In this paper, we propose a new formalism that enables to take into account image textural features in a very robust and selective way. This approach also permits to visualize these features so experts can efficiently supervise an image segmentation process based on texture analysis. The texture concept has been studied through different approaches. One of them is based on the notion of ordered local extrema and is very promising. Unfortunately, this approach does not take in charge texture directionality; and the mathematical morphology formalism, on which it is based, does not enable extensions to this feature. This led us to design a new formalism for texture representation which is able to include directionality features. It produces a representation of texture relevant features in the form of a surface z = f(x,y). The visualization of this surface gives experts sufficient information to discriminate different textures.