We present an efficient method for maintaining a compressed quadtree for a set of moving points in R. Our method works in the blackbox KDS model, where we receive the locations of the points at regular time steps and we know a bound dmax on the maximum displacement of any point within one time step. When the number of points within any ball of radius dmax is at most k at any time, then our upda...

A rate-distortion framework is used to define a very low bit-rate coding scheme based on quadtree segmentation and optimized selection of motion estimators. This technique achieves maximum reconstructed image quality under the constraint of a target bit rate for the coding of the vector field and segmentation information. First, a complete scheme is proposed for hybrid two-dimensional (2-D) and...

Automating the process of analysis of Panoramic X-Ray images is important to help dentist procedures and diagnosis. Tooth segmentation from the radiographic images and feature extraction are essential steps. The authors propose a segmentation approach based on mathematical morphology, quadtree decomposition for mask generation, thresholding, and snake models. The feature extraction stage is ste...

sion and the resolution desired. The precision and the resolution are defined by one input value, while the shape The number of nodes of an edge quadtree is the measure of its space complexity. This number depends on the figure’s is calculated using the fractal dimension. The proposed shape, its resolution and its precision. The goal of this work is methodology uses the fractal measure also as ...

Region quadtrees are convenient tools for hierarchical image analysis. Like the related Haar wavelets, they are simple to generate within a fixed calculation time. The clustering at each resolution level requires only local data, yet they deliver intuitive classification results. Although the region quadtree partitioning is very rigid, it can be rapidly computed from arbitrary imagery. This res...

With the widespread use of GPS-enabled mobile devices, an unprecedented amount of trajectory data is becoming available from various sources such as Bikely, GPS-wayPoints, and Uber. The rise of innovative transportation services and recent break-throughs in autonomous vehicles will lead to the continued growth of trajectory data and related applications. Supporting these services in emerging pl...

An algorithm is presented that performs set operations (e.g., union or intersection) on two unaligned images represented by linear quadtrees. This algorithm seeks to minimize the number of nodes that must be searched for or inserted into the disk-based node lists that represent the trees. Windowing and matching operations can also be cast as unaligned set functions; these operations can then be...

We give a closed-form expression for the average number of n-dimensional quadtree nodes (`pieces' or`blocks') required by an n-dimensional hyper-rectangle aligned with the axes. Our formula includes as special cases the formulae of previous eeorts for 2-dimensional spaces 8]. It also agrees with theoretical and empirical results that the number of blocks depends on the hyper-surface of the hype...

We present a library for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation data locality is exploited without any prior information about the matrix sparsity pattern. A distributed quadtree matrix representation is straightforward to implement due to our recent development of the Chunks and Tasks programming model [Paral...