  We propose a novel iterative method to adapt a a graph to d-dimensional image
data. The method drives the nodes of the graph towards image features. The
adaptation process naturally lends itself to a measure of feature saliency
which can then be used to retain meaningful nodes and edges in the graph. From
the adapted graph, we also propose the computation of a dual graph, which
inherits the saliency measure from the adapted graph, and whose edges run along
image features, hence producing an oversegmenting graph. The proposed method is
computationally efficient and fully parallelisable. We propose two distance
measures to find image saliency along graph edges, and evaluate the performance
on synthetic images and on natural images from publicly available databases. In
both cases, the most salient nodes of the graph achieve average boundary recall
over 90%. We also apply our method to image classification on the MNIST
hand-written digit dataset, using a recently proposed Deep Geometric Learning
architecture, and achieving state-of-the-art classification accuracy, for a
graph-based method, of 97.86%.
