International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
only has to measure any two points along v, v?' on one image
and any two points along v, "v5" on the other image, then the
line equations could be determined. The greatest benefit of line
photogrammetry is avoiding the point identification and
correspondence problem. Similar to the points, linear features
can be used for solving intersection or resection problems. If the
image orientation has been known, measuring linear features on
the images can be used to extract 3D line segments. If the 3D
line equations have been known, measuring linear features on
the images can be used to determine image orientation.
The next development based on line photogrammetry is the
CAD-based photogrammetry which is incorporated with various
existing CAD models, such as box, cylinder, wedge, erc. The
object model can be extracted by projecting wire-frame of CAD
model onto the image and verifying the coincidence. The CAD-
based photogrammetry has been successfully applied in some
close-range photogrammetric applications, such as extracting
oil pipes at an industrial plant. However, buildings are not so
regular as industrial components. CAD models are not flexible
enough to handle various kinds of building.
To deal with the modelling problem, we proposed a naval
concept of 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. The floating models 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 and the arc. The plane includes the rectangle,
the circle, the ellipse, the triangle, the pentagon, etc. The
volumetric solid includes the box, the gable-roof house, the
cylinder, the cone, erc. 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
translation parameters (dX, dY, dZ) to represent the position and
3 rotation parameters, tilt (/) around Y-axis, swing (s) around X-
axis, and azimuth (a) around Z-axis to represent the rotation of
a primitive model. Figure 3 shows four examples from each
type of models with the change of the pose parameters. X -Y -Z'
coordinate 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, dY, 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 (/).
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 associated with
different shape parameters, e.g., a gable-roof house primitive
has an additional shape parameter — roof’s height (4). Figure 4
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. The yellow one is the
original model, while the grey one is the model after changing
the shape parameters. The figure points out the other important
characteristic of the floating model — the flexible shape with
certain constraints. Changing the shape parameters does not
affect the position or the pose of the model.
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Figure 3. Change the pose of floating models by adjusting pose
parameters.
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Line Segment Rectangle Plane Box Solid
Figure 4. Change the shape of floating models by adjusting
shape parameters.
2.2 CSG tree and Boolean Set Operation
The greatest benefit of constructive solid geometry is the
flexibility of modelling complex buildings. In this paper,
building parts are extracted by floating models one-by-one, then
combined into a complete building model via Boolean set
operations, such as union( U ), intersection( M ), and
difference( —). Figure 5 depicts the composition process of a
complex building model, which is also called a CSG tree. The
union operation may be the most commonly used. Since the
building parts are extracted independently, discrepancy between
connected walls is unavoidable. Special constraints or local
modification should be provided to assisting the attaching
process.
Figure 5. The CSG tree of a complex building model.
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