The optimal surgical treatment of complex fractures of the proximal humerus is controversial. It is proven that best results are obtained if an anatomical reduction of the fragments is achieved and, therefore, computer-assisted methods have been proposed for the reconstruction of the fractures. However, complex fractures of the proximal humerus are commonly accompanied with a relevant displacement of the fragments and, therefore, algorithms relying on the initial position of the fragments might fail. The state-of-the-art algorithm for complex fractures of the proximal humerus requires the acquisition of a CT scan of the (healthy) contralateral anatomy as a reconstruction template to address the displacement of the fragments. Pose-invariant fracture line based reconstruction algorithms have been applied successful for reassembling broken vessels in archaeology. Nevertheless, the extraction of the fracture lines and the necessary computation of their curvature are susceptible to noise and make the application of previous approaches difficult or even impossible for bone fractures close to the joints, where the cortical layer is thin. We present a novel scale-space representation of the curvature, permitting to calculate the correct alignment between bone fragments solely based on corresponding regions of the fracture lines. The fractures of the proximal humerus are automatically reconstructed based on iterative pairwise reduction of the fragments. The validation of the presented method was performed on twelve clinical cases, surgically treated after complex proximal humeral fracture, and by cadaver experiments. The accuracy of our approach was compared to the state-of-the-art algorithm for complex fractures of the proximal humerus. All reconstructions of the clinical cases resulted in an accurate approximation of the pre-traumatic anatomy. The accuracy of the reconstructed cadaver cases outperformed the current state-of-the-art algorithm.