We propose a new Rtree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting ap preach in R-trees. This is done by proposing an ordering on the R-tree nodes. This ordering has to be ‘good’, in the sense that it should group ‘similar’ data rectangles to gether, to minimize the area and perimeter of the resulting minimum bounding rectangles (...

A geodesic lamination L on a closed hyperbolic surface S, when provided with a transverse measure μ, gives rise to a “dual R-tree” Tμ, together with an action of G = π1S on Tμ by isometries. A point of Tμ corresponds precisely to a leaf of the lift L̃ of L to the universal covering S̃ of S, or to a complementary component of L̃ in S̃. The G-action on T is induced by the G-action on S̃ as deck transf...

Content-based Image Retrieval (CBIR) is a flexible approach to access modern image database with large data size, whereby the actual images are described by multi-dimensional feature vectors. These are then indexed in the database to provide low retrieval latency. Currently, many different structures have been proposed, among them, the structures of the R-tree family, especially the R-tree, R*-...

In content-based image retrieval systems, the content of an image such as color, shapes and textures are used to retrieve images that are similar to a query image. Most of the existing work focus on the retrieval e€ectiveness of using content for retrieval, i.e., study the accuracy (in terms of recall and precision) of using di€erent representations of content. In this paper, we address the iss...

R-tree based spatial join is useful because of both its superior performance and the wide spread implementation of R-trees. We present a new R-tree join method called BFRJ (Breadth-First R-tree Join). BFRJ synchronously traverses both R-trees in breadthfirst order while processing join computation one level at a time. At each level, BFRJ creates an intermediate join index and deploys global opt...