Accurate noise models are important to perform reliable robust image analysis. Indeed, many vision problems can be seen as parameter estimation problems. In this paper, two noise models are presented and we show that these models are convenient to approximate observation noise in different contexts related to image analysis. In spite of the numerous results on M-estimators, their robustness is not always clearly addressed in the image analysis field. Based on Mizera and Müller’s recent fundamental work, we study the robustness of M-estimators for the two presented noise models, in the fixed design setting. To illustrate the interest of these noise models, we present two image vision applications that can be solved within this framework: curves fitting and edge-preserving image smoothing.