In this paper, we propose a new formalism that enables to take into account textural features of the image in a very robust and selective way. This approach also permits visualization of 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 into account texture directionality; and the mathematical morphology formalism, on which it is based, does not enable extensions to this feature. This has led us to design a new formalism for texture representation capable of including 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 for discriminating different textures. We illustrate this approach by a set of results showing its interest in the frame of supervised image segmentation.