A Combinatorial Reasoning Mechanism with Topological and Metric Relations for Change Detection in River Planforms: An Application to GlobeLand30’s Water Bodies

Leng, Liang; Yang, Guodong; Chen, Shengbo

doi:10.3390/ijgi6010013

Cited by 7 publications

(2 citation statements)

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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}]

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Section: Related Workmentioning

confidence: 99%

Topological relations between a directed line and a directed region

Shen

Huang

Chen

2020

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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

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“…The formalization of topological relations among spatial objects (such as interval‐based temporal logic—Allen, ; Masunaga, , point‐set topology—Chen, Li, Li, & Gold, ; Egenhofer & Franzosa, ; Egenhofer, Sharma, & Mark, , and region connection calculus (RCC)—Cohn, Bennett, Gooday, & Gotts, ; Cohn, Randell, & Cui, ; Gotts, Gooday, & Cohn, ; Jonsson & Drakengren, ; Randell & Cohn, ; Randell, Cui, & Cohn, ) has gained increasing attention in the last few decades. Research on formalizing topological relations based on point‐set topology has been conducted, and the 4‐intersection model (4IM) (Egenhofer & Franzosa, ), the 9‐intersection model (9IM) (Egenhofer & Herring, ), the Voronoi‐based 9‐intersection model (Chen, Li, Li, & Gold, ), the dimensionally extended 9‐intersection model (DE‐9IM) (Clementini, Felice, & Oosterom, ; Open GIS Consortium, ), the intersection and difference model (Deng, Cheng, Chen, & Li, ), the extended model expressed as 4 × 4 matrices (Liu & Shi, ), the 9+‐intersection model (Kurata, ), the uncertain intersection and difference model (Alboody, Sedes, & Inglada, ), the double straight line 4‐intersection model (Leng, Yang, & Chen, ), and the 27‐intersection model (Shen, Zhou, & Chen, ) have all been proposed. The intersection models and the extended models based on these have been widely studied.…”

Section: Introductionmentioning

confidence: 99%

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

Shen

Chen

Liu

2018

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As an important topological relation model, the dimensionally extended 9-intersection model (DE-9IM) has been widely used as a basis for standards of queries in spatial databases. However, the negative conditions for the specification of the topological relations within the DE-9IM have not been studied. The specification of the topological relations is closely related to the definition of the spatial objects and the topological relation models. The interior, boundary, and exterior of the spatial objects, including the point, line, and region, are defined. Within the framework of the DE-9IM, 43 negative conditions are proposed to eliminate impossible topological relations. Configurations of region/region, region/line, line/line, region/point, line/point, and point/point relations are drawn. The mutual exclusion of the negative conditions is discussed, and the topological relations within the framework of 9IM and DE-9IM are compared. The results show that:(1) impossible topological relations between spatial objects can be eliminated by the application of 43 negative conditions; and (2) 12 relations between two regions, 31 relations between a region and a line, 47 relations between two lines, three relations between a region and a point, three relations between a line and a point, and two relations between two points can be distinguished by the DE-9IM. 514 | ). Within a given framework, the dimension of the objects, the dimension of the space, and the type of boundary play important roles in the specification of the topological relations (Zlatanova, 2000a). Therefore, the related studies categorizing the topological relations that can occur in reality within a given framework, the definition of the spatial object, the topological relation models, and the methods to determine the number and specification of the topological relations between spatial objects are reviewed as follows.Numerous spatial data models have been proposed to describe spatial objects, such as the simplicial complex (Carlson, 1987), three-dimensional formal data structure (object model (Open GIS Consortium, 1999), simplified spatial model (Zlatanova, 2000b), multi-level model (Ramos, 2002), combinatorial data model (Lee & Kwan, 2005), common information model (Open Geospatial Consortium, 2012), and geometric algebra model (Yu, Luo, Yuan, Hu, Zhu, & Lv, 2016). Although there are differences in the mode of organization, spatial data objects such as points, lines, and regions are the central concept of these spatial data models.Before categorizing the topological relations, the formalism of the topological relations between objects must be defined. The formalization of topological relations among spatial objects (such as interval-based temporal logic-Allen, has gained increasing attention in the last few decades. Research on formalizing topological relations based on point-set topology has been conducted, and the 4-intersection model (4IM) ) have all been proposed. The intersection models and the extended models based on these have been widely studie...

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