a method for detecting a watermark signal in digital image data . the detecting method includes the steps of : computing a log - polar fourier transform of the image data to obtain a log - polar fourier spectrum ; projecting the log - polar fourier spectrum down to a lower dimensional space to obtain an extracted signal ; comparing the extracted signal to a target watermark signal ; and declaring the presence or absence of the target watermark signal in the image data based on the comparison . also provided is a method for inserting a watermark signal in digital image data to obtain a watermarked image . the inserting method includes the steps of : computing a log - polar fourier transform of the image data to obtain a log - polar fourier spectrum ; projecting the log - polar fourier spectrum down to a lower dimensional space to obtain an extracted signal ; modifying the extracted signal such that it is similar to a target watermark ; performing a one - to - many mapping of the modified signal back to log - polar fourier transform space to obtain a set of watermarked coefficients ; and performing an inverse log - polar fourier transform on the set of watermarked coefficients to obtain a watermarked image .