Raster Interval Object Approximations for Spatial Intersection Joins
arxiv(2023)
摘要
Spatial join processing techniques that identify intersections between
complex geometries (e.g.,polygons) commonly follow a two-step filter-and-refine
pipeline; the filter step evaluates the query predicate on the minimum bounding
rectangles (MBRs) of objects and the refinement step eliminates false positives
by applying the query on the exact geometries. We propose a raster intervals
approximation of object geometries and introduce a powerful intermediate step
in pipeline. In a preprocessing phase, our method (i) rasterizes each object
geometry using a fine grid, (ii) models groups of nearby cells that intersect
the polygon as an interval, and (iii) encodes each interval by a bitstring that
captures the overlap of each cell in it with the polygon. Going one step
further, we improve our approach to approximate each object by two sets of
intervals that succintly capture the raster cells which (i) intersect with the
object and (ii) are fully contained in the object. Using this representation,
we show that we can verify whether two polygons intersect by a sequence of
joins between the interval sets that take linear time. Our approximations can
effectively be compressed and can be customized for use on partitioned data and
polygons of varying sizes, rasterized at different granularities. Finally, we
propose a novel algorithm that computes the interval approximation of a polygon
without fully rasterizing it first, rendering the computation of approximations
orders of magnitude faster. Experiments on real data demonstrate the
effectiveness and efficiency of our proposal over previous work.
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