  Morphological neural networks allow to learn the weights of a structuring
function knowing the desired output image. However, those networks are not
intrinsically robust to lighting variations in images with an optical cause,
such as a change of light intensity. In this paper, we introduce a
morphological neural network which possesses such a robustness to lighting
variations. It is based on the recent framework of Logarithmic Mathematical
Morphology (LMM), i.e. Mathematical Morphology defined with the Logarithmic
Image Processing (LIP) model. This model has a LIP additive law which simulates
in images a variation of the light intensity. We especially learn the
structuring function of a LMM operator robust to those variations, namely : the
map of LIP-additive Asplund distances. Results in images show that our neural
network verifies the required property.
