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

and

_

_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

and

, 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

. 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

and

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.

( , )

=

1

(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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