Using the Rotation Parameter Alone

Using the rotation parameter to perform Hough transform

is similar to the method of using the scale parameter. Some

specific details are listed below:

1. The variation range of the rotation parameter is 0 to

360 degrees.

2. The sampling interval of the parameter space is 10

degrees. Thus, the accumulate array is one dimensional

with 36 bins.

3. When performing the voting, the angle between vec-

tor

and vector

_

_0

is calculated. The angle

indicates the rotation parameter between two images.

Then, the counts of the accumulate array bins that re-

late to this angle are increased. The peak bin index and

the confidence of each match,

and

, are saved as

mentioned above. Votes from all matches are saved in

the overall accumulate array.

4. After completing 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 deter-

mined. Figure 4 shows one example of the votes of the

overall accumulate array.

5. Each match is labeled as correct or incorrect. A match

is accepted as correct if its peak bin index is within

the correct bin indexes. The confidence curve is similar

to the one provided in Figure 3b, and it can aid in de-

ciding whether a match is correct or not.

Problems of the Above Methods

When the proportion of correct matches is low, the method

of using one parameter to perform Hough transform becomes

less stable. Problems may appear as consequences, as shown

in the following examples:

1. The peak bin of the accumulate array is not outstanding;

2. Multiple peaks may come out;

3. The strongest peak could be a wrong peak, and the pa-

rameter related to the peak is not the actual parameter

of the two images.

4. The turning point of the confidence curve becomes less

clear, thereby making separating the correct matches

and incorrect matches difficult. Figure 5 presents these

phenomena.

Figure 4. Votes in the overall accumulate array when using the

rotation parameter to perform the Hough transform.

Figure 3. Voting result when using the scale parameter to perform

the Hough transform: (a) The distribution of votes in the overall

accumulate array, and (b) The confidence curve of the matches

(feature pairs).

Figure 5. Effects of the proportion of correct matches on the voting result: (a) The effect of the proportion of correct matches to peak bins

(multiple peaks and wrong peaks come out, and the correct peak is third strongest); (b) The effect of the proportion of correct matches

to the shape of the confidence curve when using only the rotation parameter; and (c) The effect of the proportion of correct matches to

the shape of the confidence curve when using only the scale parameter. (The turning point of the confidence curve becomes less clear,

thereby making separating the correct matches and incorrect matches difficult).

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