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(a) Algorithm: 8% A, 62% D, 30% E, (b) Algorithm: 22% A, 8% D, 70% E,
Mannesmann-Rexroth: 10% A, 50% D, 40% E Mannesmann-Rexroth: 20% A, 0% D, 80% E
Figure 3: Two images from the validation sample with automatic and manual classifications.
sample is used although it favors in some sense indecisive results. (It could be the safest to
assign 33.33% to each image.) 60 images were used for teaching, further 60 for evaluation.
The automatic classification using our algorithm is closer to the manual classification of
the teacher Mannesmann-Rexroth than the other manual classifications:
distance between Mannesmann-Rexroth and
our algorithm classification 1 | classification 2 | classification 3
11.8% 47.2% 18.1% 22.2%
5 Discussion
Reliable automatic classification of lamellar graphite in grey cast iron is possible. The algorithm
in its present form could be used in every laboratory provided an image analysis system and a
good teaching sample. Care is needed when adjusting the calibration factor.
The algorithm has the potential to yield a more objective classification than the manual
one. This would demand a teaching sample representing the range of images occurring in all
foundries and classified in consensus by a group of experts.
The learning step as implemented now has a rather ad hoc character. Replacing the EM-
algorithm by a learning algorithm tailored to this particular problem could improve the classifi-
cation and allow for refinements. For instance weights could indicate how sure the classification
of a teaching example is.
Acknowledgment. We warmly thank Dr. Wolfram Stets, Institut fiir Gieflereitechnik GmbH.
for providing one of the manual classifications.
References
[LR87] R. J. A. Little and D. B. Rubin. Statistical Analysis with Missing Data. Wiley, New
York. 1987.
[So198] P. Soille. Morphological Image Analysis. Springer-Verlag, Berlin, 1998.
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