The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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corresponding edge pixels. To deal with this problem, we pro 
posed a tailored Least-squares Model-data Fitting (LSMDF) 
algorithm as a major component of the building reconstruction 
framework. 
f 
To simplify the fitting problem, the model parameters are rear 
ranged into two groups, plane and height parameters. Hence the 
model-data fitting procedures are also divided into three steps. 
First, fit model to topographic maps to derive plane parameters. 
Second, interpolate datum’s height from DEM and fit model to 
LiDAR data to derive height parameters. Finally, the wireframe 
model is projected onto aerial photos for examining. The opera 
tor can make further modification of the model according to the 
photos if necessary. Fig. 1 uses a box model as an example to 
depict the proposed reconstruction procedures. The hexagons 
depict the information required from the data sources. The pa 
rameters labeled in red color are the varied ones during the pro 
cedure. 
Plane,Fitting Height Fitting 
/=19.1 
w= 4.4 
h= 1.0 
dLY=304660.5 
dF=2761940.2 
dZ=0.0 
a =121.7 
Final Examinipg. 
/=19.1 
w=4.4 
/»=22.7 
cLY=304660.5 
dF=2761940. 
2 
dZ=23.9 
/=19.1 
1 h=4.4 
1 /i=22.7 
I dA'=304660.5 
I dl-2761940.2 
\ dZ=23.9 
• a =121.7 
Figure 1. The flowchart of the reconstructing procedures. 
2. FLOATING MODELS 
Traditional photogrammetric mapping systems concentrate on 
the accurate measurement of points. The floating mark is a sim 
ple way to represent the position of a point in the space, and 
thus, has been served as the only measuring tool on the stereo 
plotters up to nowadays. However, the floating mark reaches its 
limits when the conjugate points can not be identified due to the 
occlusions or interferences from other noises. And with the in 
creasing needs of 3D object models, point-by-point measure 
ment has been become the bottleneck of the production. To deal 
with the modeling problem, we proposed floating models which 
complies with the constructive solid geometry. The floating 
model is basically a primitive CSG model, which determines 
the intrinsic geometric property of a part of building. That can 
be categorized into four types: point, linear feature, plane, or 
volumetric solid. Each type contains various primitive models 
for the practical needs. For example, the linear feature includes 
the line segment. The plane includes the rectangle, the circle, 
the triangle, etc. The volumetric solid includes the box, the ga 
ble-roof house, etc. Despite the variety in their shape, each 
primitive model commonly has a datum point, and is associated 
with a set of pose parameters and a set of shape parameters. The 
datum point and the pose parameter determine the position of 
the floating model in object space. It is adequate to use 3 trans 
lation parameters (dY, dY, dZ) to represent the position and 3 
rotation parameters, tilt (/) around 7-axis, swing (5) around X- 
axis, and azimuth (a) around Z-axis to represent the rotation of 
a primitive model. Fig. 2 shows four examples from each type 
of models with the change of the pose parameters. X’-Y’-Z’ co 
ordinate system defines the model space and X-Y-Z coordinate 
system defines the object space. The little pink sphere indicates 
the datum point of the model. The yellow primitive model is in 
the original position and pose, while the grey model depicts the 
position and pose after changing pose parameters (dX, d 7, dZ, t, 
s, a). It is very clear that, the model is “floating” in the space by 
controlling these pose parameters. The volume and shape of the 
model remain the same while the pose parameters change. The 
shape parameters describe the shape and size of the primitive 
model, e.g., a box has three shape parameters: width (w), length 
(/), and height (h). Changing the values of shape parameters 
elongates the primitive in the three dimensions, but still keeps 
its shape as a rectangular box. Various primitive may be associ 
ated with different shape parameters, e.g., a gable-roof house 
primitive has an additional shape parameter - roof’s height (rh). 
Fig. 3 shows three examples from each type of models with the 
change of shape parameters. The point is an exceptional case 
that does not have any shape parameters. Fig. 3 points out the 
other important characteristic of the floating model - the flexi 
ble shape with certain constraints. Changing the shape parame 
ters does not affect the position or the pose of the model. 
Figure 2. Adjusting the pose parameters of floating models. 
/ / 
Line Segment Rectangle Plane Box Solid 
Figure 3. Adjusting the shape parameters of floating models. 
3. LEAST-SQUARES MODEL-DATA FITTING 
Since the topographic maps are plotted by photogrammetric 
techniques, its plane accuracy would be better than the LiDAR 
data. On the contrary, the LiDAR data provides better height 
accuracy. Therefore, the proposed model-data fitting procedures 
are separated into two steps: (1) the plane parameters are de 
rived by fitting model’s bottom to the topographic map; (2) the 
height parameters are derived by fitting model’s roof to the Li 
DAR data. 
The objective of the plane fitting is the building’s boundary on 
the topographic map. However, the map contains much more 
elements than building boundaries. A “clean & build” process is 
necessary to establish the close-and-complete polygons of only 
buildings. These polygons are the bases of plane fitting. The 
operator selects an appropriate primitive model and makes the 
approximately fit according to the polygon to be measured. The 
corresponding polygon’s boundary is then re-sampled as sample