This paper presents a new framework for capturing large and complex deformations in image registration and atlas construction. This challenging and recurrent problem in computer vision and medical imaging currently relies on iterative and local approaches, which are prone to local minima and, therefore, limit present methods to relatively small deformations. Our general framework introduces to this effect a new direct feature matching technique that finds global correspondences between images via simple nearest-neighbor searches. More specifically, very large image deformations are captured in Spectral Forces, which are derived from an improved graph spectral representation. We illustrate the benefits of our framework through a new enhanced version of the popular Log-Demons algorithm, named the Spectral Log-Demons, as well as through a groupwise extension, named the Groupwise Spectral Log-Demons, which is relevant for atlas construction. The evaluations of these extended versions demonstrate substantial improvements in accuracy and robustness to large deformations over the conventional Demons approaches.