A class of attacks targeting at a feature-based affineinvariant digital watermarking technique is addressed in this paper. First, it is pointed out that the use of feature points to revert an affine transform operation is equivalent to the use of a known image size or boundary for image normalization. Therefore, any method based on feature points suffers from point shifting in much the same manner as how the image normalization scheme suffers from cropping or reframing. Some simple methods to perform a (feature) point shifting attack are next described. Although use of a sufficient large number of candidate feature points can solve the problem, the paper further points out that this solution, like any secure template- based watermarking method, results in high detection complexity. A two-stage search scheme is proposed to avoid the attack, while retaining the overall detection complexity to a reasonable level.