The basic farmland within the protection areas was required to be of high-quality and connective in the general plans for land use. A new method was developed to delineate the boundaries of high-quality, concentrated and connective cultivated land. Based on mathematical morphology principles and GIS methods, the high quality of cultivated land blocks could be identified through dilation and ero...

A relation on a hypergraph is a binary relation on the set consisting of all the nodes and the edges, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join preserving mappings on the lattice of sub-hypergraphs. This paper introduces a generalization of a relation algebra in which the Boolean algebra part is replaced by a Heyting...

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another, more recent, extension, concerns bipolar fuz...

In this paper we discuss how biresiduations provide a unifying paradigm for fuzzy formal concept analysis and mathematical morphology. In particular we provide constructions of morphological operators such as dilation and erosion within the framework of convolution algebras of action networks (also known as small covariant categories) over join complete semirings. This unifies and generalizes p...

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...