A new set of mathematical morphology (MM) operators robust to illumination changes in images is defined thanks to the Logarithmic Image Processing (LIP) model which is based on physical laws of acquisition and which is consistent with human vision. The fundamental operators of logarithmic-MM, the logarithmic-dilation and the logarithmic-erosion, are defined with the LIP-addition of a structuring function. The combination of these two adjunct operators gives morphological filters, namely the logarithmic-opening and closing, useful for pattern recognition. The mathematical relation existing between " classical " dilation and erosion-with an additive structuring function-and their logarithmic-versions is established facilitating their implementation. Results on simulated and real images show that logarithmic-MM is more efficient on low-contrasted information than " classical " MM.