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GGCS for lines
Unary constraints :
orientation of line;
length of line;
etc.
Binary constraints :
1). Collinearity.
Collinearity means that two lines have same
mathematical equation. It is easy to see that the starting
points and ending point for two lines are not necessarily
to be the same for the collinearity.
2). Overlapping.
Two lines are said to be overlapping if they are collinear
and have common range.
3). Connectivity.
Two lines are connected if lines are mathematically
intersected and the intersecting point is within the
starting point and ending point for both lines.
4). Coplanarity.
Two lines are coplanarity if they are on the same plane.
5). Parallel.
The general attributes to describe the relationship of two
lines can be summarized as following:
distance between a pair of lines (shortest distance)
distance between the endpoints of two line segments
(including shortest distance between the endpoints
of two line
segments as well as longest distance)
distance between the midpoints of two line
segments
distance from a line to the origin, and
distance from a line to an endpoints of a line
segment.
overlapping range
intersecting angle
coordinates of intersecting point
difference of lengths
What type of GGCS should be used is task and scene
dependent. The generation of suitable GGCS for specific
task, specific scenes or objects will initialize other
research issues, that is, the generic modelling, learning
mechanism, and related man-machine interface, etc.
6. FINAL MATCHING IN OBJECT SPACE
Because in the image space, it is allowed that one line
can be matched with more than one lines on the other
image, we need to implement the uniqueness constraints
together with GGCS and other constraints in object
space.
Such problem is a typical consistent labelling or
537
constrained satisfaction problem which was formulated
by Haralick and Shapiro. In our current algorithm,
we use the relaxation techniques which is frequently
used in the computer vision community.
We assign each candidate object line (i) a label LB(i)
which ranges from 0 to 1.0 . After the relaxation, the
line with label "1" means a true scene line, while a "0"
indicate a false line. The initial label value for each line
is bound in the image space matching (e.g. from
similarity measurement of contrast). The label value is
then updated in the iteration by the following formula.
LB()**! = (1.0 + 06) LB()* 4 o,a
- B,(b; + b,) - B,c 2)
where
LB(i)** is updated label value
LB(i)* is old label value
k is the number of iteration
0, is the coefficient for increment from old label
0, is the coefficient for increment from GGCS
B, is the coefficient for decrease from uniqueness
constraints.
B, is the coefficient for decrease from ordering
constraints.
a is the measure for the GGCS
b,,b, is the measure for uniqueness constraint
c is the measure for ordering constraint
7. EXPERIMENTAL RESULTS
Experiment on simulated data
Fig.4 Simulated left and right images (lines)