A formal de nition of morphological operators in (max,min)algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental prop...

In this paper we propose a new approach for laser-based environment device control systems based on the automatic design of a Fuzzy Rule-Based System for laser pointer detection. The idea is to improve the success rate of the previous approaches decreasing as much as possible the false offs and increasing the success rate in images with laser spot, i.e., the detection of a false laser spot (sin...

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 extension concerns bipolar fuzzy sets, where ...

11 We propose a fuzzy expert systems architecture for image classification, whose rules 12 are implemented through translation invariant mathematical morphology operators. 13 The use of the architecture is illustrated by an expert system that classifies an area of the 14 Tapaj os National Forest, in Brazil. 2002 Elsevier Science Inc. All rights reserved.

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Qmodule transforms, is defined. Such operators — that turn out to be precisely the homomorphisms between free objects in those categories — find concrete applications in two different branches of image processing, namely fuzz...

In this paper, we present an algorithm to infer a fuzzy partition over a set of numerical values. This algorithm is based on the mathematical morphology and is expressed in the formal language theory. We use it during the construction of a fuzzy decision tree, in the case where no fuzzy partition is available for a numerical attribute. R esum e Dans ce rapport, nous pr esentons un algorithme po...

The morphological gradient is a widely used edge detector for grey-level images in many applications. In this paper, we generalize the definition of the morphological gradient of the fuzzy mathematical morphology based on t-norms. Concretely, instead of defining the morphological gradient from the usual definitions of fuzzy dilation and erosion, where the minimum and the maximum are used, we de...