Quad-splitting algorithm for a window query on a Hilbert curve

Wu, Chin-Hsien; Chang, Youngho

doi:10.1049/iet-ipr.2008.0155

Cited by 5 publications

(8 citation statements)

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“…The iterative algorithms find target intervals of curve values in an iterative way by repeatedly calling two functions: one function to compute the next SFC value inside the window and another function to compute the next SFC value outside the window query [12]. Wu presented an efficient algorithm for 2D Hilbert curves by recursively decomposing the query window [13]. The latter type is much more efficient than the former one, but it is sequential and limited to the 2D case; we should extent it to nD support and parallel mode.…”

Section: Space-filling Curves and Current Implementationsmentioning

confidence: 99%

“…Although many classical SFC generation methods have been put forward-recursive, byte-oriented, and table-driven-these methods mainly focused on the efficient generation of n-dimensional (nD) SFC values. Very little existing work focus on efficient query support with SFC values [12,13], so there are no complete nD SFC libraries available both for mapping and query. Furthermore, when faced with millions of input points, serial generation of space-filling curves will hinder scalability.…”

Section: Introductionmentioning

confidence: 99%

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A Parallel N-Dimensional Space-Filling Curve Library and Its Application in Massive Point Cloud Management

Guan

Oosterom

Cheng

2018

IJGI

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Because of their locality preservation properties, Space-Filling Curves (SFC) have been widely used in massive point dataset management. However, the completeness, universality, and scalability of current SFC implementations are still not well resolved. To address this problem, a generic n-dimensional (nD) SFC library is proposed and validated in massive multiscale nD points management. The library supports two well-known types of SFCs (Morton and Hilbert) with an object-oriented design, and provides common interfaces for encoding, decoding, and nD box query. Parallel implementation permits effective exploitation of underlying multicore resources. During massive point cloud management, all xyz points are attached an additional random level of detail (LOD) value l. A unique 4D SFC key is generated from each xyzl with this library, and then only the keys are stored as flat records in an Oracle Index Organized Table (IOT). The key-only schema benefits both data compression and multiscale clustering. Experiments show that the proposed nD SFC library provides complete functions and robust scalability for massive points management. When loading 23 billion Light Detection and Ranging (LiDAR) points into an Oracle database, the parallel mode takes about 10 h and the loading speed is estimated four times faster than sequential loading. Furthermore, 4D queries using the Hilbert keys take about 1~5 s and scale well with the dataset size.

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Section: Space-filling Curves and Current Implementationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Parallel N-Dimensional Space-Filling Curve Library and Its Application in Massive Point Cloud Management

Guan

Oosterom

Cheng

2018

IJGI

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“…Moreover, the orientations of the parts P1, P2, P3 and P4 are o1, o2, o3 and o4, respectively. After partitioning Hilbert curve into four parts, in order to connect two neighbour parts, the orientation of each part can be determined according to the orientation of the original Hilbert curve as shown in Table 1 [20].…”

Section: Approximately Even Partition Algorithmmentioning

confidence: 99%

Approximately even partition algorithm for coding the Hilbert curve of arbitrary-sized image

Chang

2012

IET Image Process.

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The Hilbert curve is one of space filling curves and it requires that the region is of size 2 k × 2 k , where k [ N. This study relaxes this constraint and generates a pseudo-Hilbert curve of arbitrary dimension. The intuitive method such as Chung et al.'s algorithm is to use Hilbert curves in the decomposed areas directly and then have them connected. However, they must generate a sequence of the scanned quadrants additionally before encoding and decoding the Hilbert order of one pixel. In this study, by using the approximately even partition approach, the authors propose a new Hilbert curve, the Hilbert * curve, which permits any square regions. Experimental results show that the clustering property of the Hilbert * curve is similar to that of the standard Hilbert curve. Next, the authors also propose encoding/decoding algorithms for the Hilbert * curves. Since the authors do not need to additionally generate and scan the sequence of quadrants, the proposed algorithm outperforms Chung et al.'s algorithms for the square region. Then, the authors apply the Hilbert * curves in Chung et al.'s algorithms for the Hilbert curve of arbitrary dimension and experimental results show that the proposed encoding/decoding algorithms out perform the Chung et al.'s approach.

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“…The Hilbert code segment generation algorithm based on the maximum block of the quadtree has been applied to efficient image compression [20] and fast window querying [21]. After studying the filling order of the two-dimensional Hilbert curve [22], a code segment generation algorithm for recursive quad splitting of the query window is proposed. The efficiency of this algorithm is greatly improved compared with that in [18].…”

Section: Introductionmentioning

confidence: 99%

“…The efficiency of this algorithm is greatly improved compared with that in [18]. However, the algorithms in [16] and [22] only discuss two-dimensional Hilbert curves. Because the construction methods and hierarchical evolution laws of two-and three-dimensional Hilbert curves are completely different, it is impossible to combine the algorithms in [16] and [22] for direct application to the generation of a three-dimensional Hilbert curve.…”

Section: Introductionmentioning

confidence: 99%

MI-HCS: Monotonically Increasing Hilbert Code Segments for 3D Geospatial Query Window

Cao

Sun

2020

IEEE Access

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Window queries are basic but important query tasks in geospatial databases. The Hilbert curve has good clustering properties, which can be used to effectively improve the execution efficiency of window queries. The ideal goal of a window query using Hilbert curve code is to quickly convert the query window to the corresponding monotonic continuous Hilbert code segments. However, existing algorithms have shortcomings in conversion calculations and Hilbert code segments properties. We propose the state vectors that are used to describe the filling rules of a three-dimensional Hilbert curve. In addition, we designed a direct generation algorithm for monotonically increasing Hilbert code segments (MI-HCS) for a three-dimensional window query. The MI-HCS algorithm is characterized by the direct generation of a monotonically increasing code segment set without the need to traverse all grid elements or the requirement of separate sorting steps. For a given query window W (x, y, z, l, w, h) and a Hilbert curve of size T × T × T , the maximum complexity of our MI-HCS algorithm is O α 1 × α 2 × log 2 T + 1 , where α 1 = median (l, w, h) and α 2 = max (l, w, h). The experimental results of the MI-HCS algorithm complexity are consistent with the specific theoretical analysis. The experimental results show that the Hilbert code segment generation efficiency of the proposed MI-HCS algorithm is 260.5% to 423.9% higher than that of existing algorithms.

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Quad-splitting algorithm for a window query on a Hilbert curve

Cited by 5 publications

References 23 publications

A Parallel N-Dimensional Space-Filling Curve Library and Its Application in Massive Point Cloud Management

A Parallel N-Dimensional Space-Filling Curve Library and Its Application in Massive Point Cloud Management

Approximately even partition algorithm for coding the Hilbert curve of arbitrary-sized image

MI-HCS: Monotonically Increasing Hilbert Code Segments for 3D Geospatial Query Window

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