Extensions of CCM
What looks like a complete approach and system from a scientific point of view may not necessarily fulfill some specific practical requirements efficiently. This is the case with the original approach of CCM. Whereas it is acceptable in most projects very well there are always some specifications, which require modifications and additions. One of those is geometric regularization. While CCM was built to model the objects as close to their existing size and shape as possible, there arises sometimes the need to regularize the geometry. Under these constraints do fall the requests to make straight lines parallel and perpendicular where they are actually not, or to have all points of a group (e.g. eaves or ridge points) at a unique height. Another problem grew from the fact that CCM was designed to handle individual buildings sequentially and independent of each other. Building neighborhood conditions were not considered. The geometrical inconsistencies originating from that fact, like small gaps or overlaps between adjacent buildings (in the cm/dm range), are not dramatic and tolerable in many applications, especially those

which are purely related to visualization. However, the topological errors constitute a serious problem in projects where the 3-D model is subject to legal considerations or some other kind of analysis which requires topologically correct data.

Another significant extension refers to the precise modeling of building facades. Facades are usually not visible in aerial images, but available in cadastral maps. We combine this facade information with the roof landscape modeled with CCM in order to be able to represent the roof overhangs.

In the following, we will describe some extensions in more detail. Figure 3 shows an example of improving geometric quality.

Figure 3. Workflow of CCM extensions
Geometrical regularization and neighborhood topology
Geometrical regularization refers to the task of modifying the geometry in such a way that regular structures are obtained. Measurements from images are always erroneous, although the errors may be very small. In addition, in particular with older buildings, the geometry deviates from regular patterns sometimes significantly. Edges are not parallel, intersections not perpendicular, roof faces not planar. We therefore have developed two strategies for regularization: A fully automatic adjustment based on least squares and a semi-automated approach of CAD editing. Both approaches are integrated in the software package CC-Edit.

The requirements for geometrical regularization are as follows:

• Same height for groups of eaves points, ridge points and other structure points
• Roof patches containing more than 3 points should form planar faces
• Parallelism of straight edges
• Right angles of intersecting roof edges
• Collinearity of edge points

Least squares adjustment
We solve these requirements by formulating the constraints as stochastic constraints, i.e. as weighted observation equations in a least squares context. Details may be found in Gruen Wang 2001.

Figure 4. Correction of roof group by automated geometry regularization.