FLAT ZONES FILTERING, CONNECTED OPERATORS, AND FILTERS BY RECONSTRUCTION

This correspondence deals with the notion of connected operators, Star ting from the definition for operator acting on sets, it fs shown how to extend it to operators acting on function, Typically, a connected o perator acting on a function is a transformation that enlarges the par tition of the space created by the flat zones of the functions, It is shown that from any connected operator acting on sets, one can constru ct a connected operator for functions (however, it is not the unique w ay of generating connected operators for functions), Moreover, the con cept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functio ns increase with the level of the pyramid, In other words, the flat zo nes are nested, Filters by reconstruction are defined and their main p roperties are presented, Finally, some examples of application of conn ected operators and use of flat zones are described.