A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space

Zhou, Mengyun; Guan, Qingfeng

doi:10.3390/ijgi8040182

Cited by 9 publications

(11 citation statements)

References 14 publications

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“…Therefore, a 25-Intersection Model (25-IM) was developed to characterize topological relations between 3D objects. The 25-IM represents the topological property of an object as a boundary which consists of five topological parts such as vertex, edge, face, interior and exterior [22]. A 5 × 5 intersection matrix represents the intersections of topological parts that determine the topological relationship between two objects in 3D space.…”

Section: Topological Rulesmentioning

confidence: 99%

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

Salleh

Ujang

Azri

2022

GaEE

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Topological properties of objects should be maintained and preserved to concisely represent objects. However, the implementation of 2D topological rules requires the decomposition of 3D objects into lower dimensions to determine topological relationships. This results in 2D topological relationships although the connected objects are in 3D. Hence, accurate representation of 3D connectivity in 3D models is limited. 3D topological rules can be implemented to include topological connectivity in 3D space. This paper implemented an extension of the 27-Intersection Model (27-IM) called the 36-Intersection Model (36-IM) to represent 3D topological adjacencies of two objects in 3D space. This resulted in a 12 × 3 intersection matrix or 36-IM that represented the intersections in terms of dimension and number of separations. Six cases were tested, consisting of “meets”, “disjoint” “intersects at a line”, “intersects at a point”, “contains”, and “overlaps”. The resulting 36-IM matrices provided an accurate representation of how the objects in 3D space were related and their dimension of intersections. The formalisms of the 36-IM matrices were also interoperable which allowed the interpretation of 36-IM using the 9IM and DE-9IM to determine general topological relationships. By examining the intersection of interiors, boundaries and exteriors of 3D objects without object decomposition, 3D topological relationships can be determined as well as the dimension and manner of intersection.

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Section: Topological Rulesmentioning

confidence: 99%

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

Salleh

Ujang

Azri

2022

GaEE

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“…Based on point-set topology, the first IM was formerly presented in [ 10 ], based on which many other IM versions have been developed over time. The followings are the most prominent IM: the 4-intersection model (4IM), which has been extended to cope with various spatial considerations into many IM releases[ 10 ], the 6-intersection model 6-IM [ 15 ], the 9-intersection model (9IM) [ 11 ], fuzzy 9-Intersection Model (F9-IM) [ 29 ], the 16-intersection model (16-IM) [ 18 , 30 ], the 25-intersection model (25-IM) [ 20 , 31 ]. …”

Section: Background On Spatial Reasoning and Computing Models For Topological Relationsmentioning

confidence: 99%

“…These relations correspond to RCC-8 relations: DC, EC, PO, NTPP, TPP, TPPi, NTPPi, EQ, respectively [ 32 ]. The 4IM has a limited ability to distinguish topological relations because it is easy to confuse relations (for example between line/line relations and line/region) [ 31 ]. Furthermore, there is no consideration about the eventual broad nature of boundaries.…”

Section: Background On Spatial Reasoning and Computing Models For Topological Relationsmentioning

confidence: 99%

“…This

was presented in [ 18 ] and implemented in modeling cases of spatial relations between 3D spatial objects [ 31 ] and between fuzzy regions on a digital sphere [ 20 ]. However, to our knowledge, there is still no research work using

in modeling and computing topological relations among vague-shaped phenomena in distributed computing systems as in sensor networks.…”

Section: Computing and Modeling Fuzzy Spatial Relations Using In Snsmentioning

confidence: 99%

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A Decentralized Fuzzy Rule-Based Approach for Computing Topological Relations between Spatial Dynamic Continuous Phenomena with Vague Boundaries Using Sensor Data

Njila

Mostafavi

Brodeur³

2021

Sensors

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Sensor networks (SN) are increasingly used for the observation and monitoring of spatiotemporal phenomena and their dynamics such as pollution, noise and forest fires. In multisensory systems, a sensor node may be equipped with different sensing units to observe and detect several spatiotemporal phenomena at the same time. Simultaneous detection of different phenomena can be used to infer their spatial interactions over space and time. For this purpose, decentralized spatial computing approaches have shown their potential for effective reasoning on spatial phenomena within a sensor network. However, in most cases, spatial extents of continuous dynamic phenomena are uncertain, and their relations and interactions cannot be inferred by the existing approaches at the sensor node level. To address this limitation, in this paper, we propose and develop a decentralized fuzzy rule-based spatial reasoning approach to depict the spatial relations that hold between two evolving spatial phenomena with fuzzy boundaries. The proposed method benefits from a more adapted fuzzy-crisp representation of dynamic phenomena observed by SN where each vague phenomenon is composed of five distinguished zones including the kernel, conjecture and exterior zone and their boundaries. For each detected phenomenon, a sensor node will report one of these zones based on its location. Aggregation of the information reported from the sensor nodes allows reasoning on spatial relations between the observed phenomena and their evolution. Such spatial information provides users with more valuable near real-time information on the state of different phenomena that can be used for informed decision-making.

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“…In the past decades, researchers have done a lot of work about the spatial topological relations analysis [ 22 , 23 , 24 ]. The earliest research is used in geographic information systems (GIS).…”

Section: Related Workmentioning

confidence: 99%

Spatial Topological Relation Analysis for Cluttered Scenes

Zhang

et al. 2020

Sensors

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The spatial topological relations are the foundation of robot operation planning under unstructured and cluttered scenes. Defining complex relations and dealing with incomplete point clouds from the surface of objects are the most difficult challenge in the spatial topological relation analysis. In this paper, we presented the classification of spatial topological relations by dividing the intersection space into six parts. In order to improve accuracy and reduce computing time, convex hulls are utilized to represent the boundary of objects and the spatial topological relations can be determined by the category of points in point clouds. We verified our method on the datasets. The result demonstrated that we have great improvement comparing with the previous method.

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A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space

Cited by 9 publications

References 14 publications

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

A Decentralized Fuzzy Rule-Based Approach for Computing Topological Relations between Spatial Dynamic Continuous Phenomena with Vague Boundaries Using Sensor Data

Spatial Topological Relation Analysis for Cluttered Scenes

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