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This paper addresses the problem of category-level image classification. The underlying image model is a graph whose nodes correspond to a dense set of regions, and edges reflect the underlying grid structure of the image and act as springs to guarantee the geometric consistency of nearby regions during matching. A fast approximate algorithm for matching the graphs associated with two images is presented. This algorithm is used to construct a kernel appropriate for SVM-based image classification, and experiments with the Caltech 101, Caltech 256, and Scenes datasets demonstrate performance that matches or exceeds the state of the art for methods using a single type of features.