Classification of topological relations between spatial objects in two‐dimensional space within the dimensionally extended 9‐intersection model

Shen, Jingwei; Chen, Min; Liu, Xintao

doi:10.1111/tgis.12328

Cited by 13 publications

(3 citation statements)

References 28 publications

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“…The topological relations between undirected spatial objects have been widely studied (Alboody, Sedes, & Inglada, ; Clementini et al, ; Egenhofer, Clementini, & Di Felice, ; Egenhofer & Franzosa, ; Egenhofer & Herring, ; Güting, de Ridder, & Schneider, ; Güting & Schneider, ; Li & Li, ; Liu & Shi, ; Leng, Yang, & Chen, ; Open Geospatial Consortium, ; Randell & Cohn, ; Randell, Cui, & Cohn, ; Shen, Chen, & Liu, ).Among these models, Egenhofer and Franzosa () presented a 9IM to describe the topological relations of two spatial objects. The 9IM is a 3 × 3 matrix, represented as:

R_{9 I M} false(A, B false) = [\begin{matrix} A^{o} \cap B^{o} & A^{o} \cap \partial B & A^{o} \cap B^{-} \\ \partial A \cap B^{o} & \partial A \cap \partial B & \partial A \cap B^{-} \\ A^{-} \cap B^{o} & A^{-} \cap \partial B & A^{-} \cap B^{-} \end{matrix}]

…”

Section: Related Workmentioning

confidence: 99%

Topological relations between a directed line and a directed region

Shen

Huang

Chen

2020

Transactions in GIS

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Representing the topological relations between directed spatial objects has gained increasing attention in recent years. Although topological relations between directed lines and other types of spatial objects, such as regions and bodies, have been widely investigated, few studies have focused on the topological relations between directed lines and directed regions. This research focuses on the representation and application of directed line–directed region (DLDR) topological relations, and may contribute to spatial querying and spatial analyses related to directed spatial objects or time‐varying objects. Compared with other topological relation models, a DLDR model that considers the starting and ending points of the directed line and the front and back faces of directed regions is proposed in this research to describe the topological relations between directed lines and directed regions. DLDR topological relations are presented, the completeness of the 111 DLDR topological relations is proved, and the topological relations based on the 9‐intersection model (9IM), 9+‐intersection model (9+‐IM), and DLDR model are compared. The formalism of the DLDR model and the corresponding geometric interpretations of the 111 DLDR topological relations are presented, seven propositions are stated to prove the completeness of the 111 DLDR topological relations, and the case study shows that more detailed topological relation information can be obtained based on the DLDR model.

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R_{9 I M} false(A, B false) = [\begin{matrix} A^{o} \cap B^{o} & A^{o} \cap \partial B & A^{o} \cap B^{-} \\ \partial A \cap B^{o} & \partial A \cap \partial B & \partial A \cap B^{-} \\ A^{-} \cap B^{o} & A^{-} \cap \partial B & A^{-} \cap B^{-} \end{matrix}]

…”

Section: Related Workmentioning

confidence: 99%

Topological relations between a directed line and a directed region

Shen

Huang

Chen

2020

Transactions in GIS

Self Cite

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“…Subsequently, the topic has been vastly studied and applied in GIS related studies. [2][3][4][5][6] are some of the recent studies where the intersection matrix model has been defined. The primary model by Egenhofer et al [1] was constructed using the point set topological properties of the objects; hence, it comes with an advantage that the relations remain same despite any scale change, translation, rotation.…”

Section: Introductionmentioning

confidence: 99%

A method to obtain fuzzy relations between uncertain objects using similarity measure

Jana

Mahanta

2022

Preprint

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Topological relation between geographical objects is one of the key components of geographical information system (GIS). Considering the objects to be exact with sharp boundaries, 4 intersection and 9 intersection matrices initiated the study of calculating the topological relations. Due to the extensive existence of vague spatial phenomenons, the study of uncertainty object modeling has grown rapidly. Parallelly, the relationship calculating tools have been upgraded to handle the vague concepts. The fuzzy 9 intersection matrix and Egg yolk methods are such popular tools. Although the geographical objects are themselves uncertain, surprisingly, most of these tools generate certain relations between the objects. Thereby, the qualitative nature of these tools overlook the very essence of their uncertainty. To overcome these drawbacks, we propose a quantitative fuzzy valued 9 intersection matrix to obtain a fuzzy relationship between uncertain geographical objects. Then two new similarity computation techniques have been introduced to calculate the membership grade of similarity between the proposed matrix and the known crisp matrices. These similarity computations allow two spatial objects to have partial membership against the eight established topological relations. The quantitative calculations indicate the strength of the relationship. The superiority of the proposed model is established through various numerical examples. Further, certain linguistic variables are linked to the evaluated membership grades to generate an immediate association with the known crisp relations. An example is provided in support of this association.

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“…• 225 Schneider and Behr 2006;Shen et al 2018]. Hence, several types of spatial queries have been defined in the literature, such as the window query, containment query, and point query (see [Carniel 2020] for a survey).…”

Section: Introductionmentioning

confidence: 99%

A Systematic Review of Spatial Approximations in Spatial Database Systems

Bertella

Lopes

Oliveira

et al. 2022

jidm

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Many applications rely on spatial information retrieval, which involves costly computational geometric algorithms to process spatial queries. Spatial approximations simplify the geometric shape of complex spatial objects, allowing faster spatial queries at the expense of result accuracy. In this sense, spatial approximations have been employed to efficiently reduce the number of objects under consideration, followed by a refinement step to restore accuracy. For instance, spatial index structures employ spatial approximations to organize spatial objects in hierarchical structures (e.g., the R-tree). It leads to the interest in studying how spatial approximations can be efficiently employed to improve spatial query processing. This article presents a systematic review on this topic. We gather relevant studies by performing a search string on several digital libraries. We further expand the studies under consideration by employing a single iteration of the snowballing approach, where we track the reference list of selected papers. As a result, we provide an overview and comparison of existing approaches that propose, evaluate, or make use of spatial approximations to optimize the performance of spatial queries. The spatial approximations mentioned by the approaches are also summarized. Further, we characterize the approaches and discuss some future trends.

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Classification of topological relations between spatial objects in two‐dimensional space within the dimensionally extended 9‐intersection model

Cited by 13 publications

References 28 publications

Topological relations between a directed line and a directed region

Topological relations between a directed line and a directed region

A method to obtain fuzzy relations between uncertain objects using similarity measure

A Systematic Review of Spatial Approximations in Spatial Database Systems

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