In this paper we study robustness of nonlinear filters for image processing by using a recently introduced method called output distributional influence function (ODIF). Unlike the traditionally used asymptotic methods, such as the influence function and the change-of-variance function, the ODIF provides information about the robustness of finite length filters used in image processing. The ODIF is not only a good theoretical analysis tool but it can also be used in real filtering situations for selecting filters behaving as desired in the presence of contamination. The applicability of the ODIF to the real image processing tasks is validated by experiments on images. We present the ODIFs for stack and L-filters which include many of the filters useful in the image processing applications. The usefulness of the ODIF in the analysis of the robustness of different filters is demonstrated in several illustrative examples by using the ODIFs for the expectation and variance.