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The method starts with finding basic components of straight
lines or regular curves by the assessment of the edge direction
at the edge points along a whole edge. Straight lines or regular
curves are then extended to their end points using geometric
parameters determined by their components. Those lines with
the same properties extracted from different edge sections can
be merged in terms of their geometric similarity. In order to
close boundaries of objects in image space, straight lines and
open regular curves are linked at their terminal points. Finally,
surface patches are generated by constrained chaining the
geometrical lines. Figure 4 illustrates the results of line
segmentation.
2.3 Stereo Matching
Using two or more CCD cameras, 3D surfaces of an object can
be constructed by matching straight lines and ellipses. The
reliability of the matching is confirmed by epipolar geometry,
based on the camera orientation. The correspondence of a pair
of straight lines in stereo images is determined in terms of their
terminals, which should satisfy the epipolar constraint. A 3D
straight line is simply presented by 3D coordinates of its two
terminals, using ray intersection.
To find the correspondence of regular curves, it 1s necessary to
consider their size and location. An epipolar line, which is
tangential to a given ellipse in one image, must be tangential to
a matching ellipse in the other. This condition includes the
basic requirement for the size and location of matching ellipses.
The matched elements of an ellipse can be presented as a
straight line with two tangent points at its ends as shown in
figure 5. In a similar manner to matching straight lines, the
ellipses being matched should satisfy the condition that their
corresponding tangent points lie on the same epipolar line.
Epipolar Line
Left “Tangent Point m Right
Figure 5 : Matching of an ellipse
Image Plane
Object Plane
Figure 6 : Intersection of a conic surface with planes
The calculation of 3D ellipses is based on the assumption that a
Special ellipse is an intersection of an object plane with a conic
surface, whose apexes are at the projection centre. An ellipse in
an image can also be referred to as the intersection of an image
plane with the conic surface, as shown in figure 6. The
parameters of an ellipse on two different planes can be
transformed, if the relations of the two planes are known. The
determination of an ellipse in object space, therefore, contains
two aspects: one is to determine an object plane; the other is to
establish the relation between image and object planes.
An object plane is determined by a few intersection points on
the corresponding ellipses in the stereo images. The relation
between image and object planes is established in terms of the
camera orientation. The ellipse on the image plane is then
transformed onto the object plane. A 3D ellipse can be
described by a plane in object space and the 2D curve
parameters on the plane.
3. GENERATION OF MODELS IN DATABASE
In an industrial environment, CAD systems are usually used to
design objects for the manufacturing task. Automatic genera-
tion of the same recognition code for object information used
for design and manufacture would be an efficient, cost-effective
approach. AutoCAD is a general purpose Computer Aided
Design program for preparing two dimensional drawings and
three dimensional models. The speed and ease with which a
drawing can be prepared and modified using a computer, offer
a significant advantage over hand preparation. Using the
AutoCAD system, models can be created and output in a DXF
file, a drawing interchanging file. CAD models serve as a basic
description of object geometry. Inference procedures of various
sorts are then applied to the CAD models to produce a graphic
presentation in the database for object recognition.
3.1 CAD Output: The DXF Format
DXF files are standard ASCII text files, which can easily be
submitted to other programs for specialised analysis. Since a
DXF file is a complete representation of the drawing database,
for the presentation of matching features, it is not necessary to
use all information in the file. In the research, the attention is
concentrated on that portion of the DXF standard devoted to the
description of 3D geometry.
A DXF file is subdivided into four editable section, plus the
END OF FILE marker. The HEADER section contains settings
of variables associated with the drawing. The TABLES section
contains several tables, each of which contains a variable
number of table entries. The BLOCKS section contains the
entities that make up the blocks used in the drawing, including
anonymous blocks generated by associative dimensioning. All
basic geometric elements in the sequence design stage of a
model are stored in this section. The ENTITIES section
contains entity items, which can also appear in the block
sections. The appearance of entities in the two sections is
identical, but this section provides the final drawing of the
CAD design.
A DXF file is composed of many groups, each of which
occupies two lines in the DXF file. The first line of a group is a
group code, used to indicate both the type of the value of the
group and the general use of the group. The second line is the
group value, in a format that depends on the type of group
specified by the group code. For example, a line is presented by
two points. The codes for the coordinates of a start point are
(10, 20, 30), and for the coordinates of a end point are (11, 21,
255
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
