We demonstrate that a resolution-r PR quadtree contaihing II points has, in the worst case, at most 8&r [log,(rt/2)]) + 8n/3 l/3 nodes. This captures the fact that as n tends towards 4’, the number of nodes in a PR quadtree quickly approaches O(n). This is a more precise estimation of the worst case space requirement of a PR quadtree then has been attempted before.

Query optimizers in object-relational database management systems require users to provide the execution cost models of user-defined functions(UDFs). Despite this need, however, there has been little work done to provide such a model. Furthermore, none of the existing work is self-tuning and, therefore, cannot adapt to changing UDF execution patterns. This paper addresses this problem by introd...

Ang, C.-H. and H. Samet, A fast quadtree normalization algorithm, Pattern Recognition Letters 15 (1994) 57 63. A region quadtree representation of an image can be normalized thereby yielding a quadtree that contains the least number of nodes in O(s 2 log2 s) time where s is the length of the grid. A new algorithm is proposed whose asymptotic time bound is the same but whose first part only take...

I introduce two strategies to overcome the slow convergence of least squares sparse data interpolation: 1) a 2-D multiscale Laplacian regularization operator, and 2) an explicit quadtree-style upsampling scheme which produces a good initial guess for iterative schemes. The multiscale regularization produces an order-of-magnitude speedup in the interpolation of a sparsely sampled topographical m...

A formula is provided to compute the number of new blocks resulting from the decomposition induced by a shift of a single quadtree node of arbitrary size by an arbitrary amount. A precise calculation is also presented for the average number of BLACK nodes required to represent a square of width 2 m in a region quadtree.

In this paper, the combination of quadtree and block encoding compression approach is proposed for lossless compression of raster maps. This application is implemented on the mobile phone. Firstly, this approach iteratively split the raster map into quarter sections and the quadtree structure will construct. To index the spatial data, quadtree uses Morton encoding method. This approach defined ...

An algorithm is presented for reconstructing a quadtree from its quadtree medial axis transform (QMAT). It is useful when performing operations for which the QMAT is well suited (e.g., thinning of an image). The algorithm is a postorder tree traversal which propagates the subsumption of each BLACK QMAT node in the eight possible directions. Analysis of the algorithm shows that its average execu...

This article presents a quadtree-based data structure for effective indexing of images. An image is represented by a multi-level feature vector, computed by a recursive decomposition of the image into four quadrants and stored as a full fixed-depth balanced quadtree. A node of the quadtree stores a feature vector of the corresponding image quadrant. A more general quadtree-based structure calle...