Oversegmenting Graphs

We propose a novel method to adapt a graph to 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 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. This dual graph captures the structure of the underlying image, and therefore constitutes a sparse representation of the image features and their topology. The proposed method is computationally efficient and fully parallelisable. We propose two distance measures find image saliency along graph edges, and evaluate its performance on synthetic images and on natural images from publicly available databases. In both cases, the salient-most nodes of the graph achieve average boundary recall over 90%. We also provide a qualitative comparison with two related techniques: superpixel clustering, and variational image meshing, showing potential for a large number of applications.