Extension of RCC Topological Relations for 3d Complex Objects Components Extracted From 3d Lidar Point Clouds

Abstract

ABSTRACT:Topological relations are fundamental for qualitative description, querying and analysis of a 3D scene. Although topological relations for 2D objects have been extensively studied and implemented in GIS applications, their direct extension to 3D is very challenging and they cannot be directly applied to represent relations between components of complex 3D objects represented by 3D B-Rep models in 3 R . Herein we present an extended Region Connection Calculus (RCC) model to express and formalize topological relations between planar regions for creating 3D model represented by Boundary Representation model in 3 R . We proposed a new dimension extended 9-Intersection model to represent the basic relations among components of a complex object, including disjoint, meet and intersect. The last element in 3*3 matrix records the details of connection through the common parts of two regions and the intersecting line of two planes. Additionally, this model can deal with the case of planar regions with holes. Finally, the geometric information is transformed into a list of strings consisting of topological relations between two planar regions and detailed connection information. The experiments show that the proposed approach helps to identify topological relations of planar segments of point cloud automatically.* Corresponding author INTRDUCTIONSpatial relations include topological, metric and directional relations and together with semantic information are used for describing a scene qualitatively (Mark, 1994). Topological relations between geographical objects are necessary for spatial analysis in GIS. These relations can be queried and analysed independently from geographic coordinate system definition and the specific location of objects. Topological relations describe relative spatial relations with respect to reference objects. Hence topological relations are invariant and do not change with topological transformations, such as translation, scaling, and rotation (Egenhofer, 1990b).In general, topological relations between spatial objects are derived from Region Connection Calculus (RCC-8) (Egenhofer, 1989;Egenhofer, 1991) Here, a region is defined as a 2-cell with a non-empty, connected interior (Egenhofer, 1990a). Additionally, the 4-Intersection Model (4IM) (Egenhofer, 1991), 9-Intersection Model(9IM) (Clementini, 1993) and Dimensionally Extended models (DE) (Clementini, 1993) are widely adopted and implemented for describing topological relations for spatial analysis. Topological relations between spatial objects can be described based on relations defined for 2D regions in RCC model. Basic relations between two regions include disjoint, meet, overlap, contain, cover, coveredBy, containedBy and equal (Egenhofer, 1990b;Randell, 1992).The definitions of topological relations between spatial objects in 3 R are closely related to 3D objects models. A 3D spatial object can be modelled as a solid geometry or represented by its boundaries. Thus, topological relations between spatial objects in 3 R can be divid...

Ontology-Based Semantic Conceptualisation of Historical Built Heritage to Generate Parametric Structured Models from Point Clouds

“…The topological relations between the components are summarised as a 3*3 matrix of the dimensionally extended 9-intersection model (DE-9IM) [42] to represent topological relations. As the description presented in [43], the matrix is composed of the dimension operation on the interior, the boundaries of the two planar regions that represent building elements, and the intersection line between the two plane regions in 3D space. Based on the representation of DE-9IM for recording topological relations between planar regions, the semantic representation of the topological relations between the two planar regions is determined by analysing the relation between the intersection line and two planar regions, and the relations between the intersected parts composed of the intersection operation between planar regions and the intersection line.…”