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The automation of extracting planner surfaces is a main field of research in digital photogrammetry. These surfaces are essential to generate three dimensional GIS databases. Surfaces are usually determined from either DEMs or images. Each dataset provides a different type of information. Thus, the combination of the two datasets should enhance the surface reconstruction process. This paper presents a new technique for generating 3D surfaces by combining both correlation-based DEMs and aerial images. The process starts by discriminating DEM points that represent planner surfaces using local statistics of neighboring elevations and intensities and point elevations. A segmented orthophoto is then used to group these points into different regions. The elevations of the points in each region are fed into a least squares adjustment model to compute the best-fit planner surface parameters. Refinement of surface borders is then performed using a region growing algorithm. The RMSE for five test sites showed a spatial accuracy of 5 - 8 cm.

Three dimensional surfaces support a great number of applications including; city modeling, generation of 3D Geographic Information Systems (GIS), and topographic analysis. Hence, there is an increasing demand for automatic generation of 3D surfaces. However, the end products of current digital photogrammetric stations are usually Digital Elevation Models (DEMs). These models are digital representation of the terrain elevations sampled at a fixed grid interval over the surface of the Earth. Thus, the output is usually named 2.5D. The interval between the grid points is an important aspect that affects the user of such model. Automation of object surface reconstruction from digital images is currently one of the most important research fields in Photogrammetry [

Some researchers worked on extracting rood planes from LIDAR dataset. A multi-scale LIDAR point cloud uses decomposition algorithm to exclude ground points and later form planer surfaces through local fitting methodologies is implemented in [

Other researchers employed both aerial images and LIDAR point cloud for the same purpose. For example, an algorithm to delineate roof patches from LIDAR point cloud and orthorectified photos is presented in [

While laser scanners pose several challenges due to their size and cost [

The proposed method includes the following steps. An orthophoto is first generated. In the next step, points representing planner surfaces are discriminated from the DEM and the orthophoto using three criteria. These criteria include two local measurements for the likelihood of a point to be a planner surface point. Point elevations are also employed in the discrimination process. Image regions are then extracted from the orthophoto using the split and merge image segmentation technique. A least squares adjustment model, [

The aerial images used in this research are fully triangulated, i.e. interior and exterior orientation elements have been defined, using a photogrammetric software. The images are conventional vertical photographs at the scale of 1:4000 scanned at 30 mm. In addition, the employed DEM is generated using the previous software. Hence, the ground space coordinates for each DEM point is known. For each DEM point, the collinearity equations, Equation (1), [

where: x_{o}, y_{o} ,and f are the camera interior parameters, x_{i}, and y_{i} are the corresponding pixel coordinates of point (i),

rotation matrix for the image, X_{c}, Y_{c}, and Z_{c}: are the exposure station coordinates for the image, and (X^{i}, Y^{i}, and Z^{i}) are the object space coordinates of point (i).

Planner surface points have several characteristics that could be used to discriminate them from other points. In this research three major characteristics are used. These characteristics include; a measure for the local plane fitting quality, the homogeneity of the gray levels for the surrounding points, the point height. Each characteristic could be used as a criterion in detecting planner surface points. However, the combination of the three criteria should lead to better detection of planner surface points.

This measure is calculated using a least squares adjustment model for a 3 × 3 local window. Input to the least squares model are the elevations for one DEM point and the surrounding eight points in the window. Equation (2) shows the employed least squares adjustment model. The output of the model are three parameters that represent the local plane that fit thought the local window. A local horizontal coordinate system is used in each window and centered at the center point of the window. To find a, b, and c, we use the principles of regres-

sion. We want to find a, b, and c, such that

Therefore, we take the partial derivative with respect to a and set it equal to zero and we do the same for b and c. Hence, the unknown parameters are computed directly as shown in Equation (3). The parameters are then used to calculate an adjusted elevation for each point in the window.

where:

l_{i} is the measured elevation for point (i),

v_{i} is the residual of the measured elevation for point (i),

X_{i} and Y_{i} are the X and Y ground coordinates for point (i),

a, b, and c are the local plane parameters, and

where:

a, b, and c are the three parameters that represent the planner surface,

l_{i} is the elevation of point (i) measured from the DEM, and

X_{i}, and Y_{i} are the coordinates of the point (i) the local window.

The residual vector (V) is then computed and the value (V^{T}V) for each window is then computed. This quantity is used as a measure of the fitting quality. Smaller quantities imply that the DEM point belongs to a planner surface. Large values mean that the DEM point doesn’t fit in a planner surface. ^{st} test area. Dark areas represent high quantities, while light areas represent low quantities.

Pixels that represent planner surfaces should have similar intensities. The variation of the gray levels in the vicinity of such pixels should be small. For each pixel in the generated orthophoto a local window is generated. The size of the local window is 3 × 3. For each pixel, the standard deviation of the gray levels in the local window is computed. The standard deviation of the gray levels is used as

another criterion in the process of detecting planner surface points. ^{st} test area.

Planner surfaces usually describe man made features. These surfaces tend to be elevated above the bare terrain. However, DEMs measure the elevations of the ground surfaces. The combination of the DEM and the DSM should lead to information about elevated points. Hence, the extraction of the DSM is essential. Minimum filters are usually used in this task, [^{st} test site. The first view represents the original DEM, while the second view represents the extracted DSM. In this test site, the maximum height in the DEM is 227 meters, while the maximum height in the DSM is 206 meters. The minimum elevation in both models is 195.6 meters. The results show that even when the bare ground is not flat, the filtering process is capable of extracting the DSM.

There are several image segmentation techniques in the literature that could be used to extract image regions. These techniques show good results if the intensities of the image regions are approximately the same. In addition, high contrast between the region and surrounding objects should exist. The split and merge image segmentation technique [

The split and merge image segmentation is described as follows: first, splitting the image. The image is recursively divided into smaller regions until a homogeneity condition is satisfied. This is done using a quad-tree representation. Then adjacent regions are merged to form larger regions based upon the previous criterion. In the last step, small regions are either eliminated or merged with bigger regions. The criterion used in the split and merge image segmentation method is that the difference between the minimum and maximum intensities is less than a certain threshold. Holes are then automatically detected using a region growing algorithm [^{st} test site.

Each outcome of the previous processes could be used individually for the detection of the planner surface points. However, the combination of the previous

criteria in the discrimination process should lead to higher quality description of planner surfaces. The literature describes a number of techniques for the combination of such information. An object-based classification rather than pixel-based classification is used in [

In this research a rule based algorithm is used to detect planner surface points. The algorithm starts by normalizing the output of the three computed criteria. For the first and second criteria the differences between the maximum and minimum values is computed. Then, for each criterion a normalized value is computed using Equation (4). The larger the value in each normalized output, the more likely the point will belong to a planner surface. In the next step, the differences between the DEM and the DSM are computed. Equation (3) is then used to normalize the differences between the two models.

where:

d is the difference between the maximum and minimum values of the output.

The three normalized values and the segmented image are used to detect planner surface points as follows. First, the average of the three normalized outputs are computed for each point. If the average is greater than 0.75 and the value of each normalized value for that point is greater than 0.9 the point is detected as a planner surface point. Noise and small regions are removed using a region growing process. Neighboring planner surface points are connecting and if the size of the region is smaller than a given threshold the region is removed. In this research a threshold of 10 - 25 points is used. The result for the 1^{st} test area is shown in

For each region in the region-based orthophoto, its correspond planner surface points are counted. If the number of these points is more than 90%, this region is believed to be a planner surface. Other regions are eliminated. Elevations of points belonging to a planner surface region are employed in a least squares adjustment. In the adjustment model, the elevations of all the region points are used as observations. Unknowns are the surface parameters. Since only planner surfaces are assumed, only three parameters for each region are used. Equation (5) shows the least squares adjustment model employed to compute the plane parameters. These parameters are then used to compute the adjusted elevations of each point in the DEM that belongs to a planner surface.

where:

a, b, and c are the three parameters that represent the planner surface,

l_{i} is the elevation of point (i),

X_{i}, and Y_{i} are the coordinates of point (i), and

n is the number of points in the planner surface region.

In order to delineate border points for each region, a refining step is then implemented. For each region, the neighboring points for each border point are located. Each neighboring point that doesn’t belong to the region is tested if it could be appended to the region. The test is based on the difference between the point elevation and the expected elevation using the three parameters of the planner surface of the region. If the point is appended to the region the parameters are recomputed and updated. In addition, the elevations of the region points, including the appended points, are recomputed. This process is repeated iteratively until no more neighboring points are appended. ^{st} test site.

To test and verify the proposed algorithm, a C++ program was developed using Microsoft Visual Studio 6.0. The employed DEMs are generated with a one meter interval. Five test sites are used to test the proposed algorithm.

ner surfaces in all test sites are detected. Moreover, no false surfaces were extracted. However, for some surfaces the borders are not well delineated. The process is affected by outlier or missing points in the extracted regions. This is due to the sensitivity of the segmentation process. In addition, noise in the vicinity of elevation discontinuities also affects the results.

Numerical evaluation is based on computing the Root Mean Square Errors (RMSE) for differences in elevations. Numerical evaluation is performed only for points contributing to planner surfaces. Extracted surfaces are divided to two groups, horizontal and non-horizontal. For horizontal surfaces, reference elevations are measured manually for all corner points and a mean value is computed. This value is used to evaluate the elevations of the planner surface corners. For

Test Area | RMSE | |
---|---|---|

Horizontal surfaces | Non-Horizontal surfaces | |

1 | 5.2 cm | 8.3 cm |

2 | --- | 6.4 cm |

3 | 6.4 cm | --- |

4 | 3.2 cm | 9.5 cm |

5 | 6.7cm | --- |

non-horizontal surfaces, the reference elevations are measured manually for three corner points and used to compute the true parameters of the planner surfaces. These parameters are then used to compute several reference elevations using the exact horizontal coordinates (X and Y). The RMSE of the differences between the reference elevations and the computed elevations using the presented technique are computed and presented in

This paper shows the potential of generating 3D planner surfaces by integrating elevation data, provided by correlation-based DEMs, and image intensities. DEM points contributing to planner surfaces are discriminated from other DEM points using different features. Points contributing to each planner surface are then used to fit a plane through this surface using a least squares adjustment model. Input to the model are the 3D coordinates of all DEM points that contribute to the surface. The model is then solved to find the best plane that fit these points. Results show that the proposed process is able of detecting all tested planner surfaces with no false surfaces. The spatial accuracy shows that the RMSE for the elevations of a number of manually selected planner surface points is about 5 cm to 8 cm. The RMSE depends on the inclination of the surface. Future research will focus on testing the proposed algorithm on laser-based DEMs. In addition, other discrimination features to classify planner surface points could be tested. Other techniques for combining the proposed features such as belief networks, expert systems, or fuzzy logic systems could be used. Our algorithm should work with any configuration of roofs; however, if any part of the building is covered by trees it could fail.

Elaksher, A.F. (2017) Automatic Correction of DEM Sur- face Errors. Journal of Geographic Information System, 9, 326-338. https://doi.org/10.4236/jgis.2017.93020