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Fuzzy classification
Classifier structure
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The fuzzy system consists of six subsystems referred to six ROIs. Each subsystem includes two classifiers: one, for younger children, uses the shape and size features and another one, for older children, applies the wavelet features. When both stages of development interfere and all features are available, the outputs of both subsystems are averaged.
The bone age is assessed in two stages. First, the age is assessed independently for each ROI. This yields fuzzy sets. Then, the results are combined into the fuzzy verdict of the system. Finally, the fuzzy output is defuzzyfied with a center of gravity method in order to give an exact classification of the bone age.
At the final aggregation step the classifier has to deal with a changing number of inputs and a tolerance to partially erroneous features. The former happens when an error in processing of a ROI is automatically detected and the features are not extracted. The latter problem is due to minor errors in the processing of a ROI that have passed undetected. It has been solved by applying an aggregation method that extracts a common kernel of the age assessment for all ROIs.
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Mimics human reasoning by mathematical operations. Processing is performed on fuzzy (approximate) values described by membership functions with added linguistic interpretation.
Knowledge is expressed as set of if-then rules (rule base).
In our application rules link feautures and bone age, and classes correspond to years of age eg. Class 12 means age is ca. 12.5 years
Details: System creation and parameters,
Evaluation of bone age:example
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The accompaning figure shows the results of bone age asessment as they appear in the output window. The system displays:
- fuzzy bone age asessessment for every ROI
- aggregated fuzzy bone age
- bone age as classical number calculated with a center-of-gravity method
The radiologist can accept the assessment of the system or choose another value on base of undelining fuzzy asseessment. The shape of a fuzzy set yields information about the accuracy of the assessment.
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Interpetation of this case: Distal ROI finger II: bone age matches equally two clasess 7 and 8. Middle ROI finger IV: very low membership values suggest untypical or ambigous values of the features probably due to error in feature extraction (user may verify the extracted ROIS in main window of the program). Other ROI show distinct maxima. The final bone age is 7.51 however the user may shift it a little towards 8, if s/he feels that the defuzzification result is too much influenced by tails of the membership function.
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