An important problem constraining the practical exploitation of robust watermarking technologies is the low robustness of the existing algorithms against geometrical distortions such as rotation, scaling, cropping, translation, change of aspect ratio and shearing. All these attacks can be uniquely described by general affine transforms. In this work, we propose a robust estimation method using apriori known regularity of a set of points. These points can be typically local maxima, or peaks, resulting either from the autocorrelation function (ACF) or from the magnitude spectrum (MS) generated by periodic patterns, which result in regularly aligned and equally spaced points. This structure is kept under any affine transform. The estimation of affine transform parameters is formulated as a robust penalized Maximum Likelihood (ML) problem. We propose an efficient approximation of this problem based on Hough transform (HT) or Radon transform (RT), which are known to be very robust in detecting alignments, even when noise is introduced by misalignments of points, missing points, or extra points. The high efficiency of the method is demonstrated even when severe degradations have occurred, including JPEG compression with a quality factor of 50%, where other known algorithms fail. Results with the Stirmark benchmark confirm the high robustness of the proposed method.