Image registration is a building block for many applications in computer vision and medical imaging. However the current methods are lim- ited when large and highly non-local deformations are present. In this pa- per, we introduce a new direct feature matching technique for non-parametric image registration where efficient nearest-neighbor searches find global corre- spondences between intensity, spatial and geometric information. We exploit graph spectral representations that are invariant to isometry under complex deformations. Our direct feature matching technique is used within the estab- lished Demons framework for diffeomorphic image registration. Our method, called Spectral Demons , can capture very large, complex and highly non-local deformations between images. We evaluate the improvements of our method on 2D and 3D images and demonstrate substantial improvement over the con- ventional Demons algorithm for large deformations