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...

A Knowledge Base for Automatic Feature Recognition from Point Clouds in an Urban Scene

“…Finally, the formal representation of topological relations between planar regions is composed of four parts: (1) the overall topological relation of two planar regions; (2) the relation between planar region A and the intersection line; (3) the relation between planar region B and the intersection line; and (4) the topological relations of primitives on the intersection line. Some examples of topological relations in the case of Disjoint, Meet and Intersect under the "RCC-3D planar regions in Intersecting planes" can be found in [56]. In conclusion, the topological relations in 3D space are defined and formalized according to the way of representing 3D spatial objects.…”

“…Based on these concepts and topological relations, semantic rules are defined for reasoning on the knowledge related to the specific object defined above. In the following rules, the relation "isMeet_Meet_Meet_Equal" is obtained from basic geometric information of planar regions following the definition of DE-9IM for planar regions and detailed steps presented in [56]. It indicates detailed formalized representation of predefined topological relations of the two planar regions in the spatial relations module.…”

“…In the class of topological relations between planar regions, there are three cases: planar regions on coplanar planes, parallel planes and intersecting planes (as shown in Figure 6). For each case, there could be several examples as described in [56].…”

“…Based on the 4IM and 9IM topological relations definition, the topological relations among planar regions can be represented by a matrix consisting of boundaries, interiors and the intersection line of two plane equations. The definition of DE-9IM for planar regions [56] is shown as follows: For the topological relations between a planar region and an intersection line, the possible relations are Disjoint, Meet and Overlap. The possible primitives on the intersection line comprised of the common parts of the planar region and the intersection line are point (for Meet relation between a planar region and the intersection line) and line segments (for an Overlap and a Meet relations between a planar region and the intersection line) ( Table 2).…”

“…The possible primitives on the intersection line comprised of the common parts of the planar region and the intersection line are point (for Meet relation between a planar region and the intersection line) and line segments (for an Overlap and a Meet relations between a planar region and the intersection line) ( Table 2). The possible topological relations constitute point-point, point-line segment and line segment-line segment relations [56]. Finally, the formal representation of topological relations between planar regions is composed of four parts: (1) the overall topological relation of two planar regions; (2) the relation between planar region A and the intersection line; (3) the relation between planar region B and the intersection line; and (4) the topological relations of primitives on the intersection line.…”