Summary: Images of a scene observed under a variable illumination or with a variable optical aperture are not identical. Does a privileged representant exist? In which physical setting? In which mathematical context? With which meaning and criterion? How to obtain it? The authors answer to such questions in the physical setting of logarithmic imaging processes. For such a purpose, they use the logarithmic image processing (LIP) model, known to be a compatible mathematical framework. After short recalls on this model, the paper presents two image transforms: one performs an optimal enhancement and stabilization of the overall dynamic range, and the other does of the mean dynamic range. The results obtained on X-ray images, as well as for some natural scenes, are shown. Also the implementation of the transforms is addressed.