In this paper, we explore whether the geometric properties of the point distribution obtained by embedding the nodes of a graph on a manifold can be used for the purposes of graph clustering. The embedding is performed using the heat-kernel of the graph, computed by exponentiating the Laplacian eigen-system. By equating the spectral heat kernel and its Gaussian form we are able to approximate the Euclidean distance between nodes on the manifold. The difference between the geodesic and Euclidean distances can be used to compute the sectional curvatures associated with the edges of the graph. To characterise the manifold on which the graph resides, we use the normalised histogram of sectional curvatures. By performing PCA on long-vectors representing the histogram bin-contents, we construct a pattern space for sets of graphs. We apply the technique to images from the COIL database, and demonstrate that it leads to well defined graph clusters.

Abstract. The problem of learning the class identity of visual objects has received considerable attention recently. With rare exception, all of the work to date assumes low variation in appearance, which limits them to a single depictive style usually photographic. The same object depicted in other styles -as a drawing, perhaps -cannot be identified reliably. Yet humans are able to name the object no matter how it is depicted, and even recognise a real object having previously seen only a drawing. This paper describes a classifier which is unique in being able to learn class identity no matter how the class instances are depicted. The key to this is our proposition that topological structure is a class invariant. Practically, we depend on spectral graph analysis of a hierarchical description of an image to construct a feature vector of fixed dimension. Hence structure is transformed to a feature vector, which can be classified using standard methods. We demonstrate the classifier on several diverse classes.

No abstract

Affine-invariant matching is one of the challenging fields for image matching. Although several algorithms (ASIFT, Fair-SURF) have been proposed and achieved expressive performance, all these method need to simulate perspective changes and exhaust all possible match which is of high computation complexity (O(N2)). In this paper, we proposed a new method to introduce global descriptor to filter out much unnecessary coarse matches for the matching procedure. Specially, the computation complexity of matching procedure in our method reduces significantly to O(N). But, the experiment result shows that the proposed method can achieve comparable performance to ASIFT at much lower cost.

No abstract