This paper presents an efficient method for the estimation and recovering from nonlinear or local geometrical distortions, such as the random bending attack and restricted projective transforms. The distortions are modeled as a set of local affine transforms, the watermark being repeatedly allocated into small blocks in order to ensure its locality. The estimation of the affine transform parameters is formulated as a robust penalized Maximum Likelihood (ML) problem, which is suitable for the local level as well as for global distortions. Results with the Stirmark benchmark confirm the high robustness of the proposed method and show its state-of-the-art performance.