Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based o...

In this paper, duality is discussed in soft open as well as soft close in multi scale environment. Soft erosion and soft dilation will exist for various thresholds. So soft open and soft close also exist for various thresholds. If definition for soft erosion and soft dilation are studied (5), then some type of equalities are viewed among soft morphological operations. So equality may be establi...

An improvement of the majority gate algorithm suitable for grey scale morphological operations is presented in this letter. The redundancy of temporal signals led to a simplified hardware implementation. It is shown that max/min operators can be computed by the same circuit. A new pipelined systolic array architecture based on this circuit is illustrated for dilation/erosion operations. 2 Intro...

We establish the link between Mathematical Morphology and the map of Asplund’s distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice ...

A set of subsets of a set may be seen as granules that allow arbitrary subsets to be approximated in terms of these granules. In the simplest case of rough set theory, the set of granules is required to partition the underlying set, but granulations based on relations more general than equivalence relations are well-known within rough set theory. The operations of dilation and erosion from math...

In this correspondence, we present a fast thresholded linear convolution representation of morphological operations. The thresholded linear convolution representation of dilation and erosion is first proposed. A comparison of the efficiency of the direct implementation of morphological operations and the thresholded linear convolution representation of morphological operations is subsequently c...

This paper presents the first fully automatic color analysis system suited for business documents. Our pixelbased approach uses mainly color morphology and does not require any training, manual assistance, prior knowledge or model. We developed a robust color segmentation system adapted for invoices and forms with significant color complexity and dithered background. The system achieves several...

Based on similarities between fuzzy set theory and mathematical morphology Grabisch proposed a fuzzy morphology based on the Sugeno fuzzy integral [2]. This paper shows how these ideas can be applied to practical problems. Fast implementable definitions for erosion and dilation based on the fuzzy integral are given, their properties are discussed and some application examples are presented.