Figure 1.
Basic idea of proposed method.
The basic idea of the Cepel method using the example of a single linear projection.
Figure 2.
Two characteristics of basic idea.
Projections can be non-linear and multiple projections can be combined.
Figure 3.
Example of density estimation of clustered data.
The density of data with known properties is estimated in three steps. Only the first two dimensions of the multidimensional data are shown.
Figure 4.
Evaluation of precision of estimation.
Comparison of estimation with Parzen window and Cepel on clustered data as shown in figure 3.
Table 1.
Equations of some of the models used.
Figure 5.
Automatic data mining approach.
Automatic data mining by evaluating various 1d-decompositions and selecting the most likely. The decompositions correspond to the equations in table 1.
Figure 6.
Various publicly available data sets (from [7]–[8]) are analyzed with the software. The analysis creates a varying number of charts depending on the number of columns in the data and their explanatory power.
Figure 7.
Example of a result created in the analysis.
Upper diagram: the difference of the signal between the left and right half is easily missed. Lower diagram: the same data displayed as distributions. The blue curve is calculated from the left part of the signal; the right half is displayed in green. The difference between both distributions is considerable and can be detected automatically.
Figure 8.
Another example from the analysis.
The diagonal line indicates the linear relation that was automatically extracted from the data.
Table 2.
Overview of features used in segmentation.
Figure 9.
Decomposition of merging probability.
The probability that two regions are merged is decomposed into 1d-distributions of feature values (left) and the reliability of each feature depending on size of the regions (right). The left diagram shows two out of three features; on the right, texture is used as one example out of the three features.
Figure 10.
Visualization of the image segmentation process.
Three out of about one hundred intermediate images are shown. In the first one on the left, every pixel is treated as a separate region; the last shows the final segmentation.
Table 3.
Overview of segmentation results.
Figure 11.
Comparison of segmentations of a filigree structure.
Results of Maire et al. and the proposed method are compared at the example of a filigree structure. One threshold is highlighted in red for clarity.
Figure 12.
Comparison of a difficult patch.
A second example of an image with a patch that is hard to segment.