Dramatic technology progress in data manipulation induced several attempts of baleful and illegal processing. In this regard, several protection techniques, including cryptography, steganography, and watermarking have been used to avoid the illegal production and distribution of data online. On the other side, the attacks are still a major problem that limits the effectiveness of watermarking techniques. The geometric attacks involve displacement of pixels. Therefore, they induce synchronization errors between the original and attacked image that complicates the watermark recovery process. So in order to solve the de-synchronization problem, we propose to use a robust meshing technique between different geometrical data of the image to correct the geometric distortion. In this work, we propose a novel geometrically invariant digital image watermarking approach based on the geometrical feature of the cover image and the Defragmented Delaunay Triangulation on respecting the three constraints of watermarking approaches (imperceptibility of embedded watermark, embedding capacity, and robustness). The aim idea of this work is to propose a blind, imperceptible, and robust digital image watermarking scheme based on Defragmented Delaunay Tessellation and Weber's law. The defragmented triangulation provides a best synchronization of the embedded data after attacks application. The Weber's law is used to propose an auto-thresholding algorithm to compute the optimal embedding gain factor for each watermark's bit in order to ensure the imperceptibility of the hidden data. Firstly, the invariant features in the host gray scale image are extracted by using the canny edge detector. Then, the Delaunay tessellation of the saved keys points set is generated and defragmented to select the optimal robust triangles for watermark embedding. Simulation results illustrate the imperceptibility of the embedded data and the robustness of the proposed approach against intentional and unintentional geometrical attacks are presented in the finally section. Copyright (C) 2017 John Wiley & Sons, Ltd.