Scale Space
Object
Dependent
Partitioning
Viewpoint space
as 3-D space
Voxel-Based
Tessellation
Aspect Graph
Algorithms
Object
Dependent
Partitioning
Viewpoint space
as viewing sphere
Uniform
Tessellation |
|
| | General | Eggert, Bowyer, Dyer,
Polygons Christensen & Goldgof, 1992
Deformable s
Cylinders Wilkins, Goldgof & Bowyer, 1991
Articulated Sallam, Stewman & Bowyer, 1990
Assemblies Eggert, Sallam & Bowyer, 1992
Solids of Eggert, 1991
Revolution Eggert & Bowyer, 1992
Plantinga & Dyer, 1987, 1990
General | Stewman & Bowyer, 1988
Polyhedra Stewman, 1991
C Plantinga & Dyer, 1987, 1990
COT SC d | Stewman & Bowyer, 1990
y Watts, 1988
General Watts, 1988
Polygons
Convex | Gualtieri, Baugher & Werman, 1989
Polygons
General
H—— Polyhedra | Wang & Freeman, 1990
General Ponce & Kriegman, 1990
Curved Petitjean, Ponce & Kriegman, 1992
Rieger, 1990, 1992
Surface Sripradisvarakul & Jain, 1989
Quadric | Chen & Freeman, 1991
Surface
Solids of | Eggert & Bowyer, 1990
Revolution Kriegman & Ponce, 1990
Gigus, Canny & Seidel, 1991
General Gigus & Malik, 1990
Polyhedra Plantinga & Dyer, 1987, 1990
Seales & Dyer, 1990
Convex | Plantinga & Dyer, 1986
Polyhedra
2.5-D Castore, 1984
Polyhedra Castore & Crawford, 1984
Goad, 1983
Fekete & Davis, 1984
Hebert & Kanade, 1985
Korn & Dyer, 1987
Ikeuchi, 1987
Burns & Kitchen, 1988
Shapiro, 1988
Chen & Kak, 1989
Hansen & Henderson, 1989
Hutchinson & Kak, 1989
Camps, Shapiro & Haralick, 1991
Dickinson, Pentland & Rosenfeld, 1992
Raja & Jain, 1992
Figure 1. Classification of algorithms for aspect graph creation. Algorithms are categorized by model of viewpoint space,
method of creation and class of object shape allowed. Cited references are in the bibliography.
2.1 Models of Viewpoint Space
The model of viewpoint space has perhaps had the greatest
effect on the various algorithms. Two basic models of view-
point space are commonly used. One is the viewing sphere.
In this model, the space of possible viewpoints is the surface
of a unit sphere, defining a 2-D parameter space. The sphere
is considered to be centered around a model of the object,
which is located at the origin of the coordinate system. A
viewpoint on the surface of the sphere defines a line of sight
vector from the viewpoint toward the origin. This direction
vector is usually used to create an orthographic projection
view of the object. It is possible to use perspective pro-
jection with the viewing sphere model, but this requires an
assumption of a known viewer-to-object distance.
A more general model of viewpoint space is to consider all
positions in 3-D space as possible viewpoints. As in the case
of the viewing sphere, the object can be considered to be
located at the origin of the coordinate system. Specifying
a direction vector for the line of sight and a focal length
for the imaging process allows the creation of a perspective
projection view of the object. This normally would require
potentially a 7-D parameter space to describe the viewing
process. However, a simplifying assumption is made such
that an aspect is concerned with all potential features seen
from a given viewpoint, if the line of sight is directed ap-
propriately. Thus only three parameters are necessary to
specify the viewpoint position, and the viewer will possess
a 360? field of view in all directions. Later, during the pose
estimation portion of the object recognition task, the exact
