We present a novel method for graph based image representation and matching. The image is represented as a graph of affine invariant regions. A local affine invariant coordinate system is used to describe the geometry at the location of each graph vertex. Once an image is encoded as a graph, a graph matching process can be initiated against the graph of any other image. Each pair of matched features induces an affine approximation of the deformation. The similarity of the affine approximations between different matchings is the foundation of a graph matching algorithm presented here, as it greatly reduces the ambiguity in matching. The algorithm is much faster than state of the art feature matching methods and produces similar results in the presence of highly complex scenes that contain background clutter, occlusion, viewpoint changes, and elastic geometric deformations.