An analysis of the expected size occupied by a Quadtree is presented. The analysis is based on the general assumption that the storage requirements of internal and external nodes differ. Besides, formulae for the expected number of internal and external nodes at a specific level of the tree are given. Next, the space efficiency of the most popular Quadtree implementations is examined. Finally, ...

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...

This paper presents the use of hierarchical spatial data structures to visualise attribute and spatial uncertainty when using spatial information systems. This is demonstrated using spatially-referenced data from the New Zealand 2001 Census. Firstly, selected current spatial visualisations created to show uncertainty were assessed in an Internet survey, revealing that overall there is not many ...

This paper describes parallel algorithms for the following operations on qua.dtreesboolean operations (union, intersection, complement), collapsing a quadtree, and neighbor finding in an image represented by a quadtree. The architecture assumed in this paper is a. hypercube with one processing element (PE) per hypercube node. We assume that the architecture is SIMD, i.e., all PEs work under the...

Objects used in real life are normally three dimensional, although many objects are close to being twoor even one dimensional. In geometry, objects can have any number of dimensions, although we cannot visualize objects in more than three dimensions. An N -tree data structure is a special tree that stores an N -dimensional object. The most common example is a quadtree, a popular structure for s...

The results of an investigation in developing a generalized toolkit for Quadtree based Finite Volume models, exemplarily applied on the Shallow Water Equations, are given in this report. The developed application model: (i) discretizes a given topography using a quadtreebased grid system and (ii) solves the Shallow Water Equations by a numerical method based on the Finite Volume Method on the a...

Embedded ZeroBlock Coding and context modeling (EZBC) algorithm has high compression performance. However, it consumes large amounts of memory space because an Amplitude Quadtree of wavelet coefficients and other two link lists would be built during the encoding process. This is one of the big challenges for EZBC to be used in real time or hardware applications. An improved EZBC algorithm based...

In this paper we present a model and experimental results for performing parallel fractal image compression using circulating pipeline computation and employing a new quadtree recomposition approach. A circular linear array of processors is employed and utilized in a pipelined fashion. In this approach, a modification of the scheme given by Jackson and Blom, quadtree sub-blocks of an image are ...

In this paper we present a performance comparison of access methods for time-evolving regional data. Initially, we briefly review four temporal extensions of the Linear Region Quadtree: the Time-Split Linear Quadtree, the Multiversion Linear Quadtree, the Multiversion Access Structure for Evolving Raster Images and Overlapping Linear Quadtrees. These methods comprise a family of specialized acc...