Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems
Journal of Mathematical Imaging and Vision
On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering
Computers & Mathematics with Applications
Improved fusion machine based on T-norm operators for robot perception
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 4
Recognition of linkage curve based on mathematical morphology
ICICA'10 Proceedings of the First international conference on Information computing and applications
Adaptive filter and morphological operators using binary PSO
ICICA'10 Proceedings of the First international conference on Information computing and applications
Generalized fuzzy morphological operators
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
Efficient non-linear filter for impulse noise removal in document images
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Hi-index | 0.01 |
In this paper, the generalized fuzzy mathematical morphology (GFMM) is proposed, based on a novel definition of the fuzzy inclusion indicator (FII). FII is a fuzzy set used as a measure of the inclusion of a fuzzy set into another, that is proposed to be a fuzzy set. It is proven that the FII obeys a set of axioms, which are proposed to be extensions of the known axioms that any inclusion indicator should obey, and which correspond to the desirable properties of any mathematical morphology operation. The GFMM provides a very powerful and flexible tool for morphological operations. The binary and grayscale mathematical morphologies can be considered as special cases of the proposed GFMM. An application for robust skeletonization and shape decomposition of two-dimensional (2-D) and three-dimensional (3-D) objects is presented. Simulation examples show that the object reconstruction from their skeletal subsets that can be achieved by using the GFMM is better than by using the binary mathematical morphology in most cases. Furthermore, the use of the GFMM for skeletonization and shape decomposition preserves the shape and the location of the skeletal subsets and spines