A method is provided for inserting a digital watermark in an image by an insertion device. Inserting includes: applying a Fourier transform to the image, delivering a 2D Fourier spectrum; inserting the watermark in the Fourier spectrum delivering a modified Fourier spectrum; and applying an inverse Fourier transform to the modified Fourier spectrum delivering a watermarked image. The watermark includes a set of watermarking coefficients each associated with a distinct determined position of a given quadrant among the quadrants of the Fourier domain, the spectral coordinates u and v of which, measured along the two axes of coordinates of the given quadrant and starting from the continuous component and expressed in percentage of the dimensions U and V of the given quadrant, are such that: u>66%×U and v>66%×V. The set of positions associated with the watermarking coefficients defines a convex pattern in the given quadrant.