31). Each code is followed by a coordinate value. A program
can easily read the value following a group code without
knowing the particular use of this group in an item in the file.
A DXF file can often specify object geometry in terms of group
entities such as: lines, circles, arcs and polylines. The basic
geometry of models can be used to construct graphic
presentations for object matching.
3.2 CAD Models to Graphic Presentation
An ideal 3D representation is unique and unambiguous, and
has a rich set of representable parameters. The graphic presen-
tation of models used in this research is constructed by deriving
a subset of the basic geometric entities from DXF files. The
computational burden of graphic presentation is not incurred at
object recognition time, since the transformation of CAD
models to graphic presentations need only be applied when a
new model definition is created and the corresponding vision
object is needed. Each model is handled separately, so that the
addition of a model to the database does not change the
representations of existing models.
3.2.1 Attributes of Geometric Primitives
The basic geometric elements of object boundaries are stored
explicitly in the analytic format in DXF file, in terms of lines,
circles and arcs.
1) Line Segments: In the DXF specification, a line segment is
characterised by a starting point and an ending point. The
coordinates of points are stored in the list of vertices. A line is
presented as two numbers of vertex and length.
2) Circular arc: In the DXF file, a circular arc is specified in its
own (arc-centred) coordinate system (x,, y,, z,) , in which the
plane of the arc is parallel to the x,y, -plane, and displaced
from it along the z, axis. The direction of the z, axis is given
and related to the world coordinate system. The primitives of
an arc contain its central coordinates, z axis direction, radius,
start angle and end angle. A circle is presented similarly to an
arc without start angle and end angle, while an ellipse is
presented by 12 arcs which link smoothly at their ends. This
system computes major axis and minor axis of an ellipse from
these symmetrical arcs. The attributes for an ellipse are radius
(an average of major axis and minor axis), and ratio (major axis
divided by minor axis). These attributes are identical with
those of circles, where the ratio is 1.0.
3.2.2 Planar Surface and Their Topologic
The inference system does not attempt to present objects in a
complete way, but rather dominant features are used for model
matching. Planar surfaces are chosen as the main features
which are related to each other. In the inference system, planar
surfaces are generated from basic geometric elements of object
boundaries, which are classificated into two kinds: regular
curves (circles and ellipses) and polygons. Each planar surface
is presented by the normal direction of the plane (o, f, y), its
central coordinates and bounded edges. A 3D regular curve for
a planar patch is presented by 2D parameters projected on the
plane, while a polygon is simply a group of straight lines.
Additional primitives of a planar surface are radius and ratio
for an ellipse or a circle, and perimeters and area for a polygon.
To establish the topological relation among planar surfaces, the
surfaces are grouped in terms of their normal directions. The
planar surfaces are also related by their common edges and the
distances between their central coordinates.
3.2.3 Graphical Presentation of a Model
The graphical presentation of a model can be created from the
DXF file. The presentation of each model includes: model
name, range of element sizes, and orientation, ellipse, polygon,
line and vertical point sections. Model name stands for a model
listed in a database, which is followed by the four values for
maximum and minimum lengths of lines, and maximum and
minimum values of circle or ellipse radius. Since objects are
constructed to high accuracy, by comparing the dimension
between sensed objects and models, most models whose
dimensions are beyond the range of object dimension can be
ignored. An orientation section contains the main orientations
of planar surfaces, each of which includes the list of ellipses
and polygons. Figure 7 displays an industrial model, whose
surfaces are grouped in terms of their directions. An ellipse
section lists all ellipses whose elements are central coordinates,
radius and ratio. The direction of each ellipse is derived from
the orientation section. A polygon section contains all polygons
whose elements are central coordinates, perimeter, area and the
list of bounded lines. A line section lists all lines, where the
first two numbers are vertices, and the next numbers are
polygons between which the line lies. The final element is the
length of a line. A vertical point section lists the coordinates of
all vertices.
Figure 7: Surfaces are grouped in terms of their directions
4. MODEL MATCHING
Matching between an objects in the scene and the models in the
database is performed by a detailed comparison between their
graphic presentations. A sensed object is presented in the same
way as the models in the database. Since the object in the
images are only partly visible, its description will not be
complete. Therefore, the number of detected surfaces in an
object will always be less than the number of surfaces in its
corresponding model. The matching process contains two steps:
the screener, in which most models unmatched to the given
256
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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