We generated small spatial perturbations by smoothing two i.i.d random noise images (for the x and y components of the perturbation) with a Gaussian filter. We limit the maximum perturbation in each direction to a defined value (we used a maximum 0.5 and 1 pixels). We then used those as displacement fields to warp the original watermark and alpha matte (using bilinear interpolation).
Here is an example of a generated perturbation field and its affect on a watermark:
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