Decomposition of Interval-Valued Fuzzy Morphological Operations
One of the extensions of binary morphology to greyscale images is given by the classical fuzzy mathematical mor- phology. Interval-valued fuzzy mathematical morphology further ex- tends the latter theory by now also allowing uncertainty in the grey values of the image. In this paper, the decomposition of the interval- valued fuzzy morphological operations into their binary counterparts is studied both in a general continuous framework and a discrete framework. It will be shown that some properties that do not hold in the continuous framework, do hold in the discrete framework, which is the framework that is used in practice. Keywords— Decomposition, interval-valued fuzzy sets, mathe- matical morphology.
OBJECTIVE ::: To establish a new method to discriminate Aaron's beard by Fourier transformation infrared spectrometry. ::: ::: ::: METHODS ::: Attenuation Reflection-Fourier transformation infrared spectrometry with clustering analysis was used to the identification of Aaron's beard. ::: ::: ::: RESULTS ::: There were obvious differences in Aaron's beard. The results are consistent with that of morphologic study. ::: ::: ::: CONCLUSION ::: This method is rapid, simple and economical, and can be used to the quality control.