A method for watermarking a three-dimensional object is disclosed. The watermarking method comprises computing shape descriptor of a local neighborhood of a current vertex among the plurality of vertices of the three-dimensional object; obtaining a target shape descriptor from the shape descriptor using a quantization grid associated with a watermark payload; and modifying said local neighborhood wherein a position of at least one vertex of said local neighborhood is modified such that a shape descriptor of said modified local neighborhood is close to said target shape descriptor and wherein said current vertex is not modified.A method for obtaining payload from a three-dimensional object, a 3D object carrying a watermark and devices implementing the disclosed methods are further disclosed.