Paper:

# Modelling Numerical and Spatial Uncertainty in GrayscaleImage Capture Using Fuzzy Set Theory

## Mike Nachtegae^{∗}, Peter Sussner^{∗∗}, Tom Mélange^{∗},

and Etienne E. Kerre^{∗}

^{∗}Dept. of Applied Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit

Krijgslaan 281 - S9, 9000 Gent, Belgium

^{∗∗}Dept. of Applied Mathematics, University of Campinas, Campinas, SP 13083 859, Brazil

In this paper, we will discuss interval-valued and intuitionistic fuzzy sets as a model for grayscale images, taking into account the uncertainty regarding the measured grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. We will demonstrate the practical potential of this image model by introducing an interval-valued morphological theory and by illustrating its application with some examples. The results show that the uncertainty that is present during the image capture not only can be modelled, but can also be propagated such that the information regarding the uncertainty is never lost.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.13, No.5, pp. 529-536, 2009.

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