Zheng Wang 
  
z2.2 TIN-Based Building Reconstruction 
To reconstruct a building, this approach generates building surfaces and their orientations first and then uses 
the tri-intersections of the surfaces to derive building corners and their relative orientations and associations. The 
derived corners are used to reconstruct the building. Here, a surface is a plane defined by its orientation and position. 
Building surfaces include ground floor surface as well. The surfaces of a building are derived from triangles of a TIN 
model that is created from the points of the building. Figure 2 shows the framework of the TIN-based building 
reconstruction. In figure 2, the reconstruction starts with a set of 3-D points that belong to a building. The 3-D points 
are extracted by using the corresponding building edge as boundary. A TIN model is created first, then every triangle in 
the TIN model is converted to a plane and all converted planes are grouped based on their orientations. Planes that have 
similar orientation are grouped together and an average plane is derived for each group of planes by a least squares 
error fitting process in iterations. In each iteration, points with large error residuals will be removed and remaining points 
will be processed to fit to a new plane. Iteration stops when no further points are removed. Final planes are generated 
after another grouping of average planes and spatial intersections of final planes define the corners needed to describe a 
building. This approach has advantages in several aspects. First, converting triangles in a TIN model to planes will make 
every converted plane be related to a building surface, i.e., a roof, a wall, or ground. Although each plane may not 
accurately fit to a building surface, there will be no irrelevant planes. Additionally, this method will make vertical 
surfaces (walls) extraction possible. Triangles or planes formed by points around boundaries of a building and points 
along roof edges of the building will represent vertical walls. Second, the approach is not noise critical, although it is still 
noise sensitive, because the surfaces are generated from a least squares error fitting process. Third, the approach can 
recover edges and corners of a building roof even if the spacing of the data is so large that no points are actually on 
edges or corners. This is made possible because edges can be recovered by intersection lines between two neighboring 
planes and corners can be recovered by intersection points of tri-planes. Fourth, the approach generates surfaces that 
can be easily used for future building verification and reconstruction. For instance, building roof edges determined by 
surface intersections can be projected onto an image, if available, to be verified. And fifth, ridges formed by roof 
surfaces represent surface orientation discontinuities. 
À Set of 3-D Points 
TIN Model Creation 
TIN Model 
   
  
| Triangle to Plane Conversion | 
  
   
Planes 
    
Grouping of Planes 
  
.|, Plane Groups 
  
Average Plane Generation by 
Least Squares Error Fitting 
  
  
  
Average Planes 
  
| Grouping of Average Planes 
  
Final Planes 
  
  
Generation of Building Comers by 
Space Intersections of Final Planes 
| 
Building Corners 
  
  
  
Figure 2. A flowchart of the TIN-based building reconstruction. 
3. EXPERIMENTAL RESULTS 
Four real LIDAR data sets covering an industrial area were selected for the test. The data sets were provided by 
Earthdata Technoligies. An area of roughly 650m x 650m was cropped out of the data sets. The cropped area had nine 
buildings ranging from large to medium to small sizes. The area also had many trees. Because each of those four data 
sets had a point spacing of 5 meters, which was too coarse to detect small buildings, the four data sets were merged 
together to create a single data set with an average point spacing of 1.25 meters. Figure 3 is an elevation image of the 
test area generated by the merged data set. All the buildings in the area have rectangular or near rectangular shape with 
peaked roof, flat roof, and multiple level flat roof, respectively. An aerial photo of the area was also obtained from a 
  
960 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.