(a) (b)
Figure 12. Distribution of Linear Voting Numbers under Different Values of m

2.4 Improved clustering centroid calculation method

The clustering centroid for k-means will eventually move to the average of all samples within the cluster, which is greatly affected by errors. This article proposes an improved clustering centroid calculation method to replace the original clustering centroid of k-means as the basis for line fitting. Take the weight of the votes of each line into the calculation formula. Figure 13 shows the local image of line detection. When the edge image is affected by uncontrollable factors such as lighting, a small portion of correct edge pixels are lost, but the overall linear relationship does not change much. Therefore, this type of straight line still has some reference value for line fitting and cannot be directly removed. Using the optimal adaptive threshold method proposed in 2.3, find a series of lines with high voting numbers in each cluster. In Figure 13a, in detection lines 1, 2, and 3, detection line 2 shows the detection results of missing edge pixels, but its linear relationship is basically consistent with other detection lines, with slight errors. Therefore, based on the weight of the number of straight line votes, a formula is proposed:
The improved clustering centroid calculation method proposed in this article takes into account the weight proportion of each line, and the calculation results are theoretically more in line with the linear relationship of real edge points. By using the method of determining adaptive thresholds based on the number of votes counted, lines with low votes are deleted, improving the reliability of the lines to be fitted in each cluster. And the improved clustering centroid calculation method further brings the straight line fitting results closer to the real edge in theory. The detection results are shown in Figure 13c.