Many segmentation algorithms describe images in terms of a hierarchy of regions. Although such hierarchies can produce state of the art segmentations and have many applications, they often contain more data than is required for an efficient description. This paper shows Laplacian graph energy is a generic measure that can be used to identify semantic structures within hierarchies, independently of the algorithm that produces them. Quantitative experimental validation using hierar chies from two state of art algorithms show we can reduce the number of levels and regions in a hierarchy by an order of magnitude with little or no loss in performance when compared against human produced ground truth. We provide a tracking application that illustrates the value of reduced hierarchies.

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We are interested in matching objects in photographs, paintings, sketches and so on; after all, humans have a remarkable ability to recognise objects in images, no matter how they are depicted. We conduct experiments in matching, and conclude that the key to robustness lies in object description. The existing literature consists of numerous feature descriptors that rely heavily on photometric properties such as colour and illumination to describe objects. Although these methods achieve high rates of accuracy in applications such as detection and retrieval of photographs, they fail to generalise datasets consisting of mixed depictions. Here, we propose a more general approach for describing objects invariant to depictive style. We use structure at a global level, which is combined with simple non-photometric descriptors at a local level. There is no need for any prior learning. Our descriptor achieves results on par with existing state of the art, when applied to object matching on a standard dataset consisting of photographs alone and outperforms the state of the art when applied to depiction-invariant object matching.