour + lpseudo +observation j i, j i −1 +1, j +1 +1, j +1 ) equations, E Fijij , 2 = Z i −1, j − 2Z i , j + Z i +1, j − (li −1, j − 2li , j + li +1, j ) + vijij , 2 = 0

Fijij ,3 = Z i −1, j +1 − 2Z i , j − Z i +1, j −1 − (li −1, j +1 − 2li , j − li +1, j −1 ) + vijij ,3 = 0

Wh

F ijij , 4 = Z i , j +1 − 2Z i , j − Z i , j −1 − (li , j +1 − 2li , j − li , j −1 ) + vijij , 4 = 0

Fij,

(2)

Where: Zi,j Fij,1, Fij,2, Fij,3, and Fij,4 are the pseudo observation equations, Zi,j, Zi+1,j+1, Zi+1,j, Zi+1,j-1, Zi,j+1, Zi,j-1, Zi-1,j+1, Zi-1,j, and Zi-1,j-1 are the elevations o and The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010) its eight neighboring posts, li,j, li+1,j+1, li+1,j, li+1,j-1, li,j+1, li,j-1, li-1,j+1, li-1,j, and li-1,j-1 are the measured elevatio li,j,


71

Figure 1. Neighboring posts for post (i,j) and the directions for the four continu-

ity equations

Where:

igure 1. Neighboring posts forthe post (i,j) observation and the directions F are pseudo equations,for the four continuity equations F , F , F , and ij,1

j ,1

Zi

1, j

j,2

Zi

1, j

j ,3

Zi

1, j 1

ij,3

ij,4

2Z i, j

Zi

1, j

(l i

1, j

2l i , j

li

1, j

) v ij , 2

0

2 ZRefinement Z i 1, j 1 using (l i 1, j breaklines 2l i , j l i 1and v ij , 3 intensities 0 2.2. 1 , j 1 ) image i, j

In method, 2 Zthis Z i , j 1 a unified (l i , j 1 least 2l i , jsquares l i , j 1adjustment ) v ij , 4 0model is formulated to incori, j porate both breaklines and image intensities in the refinement process. Breaklines are used as explained earlier, while image intensities are utilized through the multiphoto least squares matching technique (Gruen and Baltsavias, 1988). In the pairwise mode of the least squares matching, pixel intensities in one image, i.e., template here: image, are arbitrarily chosen to be fixed, while pixel intensities in the other image, i.e., patch image, are treated as observations. In the multi-photo mode (Figure 2) , and Fij,4 areequation the pseudo observation equations, ,1, Fij,2, Fij,3an observation is formed for each image pair. Each observation equation states that the intensities of two corresponding pixels are identical. Consequently, , Zi,j+1, Zbetween , Zi-1,j, andareZi-1,j-1 are(Eq. the3).elevations of j, Zi+1,j+1, Zobservation i+1,j, Zi+1,j-1 i,j-1, Zi-1,j+1 equations all image-pairs formed

ij , 4

Z i, j

ij,2

Zi,j, Zi+1,j+1, Zi+1,j, Zi+1,j-1, Zi,j+1, Zi,j-1, Zi-1,j+1, Zi-1,j, and Zi-1,j-1 are the elevations of a center post and its eight neighboring posts, li,j, li+1,j+1, li+1,j, li+1,j-1, li,j+1, li,j-1, li-1,j+1, li-1,j, and li-1,j-1 are the measured elevations of a center post itsZeight neighboring 2 Zand (l i 1, j 1 posts, 2l i , j andl i 1, j 1 ) v ij ,1 0 1 i, j i 1, j 1 vij,1, vij,2, vij,3, vij,4 are the pseudo residual.

(2

1

a center pos

d its eight neighboring posts,

The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

, li+1,j+1, li+1,j, li+1,j-1, li,j+1, li,j-1, li-1,j+1, li-1,j, and li-1,j-1 are the measured elevations of a cente

intensities in the other image, i.e. patch image, are treated as observations. In the multi-pho mode (Figure (Figure equation 2) an an observation observation equation isintensities formed for for of each image pair. Each Each observatio observati states that the is two corresponding pixel mode 2) equation formed each image pair. equation states that the intensities of two corresponding pixels are identical. Consequentl equations between all image-pairs formed, Eq. (3). equation statesobservation that the intensities of two corresponding pixels are are identical. Consequentl observation equations between allJames image-pairs are formed, formed, Eq. Eq. (3). (3). 72 | Ahmed F. Elaksher and Bethelare observation equations between all image-pairs 12 Gij12 G ij 23 Gij23 G ij

1 gg ij22 gg ij1ij ij 22 g 33 g g ij g ij ij

ij

12 G0ijij12 = g iji1j − g iijj2 = 0 0

23 G00ijij23 = g ijij2 − g ijij3 = 0

 nm m nm nn g m G g n m nm Gij g ij g ij nm 00 ij

ij

ij

Gijij = g iijj − g ijij = 0

(3) (3)

(3)

Where: Where: Where: 12 23 nm 12 , and Where: are the least squares matching equations, and G Gij23 Gijnm ij ,, G are G are the the least least squares squares matching matching equations, equations,and and ij ij , and Gij 12 23m nm 1 2 3 n 1 , g2 , g3 , g n , and m, and , are the least squares matching equations, and G G G are the pixel intensities for one pixel representing post g g intensities for one pixel representing post (i,j) (i,j) in in imag g ijij , g ijij , g ijij , g ijij ij, and ijg ijij are theijpixel intensities for one pixel representing post imag (i,j) in images 1, 2, 3, n, and m, respectively. 1 2 3 n m 1, 2, 2, 3, 3, n, n, and and m m respectively. respectively. 1,

g ij , g ij , g ij , g ij , and g ij are the pixel intensities for one pixel r

1, 2, 3, n, and m respectively.

Figure 2. Multi-photo least squares matching for one DEM post

Figure 2. 2. Multi-photo Multi-photo least least squares squares matching matching for for one one DEM DEM post post Figure

Pixel intensities intensities are are related related to to the the positions positions of of their their corresponding corresponding object object space space points points (Gruen (Gruen an an Pixel Baltsavias, 1988). 1988). Consequently, Consequently, if if the the minimum minimum value value of of the the difference difference between between the the intensiti intensiti Baltsavias, in the the template template and and patch patch images images is is reached, reached, adjusted adjusted pixel pixel locations locations are are attained. attained. This This in achieved by minimizing a goal function, which measures the differences between the intensiti achieved by minimizing a goal function, which measures the differences between the intensiti Figure 2. Multi-photo squares matching in the the template template and and the the patch patch images. images. The goal goal function to to be beleast minimized is the the L2-normfor of tto in The function minimized is L2-norm of Figure Multi-photo leasttosquares matching forcorresponding one DEM post Pixel2.intensities are related the positions of their object Pixel and intensities related to the positions of their corresponding space points (Gruen Baltsavias,are 1988). Consequently, if the minimum value of 1988). Consequently, if patch the minimum value of the dif the difference Baltsavias, between the intensities in the template and images is reached, adjusted pixel in locations are attained. Thispatch is achieved by minimizing a goaladjusted functhe template and images is reached, pixel l tion, which measures the differences between the intensities in the template and achieved by minimizing a goal function, which measures the diff ixel intensities are related to the positions of their corresponding object space points (Gru the patch images. The goal function to be minimized is the L2-norm of the least in the template and the patch images. The goal function to be mi squares adjustment residuals. The location of the pixel is represented by the eleva- between t nd Baltsavias, 1988). Consequently, if the minimum value of the difference tion of the corresponding DEM post (Eq. 4).

ntensities in the template and patch images is reached, adjusted pixel locations are attaine

his is achieved by minimizing a goal function, which measures the differences between t The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

ntensities in the template and the patch images. The goal function to be minimized is the L

least squares residuals. The location the pixel is least squares squares adjustment adjustment residuals. Theadjustment location of of the the pixel is is represented represented by the theof elevation of the the least residuals. The location pixel by elevation of corresponding DEM post, Eq. 4. corresponding DEM post, Eq. 4. corresponding DEM post, Eq. 4. Refinement of Digital Elevation Models in Urban Areas | 73 12 12 11 , g 22 , Z ) G G ( g 112 2 1 2 G ij G ( g ij , g ij , Z ij ) ij

ij

ij

ij

23 G23 G((gg2ij2,, gg3ij3,,ZZ ij )) G G ijij ij ij ij

Gijij = G ( g iijj , g ijij , Z ijij ) 2323

2

3

Gijij = G ( g ijij , g iijj , Z iijj ) nm m nm nn m

Gij G ij

G((gg ij ,, gg ij ,,ZZ ij )) G ij ij ij

(4)

(4) (4)

Gijijnmnm = G ( g iijjn , g iijjm , Z ijij )

Where: Where: Where: 12 23 nm , and Gnm arethe theleast leastsquares squaresmatching matching equations, equations, and and G23 ij ,, G are the least squares matching equations, and G Gij12 ijij , and Gijij are Where: 1 2 3 n m m for and gg12 are23 the pixel pixelintensities intensities forone onepixel pixelrepresenting representingpost post (i,j) (i,j) in in images images nm g gij1ij ,, ggij2ij ,, ggij3ij ,, ggijnij ,, and are the pixel for one pixel representing post , and are the least squares matching equations, a Gijijij ,are Gijthe Gintensities ij (i,j) in images 1, 2, 3, n, and m, respectively, and 1, 2, 2, 3, 3, n, n, and and m m respectively, respectively, and and 1, g ij1 , for g ij2post , g ij3(i,j). , g ijn , and g ijm are the pixel intensities for one pi adjusted elevation post is the the adjusted adjusted elevation for (i,j). ZZZijijij is

1, 2, 3, n, and m respectively, and

2.3. Refinement using breaklines breaklines and and image image intensities intensities for for non-obscured non-obscured posts posts 2.3. using 2.3.Refinement Refinement using breaklines and image intensities forHowever, nonZ is the adjusted elevation for post (i,j). ij This method is similar to the second method presented in section 2.2. observation This method is similar to the second method presented in section 2.2. However, observation obscured posts equations belonging to occluded pixels, i.e. pixels hidden from DEM posts due to the heights of of equations belonging to occluded pixels, i.e. pixels hidden from DEM posts due to the heights surrounding DEM posts, are removed from the multi-photo least squares matching process 2.3. Refinement using breaklines and image intensities for surrounding DEM posts, are removed from the multi-photo least squares matching process This method is similar to the second method presented in section 2.2. However, ob(Figure 3). 3). For For each each DEM DEM post, occluded pixels are aretolocated located as follows: follows: 1) The The presented 3D ray ray between between (Figure occluded pixels as 1) This post, method is pixels, similar thehidden second in servation equations belonging to occluded i.e., pixels frommethod DEM posts3D the DEM DEM post post and and each each image image perspective perspective center center is is driven driven from from the the 3D 3D coordinates coordinates of of the the post pos the due to the heights of surrounding DEM posts, are removed from the multi-photo equations belonging to occluded pixels, i.e. pixels hidden fro and the the image image registration registration information. information. 2) 2) All All neighboring neighboring posts posts are are tested tested and and if if one one neighboring neighboring and least issquares matching process (Figure 3). For posts, each DEM post, occluded pixels are surrounding DEM are removed from the multi-pho post higher than the ray, the corresponding pixel is not included in the least squares matching post is higher than the ray, the corresponding pixel is not included in the least squares matching located as follows: (1) The 3D ray between the DEM post and each image perspecmodel. The procedure is applied for each DEM post to find hidden pixels in all images. The (Figure 3). For each DEM post, occluded pixels are located model. The procedure is applied for each DEM post to find hidden pixels in all images. The refinement process isfrom implemented recursively. In the first iteration, elevations of the origina tive center process is drivenis the 3D coordinates of the post and the image registrarefinement implemented recursively. In the first iteration, elevations of the original the DEM post and each image perspective center is driven f DEM are used used as as the the initial DEM. In In the the following iterations, the refined DEM DEM of the the preceding preceding tion information. (2) initial All neighboring posts are tested and if one neighboring post DEM are DEM. following iterations, the refined of and the image registration information. 2) All neighboring pos iteration isthan usedthe as ray, the initial initial DEM. The The iterations iterations stopincluded when the the refinement is insignificant. insignificant. iteration used as the DEM. stop when refinement is is higheris the corresponding pixel is not in the least squares post is higher than the ray, the corresponding pixel is not inc matching model. The model. procedureThe is applied for eachis DEM post to for find hidden pixels post to fin procedure applied each DEM in all images. The refinement process is implemented recursively. In the first iterarefinement process is implemented recursively. In the first tion, elevations of the original DEM are used as the initial DEM. In the following DEM are used as the initial DEM. In the following iterations iterations, the refined DEM of the preceding iteration is used as the initial DEM. iteration is used as the initial DEM. The iterations stop when t The iterations stop when the refinement is insignificant. Figure 3. Excluded (red) and included (green) image signals

The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010) Figure 3. Excluded (red) and included (green) image signals


3. EXPERIMENTAL RESULTS AND ANALYSIS 3.1. Dataset The dataset consists of a set of 1:4000 scale aerial photographs, acquired with a Wild RC30 camera and scanned at 30µm resolution. The images cover Purdue University campus in West Lafayette, Indiana, USA (Figure 4). The average overlap between the aerial images is 80%, while the average sidelap between the images is 60%. First, the camera was calibrated. Then, the exterior orientation parameters of the exposure stations were calculated from a set of well-distributed Ground Control Points (GCPs), surveyed by the Differential Global Positioning Systems (DGPS). The Global Positioning Systems (GPS) survey was carried out with two dualfrequency GPS receivers. After the GPS survey was completed, the GPS baselines were processed. Five centimeters planimetric accuracy and nine centimeters vertical accuracy were noticed in the GPS baseline adjustment results. Finally, the image correspondence of each GCP was identified manually, tie points were added, and the aerial photos were triangulated. The image triangulation showed an average accuracy of the checkpoints of about five centimeters in the horizontal and vertical directions. After the images were triangulated, eight test sites were chosen. The test sites include simple rectangular roof buildings, gabled roof buildings, and a variety of complex-shape buildings. For each test site a one-meter-post-interval DEM was generated automatically using the SocetSet® photogrammetric software. The ATE technique implemented in this software is highlighted in Zhang et al. (2006). The endpoints of the breaklines were manually digitized from the aerial photographs and their 3D coordinates were computed through the collinearity equation (Mikhail et al., 2001). To provide superior accuracy DEMs, reference DEMs were collected manually for each test site.

3.2. Results and Analysis For each test site, the differences between the elevations of the reference DEM posts, i.e., manually collected, and the ATE DEM posts are computed. Afterward, the RMSE for these differences is computed for each test site. The mean value of the RMSE for the ATE DEM in the eight test sites is about ten centimeters. The differences between the elevations of the reference DEMs and the refined DEMs for each method are also computed and summarized in Table 1. For evaluation purposes, points are divided into two groups, roof points and non-roof points. Roof points are points that belong to building roofs. Non-roof points are points representing other features, such as trees, streets, parks, and parking slots. The reason for this division is to study the effect of carrying out the algorithm in different scenarios, especially sudden changes at the edges of buildings where ATE algorithms fail to provide reliable surface representation. Figures 5 through 12 show perspective views of the original DEMs, i.e., ATE DEMs, and the refined DEMs for the eight test sites. The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

ollected manually for each test site.


75

Figure 4. Aerial images dataset and GCPs (shown in red triangles)

Figure 4.are Aerial images datasettheand Several observations provided in reviewing dataGCPs presented in Table 1. First, roof points represent planar surfaces, consequently breaklines isolate these points. The surface smoothing equations fit the DEM elevations of such points to a planer surface. However, since the DEM elevations are not perfect, the average RMSE for the roof points is reduced from 10.2 to 7.4 centimeters using the first algorithm. Second, when the image intensities are added to the adjustment process, the average RMSE for roof points is decreased from 10.2 to 5.9 centimeters without removing occluded pixels. This is due to the sub-pixel matching behavior of the least squares matching. The remaining errors are due to occluded pixels. Thus, when these pixels are removed from the adjustment process, i.e., the third algorithm, the average RMSE falls from 10.2 to 2 centimeters. Third, for non-roof points, using only breaklines did not affect the results significantly. This is due to the non-homogeneity of these points. Finally, when image signals are added to the adjustment model and occluded pixels are removed from the least squares matching, the average RMSE of non-roof points is cut down from 9.5 to 6.3 centimeters. These results show that the third algorithm succeeded in reducing the total RMSE to more than 50% for both roof and non-roof points. This is achieved as a result of the algorithm capability to separate points that belong to different surfaces using the breaklines, incorporating sub-pixel image intensities via the least squares matching, and removing occluded pixels. In addition, the surface smoothing and the image matching processes are performed simultaneously in a global mode. The The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)

sup-pixel image intensities via the least squares matching, and remove occluded pixels. In addition, the surface smoothing and the image matching processes are performed


simultaneously in a global mode. The iterative implementation of the third algorithm provides

iterative implementation of the third algorithm provides more realistic surfaces; more realistic surfaces; occludedmore pixelsaccurately. are located more accurately. Visualofinspection hence, occluded pixelshence, are located Visual inspection Figures 5 through 12 illustrates the improvement in the eight test sites. Spikes and outliers of figures 5 through 12 illustrates the improvement in the eight test sites. Spikes and outliers are removed from the DEMs. Planar surfaces such as roofs appear more even and are removed from the and DEMs. Planer surfaces such roofs appear more even and edges edges appear sharper more determined. Inasaddition, elevations of inhomogeneous such as determine. trees, areInalso smoothed. appearsurfaces, sharper and more addition, elevations of inhomogeneous surfaces, such as trees also smoothed. Table 1.are RMSE for ATE and refined DEMs

Test Original ATE DEMs site non roof roof pts. pts. 1 8.5 8.1 2

11.1

10.0

3

10.2

9.7

4

15.6

14.1

RMSE (cm) Refined DEMs Algorithm 1 Algorithm 2 roof non roof roof non roof pts. pts. pts. pts. 6.4 6.9 5.0 6.1

Algorithm 3 roof non roof pts. pts. .1 5.7

8.3

7.7

1.9

6.9

8.8

6.3

7.8

7.3

6.1

6.6

2.5

6.5

11.3

13.9

9.1

12.4

1.9

9.8

5

7.9

7.5

5.4

5.9

4.4

4.8

1.8

4.3

6

11.4

10.4

7.9

8.5

5.9

8.3

2.0

6.7

7

9.5

9.1

7.8

6.9

6.2

7.0

1.8

6.4

8

7.5

7.1

5.0 5.5 3.9 4.5 Table 1. RMSE for ATE and refined DEMs

1.9

4.4

Figure 5. Perspective views for the original DEM (left) and the refined DEM

using the 3rd algorithm (right), Test Site No. 1

Figure 5. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm (right), test site No. 1 Figure 5. Perspective views for the original DEM (left) and the refined DEM using the 3rd Figure 6. Perspective views for the original DEM (left) and the refined DEM

using the 3rd algorithm (right), Test(right), Site No. algorithm test2site No. 1

The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010) Figure 6. Perspective views for the original DEM (left) and the refined DEM using the 3rd


77



Figure 7. Perspective views for the original DEM (left) and the refined DEM using the 3rd Figure 7. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm site No. 3 and the refined DEM Figure 8. Perspective views for the (right), originaltest DEM (left) algorithm (right), test site No. 3 refined DEM using the 3rd Figure 7. Perspective views for the original DEM (left) and the using the 3rd algorithm (right), Test Site No. 4 algorithm (right), test site No. 3

Figure 8. Perspective views for the original DEM (left) and the refined DEM using the 3rd Figure 8. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm (right), test site No. 4 Figure 9. Perspective the (right), original DEM (left) and theDEM refined DEM site No. Figure 8. Perspective viewsviews for algorithm thefor original DEMtest (left) and the4 refined using the 3rd


algorithm (right), test site No. 4

Figure 10. Perspective views for the original DEM (left) and the refined DEM rd Figure 9. Perspective views for the original DEM (left) and the refined DEM using the 3 using the 3rd algorithm (right), Test Site No. 6 Figure 9. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm (right), test site No. 5 (right), site No. Figure 9. Perspective views for algorithm the original DEMtest (left) and the5 refined DEM using the 3rd algorithm (right), test site No. 5


Figure 10. Perspective views for the original DEM (left) and the refined DEM using the 3rd

Figure 10. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm (right), test site No. 6 78 | Ahmed F. Elaksher and James Bethel



Figure 11. Perspective views for the original DEM (left) and the refined DEM using the 3rd algorithm (right), test site No. 7 Figure 12. Perspective views for the original DEM (left) and the refined DEM rd Figure 11. the Perspective views(right), for the Test original using 3rd algorithm SiteDEM No. 8(left) and the refined DEM using the 3

algorithm (right), test site No. 7

4. CONCLUSIONS High-quality and accurate DEMs are required a variety applications. However, Figure 12. Perspective views for the original DEM for (left) and theofrefined DEM using the 3rd automatic terrain extraction techniques fail to produce such DEMs. In this paper, algorithm (right), site No.and 8 evaluated. In the first althree new DEM refinement algorithms aretest developed gorithm surface continuity is enforced between each DEM post and its neighboring posts, except in theviews present In the second algorithm, imageusing signals Figure 12. Perspective for of thebreaklines. original DEM (left) and the refined DEM the 3rd are added to the refinement process through a multi-photo least squares matching algorithm (right), site No. 8 are eliminated from the model. In the third algorithm, intensities of test obscured posts matching model. The matching model modifies the elevation of each DEM post in order to minimize the differences between the intensities of corresponding pixels in the employed images. The algorithms are tested on eight test sites that include a variety of simple and complex roof buildings where ATE algorithms do not succeed in modeling sudden changes. The first algorithm decreased the average RMSE of the DEMs from ten to eight centimeters, while the second algorithm reduced the RMSE to seven centimeters. The third algorithm succeeded in cutting down the RMSE to four centimeters. Additionally, the third algorithm demonstrated an 80% improvement in the elevations of building posts. This comes as a result of separating DEM posts belonging to different objects and adding image intensities of non-occluded pixels only in the refinement model. The results verify the capability of the third algorithm to produce high-quality and reliable DEMs. Future research will focus on the use of automatically extracted breaklines in the refinement process. The Journal of Terrestrial Observation | Volume 2 Number 2 (Spring 2010)


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