The generalization of mathematical morphology to multivariate vector spaces is addressed in this paper. The proposed approach is fully unsupervised and consists in learning a complete lattice from an image as a nonlinear bijective mapping, interpreted in the form of a learned rank transformation together with an ordering of vectors. This unsupervised ordering of vectors relies on three steps: d...

Manual method of feature extraction from remote sensing imagery is a tedious and time-consuming process. The current paper presents the application of Mathematical Morphology for extracting urban features like buildings and roads from remotely sensed imagery. Roads and Buildings are the major features that influence urban planning and development. Also, GIS databases are to be frequently update...

In this paper we complement the standard algebraic view of mathematical morphology with a geometric, di erential view. Three observations underlie this approach: 1) certain structuring elements (convex) are scalable in that a sequence of repeated operations is equivalent to a single operation, but with a larger structuring element of the same shape; 2) to determine the outcome of the operation,...

In many domains, it is important to be able to deal with bipolar information [5]. Positive information represents what is granted to be possible (for instance because it has already been observed or experienced), while negative information represents what is impossible (or forbidden, or surely false). This domain has recently motivated work in several directions. In particular, fuzzy and possib...

Preface Linear filters have been used as the primary tools in signal and image processing. They exhibit many desirable properties, such as the superposition, which makes them easy to design and implement. Furthermore, they are the best solution in additive Gaussian noise suppression. However, when the noise is not additive or when there exist system non-linearities linear filters are not adequa...

In the framework of structural representations for applications in image understanding, we establish links between similarities, hypergraph theory and mathematical morphology. We propose new similarity measures and pseudo-metrics on lattices of hypergraphs based on morphological operators. New forms of these operators on hypergraphs are introduced as well. Some examples based on various dilatio...

Oriented textures are characterised by a dominant orientation at each point of the texture, and can be summarised by images encoding these dominant orientations. Because of the angular values in these images, standard morphological operators are not suited to their treatment. We discuss the application of the morphological circular centred operators to the analysis of oriented textures for the ...

Since mathematical morphology is based on complete lattice theory, a vector ordering method becomes indispensable for its extension to multivariate images. Among the several approaches developed with this purpose, lexicographical orderings are by far the most frequent, as they possess certain desirable theoretical properties. However, their main drawback consists of the excessive priority attri...

The geometric and statistical physical concepts of dynamic scale-space paradigms are presented and juxtaposed to those of mathematical morphology. It turns out that the dynamic paradigms can be applied to, substantiate and even generalise the morphological techniques and paradigms. In particular the importance of the dynamic scale-space concepts in granulometry by means of size densities or sta...

Bipolarity is an important feature of spatial information, involved in the expressions of preferences and constraints about spatial positioning, or in pairs of “opposite” spatial relations such as left and right. Imprecision should also be taken into account, and fuzzy sets is then an appropriate formalism. In this paper, we propose to handle such information based on mathematical morphology op...