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We analyse the distribution of the root pattern of randomly grown multidimensional point quadtrees. In particular, exact, recursive and asymptotic formulas are given for the expected arity of the root.

A central problem in the field of geometric algorithms is to compare algorithms that process vector-type data specified in the continuous plane with algorithms that process raster-type data specified in the digitized plane. A set of criteria is proposed that a digitization of a collection of line segments should satisfy in order to be said to represent the same structure as their continuous pla...

We propose a simple, direct approach for computing the expected cost of random partial match queries in random quadtrees. The approach gives not only an explicit expression for the leading constant in the asymptotic approximation of the expected cost but also more terms in the asymptotic expansion if desired.

The spatial join operation is benchmarked using variants of well-known spatial data structures such as the R-tree, R -tree, R-tree, and the PMR quadtree. The focus is on a spatial join with spatial output because the result of the spatial join frequently serves as input to subsequent spatial operations (i.e., a cascaded spatial join as would be common in a spatial spreadsheet). Thus, in additio...

The data presented by Light Detection and Ranging (LiDAR) systems are in a dense and accurate three dimensional pattern without point classification, such as trees, roads, and buildings. Extraction of boundary points is essential for recognizing buildings. However, it is complicated to process the LiDAR data due to its irregularity and a large number of collected data points. In order to find b...

We introduce dynamic smooth (a.k.a. balanced) compressed quadtrees with worst-case constant time updates in constant dimensions. We distinguish two versions of the problem. First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to split and merge operations on the quadtree cells. Second, we show that quadtrees used to store a set of points in R c...

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...

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 ...