  Image hashing is the process of associating a short vector of bits to an
image. The resulting summaries are useful in many applications including image
indexing, image authentication and pattern recognition. These hashes need to be
invariant under transformations of the image that result in similar visual
content, but should drastically differ for conceptually distinct contents. This
paper proposes an image hashing method that is invariant under rotation,
scaling and translation of the image. The gist of our approach relies on the
geometric characterization of salient point distribution in the image. This is
achieved by the definition of a "saliency graph" connecting these points
jointly with an image intensity function on the graph nodes. An invariant hash
is then obtained by considering the spectrum of this function in the
eigenvector basis of the Laplacian graph, that is, its graph Fourier transform.
Interestingly, this spectrum is invariant under any relabeling of the graph
nodes. The graph reveals geometric information of the image, making the hash
robust to image transformation, yet distinct for different visual content. The
efficiency of the proposed method is assessed on a set of MRI 2-D slices and on
a database of faces.
