This paper presents a method to address the issue of augmenting a markerless 3D object with a complex shape. It relies on a model-based tracker which takes advantage of GPU acceleration and 3D rendering in order to handle the complete 3D model, whose sharp edges are efficiently extracted. In the pose estimation step, we propose to robustly combine geometrical and color edge-based features in the nonlinear minimization process, and to integrate multiple-hypotheses in the geometrical edge-based registration phase. Our tracking method shows promising results for augmented reality applications, with a Kinect-based reconstructed 3D model.