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archies; a class-subclass graph, and a part-whole graph. The class-subclass tree
incorporates the notion of a generic airplane as opposed to a specific type of air
plane. By parameterizing the model variables, the same basic model serves as a
representative of a class and for specific instances of the class. The part-whole tree
models each part of the object and its attachment to the other parts. The part-
whole relationship is modeled at differing levels of detail, allowing the recognition
process to focus on larger, more important pieces first and then verify the object
using the smaller parts.
The recognition process proceeds by locating “ribbons 1 in the image, sets of parallel
edges assumed to correspond to a generalized cone. By reasoning about constraints
between image and object space and on object space measurements and relation
ships, feasible interpretations of the image structure in terms of the object models
are generated.
The object modeling in ACRONYM suffers from the general shortcomings of gen
eralized cone models—the inability to precisely model complex objects and the lim
itations on representable objects. ACRONYM embodies only the recognition phase
described above (Section 3.2), since it does not try to generate a 3D description of
the world.
4.2. ThingWorld—superquadrics
Pentland describes an object modeling and recognition system, ThingWorld, which
models objects as collections of rigid parts connected by hinges or joints. Each part
of the object is represented as a superquadric. To avoid the computational problems
of fitting superquadrics, modal dynamics are used to model the deformations of the
elementary volumetric primitives. Describing the object’s deformations in terms of
its natural strain and vibration modes allows the efficient modeling of deformations
of the volumetric primitives while greatly reducing the size and complexity of the
equations involved.
This work generates models which capture the main structure of the object, with
out rendering medium- or fine-level structure. The superquadrics yield only an
approximation for objects with precisely defined geometries, such as a rectangular
prism. While Pentland discusses the possibility of recognition, no specific tests are
described. Superquadric models will be useful for recognition only if the descrip
tions produced, i.e., the superquadric parameters, are repeatable enough to use in
indexing into a database.
4.3. Deformable nodal models based on superquadrics
Terzopoulos and metaxas [Terzopoulos and Metaxas, 1991] describe an object mod
eling system based on deformable superquadrics, the basic shape of the object is
defined by the superquadric, while deviations from the superquadric are modeled by
a finite element mesh. In this way the large number of degrees of freedom of finite
element models are constrained by their attachment to the superquadric. The au
thors mention using the parameters of the superquadric to index into a recognition
database, although no experiments were performed. It is unclear how successful this