Applied to the procedure of image segmentation, cluster analysis methods group pixels to objects that have similar features. The segmentation of fluid-filled regions and ruptures is based on the gray-level intensities histogram of the B-scan by the k-means clustering algorithm.
23 The histogram represents the feature space for the clustering algorithm. Pixels with the same gray-level intensity are assigned into the same cluster but do not have to be connected in the image implicitly.
In
Figures 2A–2C the clustering by the k-means method is illustrated in an example for one iteration step. Based on the initial position of four cluster centers, the objects (crosses) were assigned to the cluster with the minimal distance to a cluster center (
Figs. 2A,
2B). Depending on the assigned objects, the cluster centers were recalculated, and based on the recalculated cluster centers, a re-assignment of the set was performed (
Fig. 2C). The assignment of objects differed within the blue and brown clusters.
Cluster analysis results obtained by the iterative k-means algorithm depend in large part on the number of cluster centers
k, which must be defined prior to the calculation. However, a definition of a “correct” or “incorrect” clustering is difficult to find. Any partitioning may reflect the structure of the underlying data and depending on the context the correctness of a clustering must be defined by the operator. In
Figures 2D–2G the segmentation by the k-means algorithm was processed for different numbers of cluster centers
k based on a SD-OCT scan from the Spectralis OCT device. With a number of cluster centers
k = 2, the bright retinal gray-level intensities with high reflectivity were separated from the dark intensities with low reflectivity (
Fig. 2E). With increasing numbers of clusters centers (i.e.,
k = 6;
Fig. 2F), more structures were separated. If the value for
k was too high, an oversegmentation resulted and individual structures that belonged together were segmented separately (
Fig. 2G). A possible way to determine the optimal number of cluster centers
k is represented by the elbow criteria, in which the clustering is processed with successive increased numbers of cluster centers and validated by an error function.
23 In such test scenarios the elbow-criteria showed an optimal value for the number of cluster centers with
k = 6 (
Fig. 2F).