(a) (b) (c)
Figure 10. Line detection results under different Hough transform
thresholds
From Figure 10a, it can be seen that when the voting threshold is 30,
the Hough transform detects multiple straight lines in the figure. That
is, the smaller the voting threshold setting, the shorter the line
segment features that can be detected, It is obvious that this will
detect the interfering pixels in the edge image as straight lines. In
Figure 10b, when the threshold of vote count is 40, the number of
interfering pixels detected in the Hough transform detection results
significantly decreases. Therefore, it can be concluded that increasing
the threshold of vote count will improve the accuracy of line detection.
But when the threshold of the number of votes is 60, the Hough transform
only detects two edge lines of the crane grabbing the boom, missing the
other two edge lines. This indicates that the edge line detection of the
crane’s grab boom cannot be achieved solely by increasing the threshold
setting of the number of votes. In the edge detection image shown in
Figure 10, Due to factors such as uneven lighting ,the linearity of the
pixel arrangement of the four edge lines of Crane grabbing boom will
undergo a sudden change , There may be slight differences in the
parameters of the lines detected on the same edge line. And these subtle
differences may directly affect the accuracy of line fitting. Therefore,
it is difficult to determine which straight line to use as the edge
straight line for the crane to grab the boom, Meanwhile, the purpose of
conducting line detection in this article is to calculate the
coordinates of the three corner points of the crane’s grab boom through
the intersection of lines, Therefore, it is necessary to fit the
detected straight lines and simplify them to four.
2.2 Clustering of Line Parameter Points Based on
k-means
The coordinate points mapped to the Hough space correspond to a straight
line in the image coordinate system, Crane grabbing boom has 4 edge
lines. Therefore, the clustering method[20-21] is adopted to cluster
all the line parameter points detected by the Hough transform into the
same number of classes as the number of edges of Crane grabbing boom .
Compared to other clustering algorithms, the k-menas algorithm has
advantages such as simple algorithm idea, fast convergence speed, better
clustering effect, and the main parameter that needs to be adjusted is
only the number of clusters K. When other clustering algorithms are
applied to edge maps with significant interference, they will cluster
the coordinates of the line parameter points detected by Hough transform
into an uncertain number of clusters. Intuitively manifested as fitting
3, 4, 5, or even more straight lines, From an engineering perspective,
it is not possible to guarantee the stability of the coordinates of the
three corner points used to obtain the crane’s grasping boom. The
k-means algorithm needs to specify the number of clustering clusters K
in advance to ensure that the lines detected by the Hough transform can
be clustered into four categories, intuitively manifested as fitting
four corresponding lines. Therefore, this article uses the k-means
algorithm to cluster linear parameter points.
K-means algorithm is a unsupervised learning clustering method.
According to the attributes of N data objects, it is divided into K
clusters, and the center point of each cluster is calculated. Make the
clustering results meet the requirements of high similarity among
samples within different clusters and low similarity among samples
between different clusters. It uses the Euclidean distance and the sum
of squared errors criterion as the evaluation criteria.
Specifically, for a given K clusters,the center point of each cluster is
, all data points in the -th cluster are in set , and represents the Nth
data point in the -th cluster.The sum of squared errors of the -th
cluster and the sum of squared errors are shown below,the goal of the
k-means algorithm is to find a partitioning method,the process of
recalculating the cluster center point and reallocating data points to
the cluster through iterative methods to minimize the total sum of
squared errors (SSE).
Perform k-means clustering analysis on the parameter coordinates of
straight lines mapped to the Hough space, as shown in Figure 11. The
edge detection results shown in Figure 11a contain a large number of
interfering edge points, which have weak linear relationships. Under low
threshold conditions, pixels with weak linear relationships are easily
detected as straight lines. The voting threshold in Figure 11 is 40,
Normalize the coordinates of parameter points with votes higher than 40
in the Hough space voter and perform k-means clustering analysis. The
clustering results are affected by the interference coordinate points in
the Hough space. Figure 11c shows that the clustering center of the red
cluster is affected by the interference data points. The intuitive
manifestation is that the fitted straight line produces a significant
deviation, as shown in Figure 11b.