Spatial data structures for point cloud analysis and visualization

Abstract

Efficient representation of multidimensional point data is a crucial task in many scientific areas such as data visualization, computational geometry, image processing, geographic information systems and others. As the point datasets are generally unsorted sets of points in the real space, their convenient organization gives the points a generalized structure which simplifies their proceeding and significantly improves the complexity of search operations and locally organizes the points to make them accessible for analysis and application fields. This thesis aims at development of fast spatial data structures and point indexing models with special focus on low-dimensional data. The existing structures can be basicly divided into space subdivision by regular grids and hierarchical subdivision. We combined both approaches to address their well-known drawbacks and to optimize them for parallel implementation. The main principle applied in this thesis is the space linearization based on the space-filling curves. We also tested the properties of regular grids, especially orthogonal and hexagonal ones. We developed a linear grid-based structure for both grids that eliminates empty areas of space and reaches query times comparable with standard regular grids. The thesis also shows that the hexagonal grids are optimal for circular queries in 2D spaces. We desined and tested our novel hexagonal space-filling curve which solves the problems of hexagonal linearization and hierarchical structure. Moreover, we developed three parallel point indexing algorithms for a GPGPU architecture that are significantly faster than general CPU-based structures.