McGlone - 5 
priate. 
Models involving hierarchical representation may be based on either part/whole 
relationships or on a scale-space type of merging of smaller parts into larger parts, 
as the scale decreases. Parametric models or generalized cones are well-suited for 
part-whole representations, since the rotations and translations necessary to attach 
the parts can be applied directly to the object parameters of individual points or 
edges. 
3.3. Model output 
If the recognized object is an instance of a generic class, then a final 3D model must 
be output by the system. Otherwise, if a specific object was recognized, only an 
identification must be output, possibly with position and orientation information. 
Several operations may need to be performed: 
Verification/completion: Locating and matching any unmatched parts, or ex 
plaining why they’re not visible (occlusion, lighting, etc). 
Model optimization: Once an object has been identified, the model may be 
optimized to improve its geometric fidelity. This may involve the localization of 
edge or corner locations or a least-squares model fitting procedure. 
If a least-squares optimization is performed on the model in order to produce the 
“best” estimate of object size, shape, or location, the type of model used can have a 
major influence on the statistics derived. As is well known from adjustment theory 
[Mikhail, 1980], the precision and reliability of any adjustment depends upon the 
type and amount of information input, specifically, the prior assumptions and the 
observed measurements. In this case the prior information is implicitly specified 
by the choice of model type. The amount of prior information implicit in a model 
can be thought of as a continuum, from nodal models which contain only relative 
information between points, to boundary representations which describe surfaces 
and edges but require additional constraints if a specific configuration is required, 
to parametric models which completely specify shape and leave only size, orientation, 
and position to be determined. 
For a given object, the model which has the fewest free parameters will generally 
have the greatest precision and best reliability. For instance, a comparison of a 
boundary-representation model of a simple rectangular prism building, with and 
without geometric constraints, and a parametric rectangular prism model was de 
scribed in [McGlone, 1995]. As would be expected, the addition of constraints to 
force the corners of the building to form right angles and the edges to be verti 
cal increased both the precision and reliability of the solution. Changing from the 
boundary representation to the parametric model improved the solution even more. 
The issue then becomes, which model uses the minimum number of parameters to 
represent the object in a suitable fashion? A parametric model will in general have 
fewer parameters than an equivalent boundary representation, but will be more lim 
ited in the types of shapes which can be represented and in the amount of detail