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2.4. Constructive solid geometry models
Constructive solid geometry (CSG) models can be considered a superset of paramet
ric models; a CSG model consists of one or more elementary parameterized shapes,
joined by boolean operations to describe the object of interest
[Foley and van Dam, 1992].
CSG models are mostly used in industrial applications, where the machining pro
cesses which produce the parts can be precisely described by the geometric primitives
of the model. It is not always straightforward to identify the proper geometric prim
itives and their composition into complicated objects, and the composition is not
always unique. There are also limitations on the level of detail obtainable.
2.5. Generalized cones
Generalized cones (or generalized cylinders) are defined by a central axis and a cross-
section which is swept along the axis to define the object’s shape [Ponce et al ., 1989].
The central axis may be straight or curved and the cross section may be regular or
irregular [Zerroug and Nevatia, 1993].
Generalized cones are particularly suitable for elongated objects, such as many man
made objects, and also have useful, well-defined mathematical properties. However,
many objects cannot be represented as generalized cones due to the lack of a well-
defined axis or a consistent cross-section.
3. Selection of models for each phase of the computer vision process
An end-to-end computer vision system involves several processing phases. Depend
ing upon their design, purpose, and capabilities, some systems do not include all
these phases, or may combine phases. Each phase has its own representational re
quirements; for that reason, the applicability of each model type is discussed with
reference to each processing phase.
3.1. Object and scene description
The description phase involves the formation of a 3D model of the visible surfaces
in the scene, without segmentation of the scene into separate semantically meaning
ful objects. This model may be incomplete or contradictory, subject to refinement
in later processing stages. The most common example of the descriptive phase is
a stereo process, which forms a mesh of elevation values across the scene with
out discriminating between buildings, trees, etc. Another example is VHBUILD
[McGlone and Shufelt, 1994], which labels edges in the scene as vertical or horizon
tal in the world and then forms chains of these edges to generate building surface
hypotheses. In this case, the 3D model is a very sparse, incomplete boundary rep
resentation of hypothetical objects.
Not all systems generate 3D scene models; many recognition systems, such as
ACRONYM (Section 4.1), work only in image space, extracting image features and
