In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is computationally attractive for adaptive numerical simulations. Mesh generation and adaptive refinement of quadtree meshes is straight-forward. However, finite elements are non-conforming on quadtree meshes due...

The variable length code design of a complete quadtree-based video codec is addressed, in which we jointly optimize the entropy-coding for the parameters of motion-compensated prediction together with the residual coding. The quadtree coding scheme selected for this optimization allows easy access to the rate-distortion costs, thus making it possible to perform rate-distortion optimized bit all...

Spatial data representation and compression has become a focus issue in computer graphics and image processing applications. Quadtrees, as one of hierarchical data structures, basing on the principle of recursive decomposition of space, always offer a compact and efficient representation of an image. For a given image, the choice of quadtree root node plays an important role in its quadtree rep...

In this thesis we study two research aspects of geographical routing: efficient geographical addressing and a new routing scheme. In the first part we offer a novel geographical routing algorithm that relies on a well known data structure called Quadtree. Quadtree is an efficient method of mapping a twodimensional area by recursively partitioning it to disjoint squares. We present a greedy, gua...

-The quadtree representation encodes a 2" by 2" binary image as a set of maximal blocks of l's or O's whose sizes and positions are powers of 2. With the aid of the quadtree, a hierarchy of approximations to the image can be defined. Several ways of doing this are described. The accuracy of these approximations is empirically evaluated by studying how fast estimates of the first few moments of ...

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A modification of the linear quadtree [3], the threaded linear hierarchical quadtree (TLHQT), is proposed for the computation of geometric properties of binary images. Since most of the algorithms used in connection with computation of geometric properties require frequent exploration of adjacencies, a structure which keeps permanently in memory some adjacency links is introduced. In this paper...

The (region) quadtree, shown in Fig. 1, is a widely studied data structure for representing digitized images. An extensive survey of quadtrees and their use in image processing and graphics appears in Samet [ 1,2]. Unfortunately, the two-dimensional nature of the information they store makes quadtree usage more subtle than, say, binary search tree usage, and efficient algorithms often demand sp...