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This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown(More)
After a formal definition of segmentation as the largest partition of the space according to a criterion σ and a function f, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 8), that identifies segmentation with the connections that are based on connective criteria. Just as connections,(More)
Classically, connectivity is a topological notion for sets, often introduced by means of arcs. A nontopological axiomatics has been proposed by Matheron and Serra. The present paper extends it to complete sup-generated lattices. A connection turns out to be characterized by a family of openings labelled by the sup-generators, which partition each element of(More)
MOTIVATION DNA microarrays are an experimental technology which consists in arrays of thousands of discrete DNA sequences that are printed on glass microscope slides. Image analysis is an important aspect of microarray experiments. The aim of this step is to reduce an image of spots into a table with a measure of the intensity for each spot. Efficient,(More)