Using Scale and Rotation Parameters Together
To solve the problems mentioned above, we strongly recom-
mend using the scale parameter and the rotation parameter to-
gether, and simultaneously employ a weighted voting strategy.
The details of the method are presented as follows:
1.
The variation range of the scale parameter is set as
1
5
to 5, and the variation range of the rotation parameter
is set as 0 to 360 degrees.
2.
The sampling intervals of the parameters are the
same as mentioned above. Thus, the accumulate ar-
ray is a two-dimensional array with a size of 17 × 36.
The accumulate array bins are initialized to zero.
3. When performing the voting process, the length ratio
and the rotation angle between vector
p p
i j
and
q q
i m j
_
_0
are calculated as mentioned above. Then, the counts of
the accumulate array bins are increased accordingly.
The difference here lies in the magnitude of the vote is based
on a weighting function. The distance between point
p
i
and
p
j
, and the similarity between the feature descriptors of the
match, can be used in deciding the weight of the vote.
1. After the voting process, the peak bin is found in the
overall accumulate array, and the indexes of bins that
can be viewed as correct bins are determined. In our
method, a bin is viewed as a correct bin if and only
if it is within±3 bins from the peak bin, and its votes
should not be less than 40 percent of the peak bin. The
method of deciding the correct bins is important. Ex-
tremely strict conditions would remove many correct
matches, whereas extremely loose conditions would
involve many false matches.
2. Each match is labeled as correct or incorrect. A match
is accepted as a correct match if its peak bin index is
within the correct bin indexes.
Figure 6 presents the confidence curve after using both the
scale and rotation parameters, which can offer a comparison
with Figure 5b and 5c. The turning point of the confidence
curve is clearer than when only one parameter is used.
Figure 7 shows the effect of a weighted voting strategy to
the voting result. The voting result of the overall accumulate
array is displayed as a gray-level image. Considering that
angle is periodic (to make it more convenient for readers to
see the distribution of votes), the image of the accumulate
array in Figure 7 has 45 rows instead of 36 by copying the
content of the first nine rows to the end of the 36
th
row (to
place 0 degrees next to 359 degrees).
The weighting function used in our method is illustrated
in Equation 1. It provides additional weight to points with a
smaller Euclidean distance to point
p
i
. This weighting func-
tion is used because, in practice, many images that require
matching have an extremely small overlapping area. Feature
points outside the overlapping area do not have correct cor-
responding points. Thus, matches formed by these feature
points become major outliers in the initial matches. Using the
inverse of the distance between
p
i
and
p
j
can weaken the ef-
fect of such matches because only closer points possess a large
weight. The similarity between the feature descriptors of the
match is not used to make our method as simple as possible.
The voting result shown in Figure 7a is the result when
all votes are equally weighted; three local peaks exist in the
accumulate array, and the top two strongest peaks are wrong
peaks. By contrast, using the weighted voting strategy dis-
played only one peak in the accumulate array, as presented
in Figure 7b. Furthermore, this peak is identified as a correct
peak. Therefore, the weighted voting strategy can further
improve the robustness of Hough transform.
( , )
weight
p p
i
j
=
1
distance
(1)
Experiments
Experiments were conducted to improve and verify the per-
formance of our method. The method used in the experiments
uses the scale parameter and the rotation parameter together,
and simultaneously employs a weighted voting strategy.
In this section, the experiments are presented in three as-
pects as follows: First, the difference between using multiple
nearest neighbors and using only the first nearest neighbor is
provided. Then, the comparison between using
LMedS
in di-
rectly solving the epipolar geometry and using our algorithm
as a prepossessing step before solving the epipolar geometry
is presented. Finally, the results of some different imaging
situations are provided, such as images with large perspec-
tive effects, planar scenes viewed obliquely, and images with
large-scale difference to show the large-scope application of
our algorithm.
Figure 6. Effect of ratio of the inliers to the shape of the con-
fidence curve when using both the scale parameter and the
rotation parameter (The turning point of the confidence curve is
clearer than using only one parameter).
Figure 7. Effect of the weighted voting strategy: (a)The voting re-
sult without using the weighted voting strategy, and (b) The voting
result using weighted voting strategy.
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July 2016
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