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

2018 ◽  
Vol 7 (8) ◽  
pp. 327 ◽  
Author(s):  
Xuefeng Guan ◽  
Peter van Oosterom ◽  
Bo Cheng
Keyword(s):  
Point Cloud ◽  
Parallel Implementation ◽  
Dimensional Space ◽  
Space Filling ◽  
Oracle Database ◽  
Space Filling Curve ◽  
Object Oriented Design ◽  
Massive Point ◽  
Locality Preservation ◽  
Cloud Management

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.

scholarly journals Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Ho-Kwok Dai ◽  
Hung-Chi Su
Keyword(s):  
Random Walk ◽  
Dimensional Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Order Curve ◽  
Cluster Distance ◽  
The Mean ◽  
Curve Family

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.

scholarly journals PointSCNet: Point Cloud Structure and Correlation Learning Based on Space-Filling Curve-Guided Sampling

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 8
Author(s):  
Xingye Chen ◽  
Yiqi Wu ◽  
Wenjie Xu ◽  
Jin Li ◽  
Huaiyi Dong ◽  
...  
Keyword(s):  
Spatial Attention ◽  
Information Fusion ◽  
Point Cloud ◽  
Point Clouds ◽  
Local Region ◽  
Space Filling ◽  
Correlation Tensor ◽  
Space Filling Curve ◽  
Correlation Information ◽  
Filling Curve

Geometrical structures and the internal local region relationship, such as symmetry, regular array, junction, etc., are essential for understanding a 3D shape. This paper proposes a point cloud feature extraction network named PointSCNet, to capture the geometrical structure information and local region correlation information of a point cloud. The PointSCNet consists of three main modules: the space-filling curve-guided sampling module, the information fusion module, and the channel-spatial attention module. The space-filling curve-guided sampling module uses Z-order curve coding to sample points that contain geometrical correlation. The information fusion module uses a correlation tensor and a set of skip connections to fuse the structure and correlation information. The channel-spatial attention module enhances the representation of key points and crucial feature channels to refine the network. The proposed PointSCNet is evaluated on shape classification and part segmentation tasks. The experimental results demonstrate that the PointSCNet outperforms or is on par with state-of-the-art methods by learning the structure and correlation of point clouds effectively.

scholarly journals USING A SPACE FILLING CURVE APPROACH FOR THE MANAGEMENT OF DYNAMIC POINT CLOUDS

2016 ◽  
Vol IV-2/W1 ◽  
pp. 107-118 ◽  
Author(s):  
S. Psomadaki ◽  
P. J. M. van Oosterom ◽  
T. P. M. Tijssen ◽  
F. Baart
Keyword(s):  
Point Cloud ◽  
Low Cost ◽  
Point Clouds ◽  
Space Filling ◽  
Space Filling Curve ◽  
Cloud Data ◽  
Time Period ◽  
Spatio Temporal ◽  
Short Time ◽  
Filling Curve

Point cloud usage has increased over the years. The development of low-cost sensors makes it now possible to acquire frequent point cloud measurements on a short time period (day, hour, second). Based on the requirements coming from the coastal monitoring domain, we have developed, implemented and benchmarked a spatio-temporal point cloud data management solution. For this reason, we make use of the flat model approach (one point per row) in an Index Organised Table within a RDBMS and an improved spatio-temporal organisation using a Space Filling Curve approach. Two variants coming from two extremes of the space–time continuum are also taken into account, along with two treatments of the z dimension: as attribute or as part of the space filling curve. Through executing a benchmark we elaborate on the performance – loading and querying time –, and storage required by those different approaches. Finally, we validate the correctness and suitability of our method, through an out-of-the-box way of managing dynamic point clouds.

scholarly journals Hilbert space filling curve using scilab

2018 ◽  
Vol 7 (1.9) ◽  
pp. 129
Author(s):  
Sushma T.V ◽  
Roopa M
Keyword(s):  
Image Processing ◽  
Hilbert Space ◽  
Image Compression ◽  
Dimensional Space ◽  
Linear Mapping ◽  
Space Filling ◽  
Space Filling Curve ◽  
Data Parallel ◽  
Locality Preserving ◽  
Filling Curve

Space filling curve is used widely for linear mapping of multi-dimensional space. This provides a new line of thinking for various applications in image processing, Image compression being the most widely used. The paper highlights the locality preserving property of Hilbert Space filling curve which is essential in numerous applications such asin image compression, numerical analysis of a large aray of data, parallel processing and so on. A simplistic approach forusingHilbert Space filling curve using Scilab code has been presented.

Region of Interest Based MRI Brain Image Compression Using Peano Space Filling Curve

2016 ◽  
Vol 11 (2) ◽  
pp. 114-120 ◽  
Author(s):  
C. Peter Devadoss ◽  
Balasubramanian Sankaragomathi ◽  
Thirugnanasambantham Monica
Keyword(s):  
Image Compression ◽  
Region Of Interest ◽  
Space Filling ◽  
Brain Image ◽  
Space Filling Curve ◽  
Mri Brain ◽  
Filling Curve ◽  
Mri Brain Image

scholarly journals Automatic Reconstruction of Multi-Level Indoor Spaces from Point Cloud and Trajectory

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3493
Author(s):  
Gahyeon Lim ◽  
Nakju Doh
Keyword(s):  
Point Cloud ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Reconstruction Method ◽  
Complex Environments ◽  
Indoor Space ◽  
Multi Level ◽  
Level Building ◽  
Indoor Spaces ◽  
Data Term

Remarkable progress in the development of modeling methods for indoor spaces has been made in recent years with a focus on the reconstruction of complex environments, such as multi-room and multi-level buildings. Existing methods represent indoor structure models as a combination of several sub-spaces, which are constructed by room segmentation or horizontal slicing approach that divide the multi-room or multi-level building environments into several segments. In this study, we propose an automatic reconstruction method of multi-level indoor spaces with unique models, including inter-room and inter-floor connections from point cloud and trajectory. We construct structural points from registered point cloud and extract piece-wise planar segments from the structural points. Then, a three-dimensional space decomposition is conducted and water-tight meshes are generated with energy minimization using graph cut algorithm. The data term of the energy function is expressed as a difference in visibility between each decomposed space and trajectory. The proposed method allows modeling of indoor spaces in complex environments, such as multi-room, room-less, and multi-level buildings. The performance of the proposed approach is evaluated for seven indoor space datasets.

A Space Filling Curve

1983 ◽  
Vol 90 (4) ◽  
pp. 283
Author(s):  
Liu Wen
Keyword(s):  
Space Filling ◽  
Space Filling Curve ◽  
Filling Curve
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