||A recurrent problem in image analysis is the presence of image data uncertainties, generically called noise. In the literature, the capacity of an algorithm to resist to such data alteration is named robustness, but without any clear formalism for image processing. During this talk, I will first remind the original and foundational definition of robustness for image processing algorithms I presented in my last CBA talk (fall 2016), by considering multiple scales of noise. Then, I will present robust techniques, supported by tools from digital geometry (DG) and mathematical morphology (MM) ; this part deals respectively with skeletonization and Reeb graph calculation, and smoothed shock denoising and enhancement filtering. The next part will be devoted to recent advances in defining robustness more accurately and to combining both DG and MM approaches for applications in liver biomedical image analysis. This talk will finish with research leads about robust image processing approaches oriented towards biomedical applications, involving numerical simulation and machine learning.