QRB−tree Indexing: Optimized Spatial Index Expanding upon the QR−tree Index

Support for region queries is crucial in geographic information systems, which process exact queries through spatial indexing to filter features and subsequently refine the selection. Although the filtering step has been extensively studied, the refinement step has received little attention. This research builds upon the QR−tree index, which decomposes space into hierarchical grids, registers features to the grids, and builds an R−tree for each grid, to develop a new QRB−tree index with two levels of optimization. In the first level, a bucket is introduced in every grid in the QR−tree index to accelerate the loading and search steps of a query region for the grids within the query region. In the second level, the number of candidate features to be eliminated is reduced by limiting the features to those registered to the grids covering the corners of the query region. Subsequently, an approach for determining the maximal grid level, which significantly affects the performance of the QR−tree index, is proposed. Direct comparisons of time costs with the QR−tree index and geohash index show that the QRB−tree index outperforms the other two approaches for rough queries in large query regions and exact queries in all cases.

A Hybrid Spatial Indexing Structure of Massive Point Cloud Based on Octree and 3D R*-Tree

The spatial index structure is one of the most important research topics for organizing and managing massive 3D Point Cloud. As a point in Point Cloud consists of Cartesian coordinates (x,y,z), the common method to explore geometric information and features is nearest neighbor searching. An efficient spatial indexing structure directly affects the speed of the nearest neighbor search. Octree and kd-tree are the most used for Point Cloud data. However, Octree or KD-tree do not perform best in nearest neighbor searching. A highly balanced tree, 3D R*-tree is considered the most effective method so far. So, a hybrid spatial indexing structure is proposed based on Octree and 3D R*-tree. In this paper, we discussed how thresholds influence the performance of nearest neighbor searching and constructing the tree. Finally, an adaptive way method adopted to set thresholds. Furthermore, we obtained a better performance in tree construction and nearest neighbor searching than Octree and 3D R*-tree.

MOLECULAR VIDEOGAMING: SUPER-RESOLVED TRAJECTORY-BASED NANOCLUSTERING ANALYSIS USING SPATIO-TEMPORAL INDEXING

ABSTRACTSingle-molecule localization microscopy (SMLM) techniques are emerging as vital tools to unravel the nanoscale world of living cells. However, current analysis methods primarily focus on defining spatial nanoclusters based on detection density, but neglect important temporal information such as cluster lifetime and recurrence in “hotspots” on the plasma membrane. Spatial indexing is widely used in videogames to effectively detect interactions between moving geometric objects. Here, we use the R-tree spatial indexing algorithm to perform SMLM data analysis and determine whether the bounding boxes of individual molecular trajectories overlap, as a measure of their potential membership in nanoclusters. Extending the spatial indexing into the time dimension allows unique resolution of spatial nanoclusters into multiple spatiotemporal clusters. We have validated this approach using synthetic and SMLM-derived data. Quantitative characterization of recurring nanoclusters allowed us to demonstrate that both syntaxin1a and Munc18-1 molecules transiently cluster in hotspots on the neurosecretory plasma membrane, offering unprecedented insights into the dynamics of these protein which are essential to neuronal communication. This new analytical tool, named Nanoscale Spatiotemporal Indexing Clustering (NASTIC), has been implemented as a free and open-source Python graphic user interface.

AN EXPERIMENTAL ANALYSIS OF SPATIAL INDEXING ALGORITHMS FOR REAL TIME SAFETY CRITICAL MAP APPLICATION

This paper presents a study that compares the three space partitioning and spatial indexing techniques, KD Tree, Quad KD Tree, and PR Tree. KD Tree is a data structure proposed by Bentley (Bentley and Friedman, 1979) that aims to cluster objects according to their spatial location. Quad KD Tree is a data structure proposed by Berezcky (Bereczky et al., 2014) that aims to partition objects using heuristic methods. Unlike Bereczky’s partitioning technique, a new partitioning technique is presented based on dividing objects according to space-driven, in the context of this study. PR Tree is a data structure proposed by Arge (Arge et al., 2008) that is an asymptotically optimal R-Tree variant, enables data-driven segmentation. This study mainly aimed to search and render big spatial data in real-time safety-critical avionics navigation map application. Such a real-time system needs to efficiently reach the required records inside a specific boundary. Performing range query during the runtime (such as finding the closest neighbors) is extremely important in performance. The most crucial purpose of these data structures is to reduce the number of comparisons to solve the range searching problem. With this study, the algorithms’ data structures are created and indexed, and worst-case analyses are made to cover the whole area to measure the range search performance. Also, these techniques’ performance is benchmarked according to elapsed time and memory usage. As a result of these experimental studies, Quad KD Tree outperformed in range search analysis over the other techniques, especially when the data set is massive and consists of different geometry types.

EFFICIENT LOADING AND VISUALIZATION OF MASSIVE FEATURE-RICH POINT CLOUDS WITHOUT HIERARCHICAL ACCELERATION STRUCTURES

Nowadays, point clouds are the standard product when capturing reality independent of scale and measurement technique. Especially, Dense Image Matching (DIM) and Laser Scanning (LS) are state of the art capturing methods for a great variety of applications producing detailed point clouds up to billions of points. In-depth analysis of such huge point clouds typically requires sophisticated spatial indexing structures to support potentially long-lasting automated non-interactive processing tasks like feature extraction, semantic labelling, surface generation, and the like. Nevertheless, a visual inspection of the point data is often necessary to obtain an impression of the scene, roughly check for completeness, quality, and outlier rates of the captured data in advance. Also intermediate processing results, containing additional per-point computed attributes, may require visual analyses to draw conclusions or to parameterize further processing. Over the last decades a variety of commercial, free, and open source viewers have been developed that can visualise huge point clouds and colorize them based on available attributes. However, they have either a poor loading and navigation performance, visualize only a subset of the points, or require the creation of spatial indexing structures in advance. In this paper, we evaluate a progressive method that is capable of rendering any point cloud that fits in GPU memory in real time without the need of time consuming hierarchical acceleration structure generation. In combination with our multi-threaded LAS and LAZ loaders, we achieve load performance of up to 20 million points per second, display points already while loading, support flexible switching between different attributes, and rendering up to one billion points with visually appealing navigation behaviour. Furthermore, loading times of different data sets for different open source and commercial software packages are analysed.