An optimal filter estimates an unobserved ideal image from an observed image. Optimality is with respect to some error criterion, which is mean absolute error for the binary images. Both the ideal and observed images are random sets and these are governed by parameterized probability laws. The optimal filter is found relative to these laws and depends on the parameters. Qualitatively, a filter is robust if its performance is acceptable for modest changes in the laws; that is, if a filter is optimal for a given vector of parameters, it performs close to optimal for parameter vectors close to the one for which it has been designed. This problem is crucial for practical application, since filters will always be applied to image processes that deviate from design processes. We provide analytic expressions for measuring filter robustness by first expressing the optimal filter analytically in terms of conditional probabilities of template transitions under the degradation operator transforming the ideal to the observed random set. Tractable expressions are derived for sparse-noise models. Robustness surfaces are computed for various text models: independent sparse noise, sparse edge noise, noise under rotation, and restoration of rotation. We show that even when the noise is independent of the signal, the signal plays an important role in robustness.