A Versatile and Efficient GPU Data Structure for Spatial Indexing

Abstract

Fig. 1. Many real-world volume data sets are sparse, lending appeal to rendering and processing techniques that benefit from such a property. Using our novel, storage-efficient data structure allows us to efficiently store such data sets as bricked textures on the GPU. From left to right: Stagbeetle (832 × 832 × 494, bricksize 7 3 , 5.01% non-empty, 245.5KB index); Pawpawsaurus Campbelli skull (958 × 646 × 1088, bricksize 15 3 , 15.1% non-empty, 50.21KB index); Angiography (416 × 512 × 112, bricksize 3 3 , 2.27% non-empty, 220.5KB index); Present (492 × 492 × 442, bricksize 7 3 , 17.3% non-empty, 78.80KB index). Our data structure introduces only minimal overhead in terms of memory and run-time, and it allows for efficient brick-level empty-space skipping.Abstract-In this paper we present a novel GPU-based data structure for spatial indexing. Based on Fenwick trees-a special type of binary indexed trees-our data structure allows construction in linear time. Updates and prefixes can be computed in logarithmic time, whereas point queries require only constant time on average. Unlike competing data structures such as summed-area tables and spatial hashing, our data structure requires a constant amount of bits for each data element, and it offers unconstrained point queries. This property makes our data structure ideally suited for applications requiring unconstrained indexing of large data, such as block-storage of large and block-sparse volumes. Finally, we provide asymptotic bounds on both run-time and memory requirements, and we show applications for which our new data structure is useful.

Data-Parallel Hashing Techniques for GPU Architectures

“…An extensive body of work has embarked on the redesign of data structures for construction and general computation on the GPU [88]. Within the context of searching, these acceleration structures include sorted arrays [3], [4], [8], [51], [66], [67], [98] and linked lists [116], hash tables (see section III), spatial-partitioning trees (e.g., k-d trees [57], [115], [120], octrees [57], [119], bounding volume hierarchies (BVH) [57], [64], R-trees [71], and binary indexing trees [59], [99]), spatial-partitioning grids (e.g., uniform [36], [53], [62] and two-level [52]), skiplists [81], and queues (e.g., binary heap priority [43] and FIFO [17], [101]). Due to significant architectural differences between the CPU and GPU, search structures cannot simply be "ported" from the CPU to the GPU and maintain optimal performance.…”

“…Schneider and Rautek [99] denote sparsity encoding as a memory overhead cost for providing unconstrained access, or empty cell querying, in the spatial perfect hashing approach of Lefebvre et al [65]. This study proposes a compact, GPU-based Fenwick tree data structure that supports unconstrained accesses without additional occupancy storage to denote empty cells.…”

Comparing Hierarchical Data Structures for Sparse Volume Rendering with Empty Space Skipping

“…be achieved by means of min-max range queries [WFKH07, KTW * 11, Wal19]. An alternative approach to update an existing data structure is the one by Schneider et al [SR17] who use Fenwick trees, which bare similarities to the summed area tables that our techniques use as auxiliary data structures.…”

Parameterized Splitting of Summed Volume Tables

“…Alternative SVT representations such as 3D Fenwick trees [Fen94,Mis13,SR17] offer a memory-efficient intermediate data structure from which an adaptive space partition can be constructed. 3D Fenwick trees have a memory consumption of O(n) bits, yet recovering the integral values requires a number of O(log 3 n) data fetch operations.…”