A More Efficient Representation of Obscuration for VRCC-3D+ Relations

Abstract

Abstract—VRCC-3D+ is an implementation of a regionconnection calculus that qualitatively determines the spatialrelation between two 3D objects in terms of connectivity andobscuration. The eight connectivity relations are conceptually thesame as RCC8, but calculated in 3D rather than 2D. The fifteenobscuration relations are calculated using the projection of the 3Dobjects on a particular 2D plane and the distance of the objectsfrom the viewpoint. Herein we present a smaller, more preciseset of VRCC-3D+ obscuration relations that retains the qualitiesof being jointly exhaustive and pairwise disjoint. However, thisnew set of relations overcomes two problems that existed in theprevious set of fifteen relations: (1) lack of a precise mathematicaldefinition for a key predicate, InFront, and (2) lack of an intuitivemapping of converse relations.Index Terms—Computer vision, qualitative spacial reasoning,VRCC-3D, region connection calculus, spatial relations. I. I NTRODUCTION Q UALITATIVE spatial reasoning (QSR) in two dimen-sions is a well-studied field, and includes models suchas the connectivity-based RCC systems [1], [2], [3], andobscuration-based systems such as LOS-14 [4], OCS-14 [5],and OCC [6]. These systems, while expressive, do notaccurately portray the real world wherein objects exist andare perceived in three dimensions, not two. As computingpower increases and the need to analyze three-dimensionaldata (e.g., stereoscopic video, robotic vision, etc.) increases,two-dimensional reasoning systems can be inefficient, or eveninadequate, for sophisticated applications.To ameliorate the shortcomings of two-dimensional QSRsystems, Albath et al. developed RCC-3D [7], whicheventually evolved into VRCC-3D+ [8]. VRCC-3D+ usescomposite relations that express both connectivity andobscuration from a given perspective. The connectivity-basedrelations are the RCC8 relations (DC, EC, EQ, PO, TPP, TPPc,NTPP, NTPPc) defined in three dimensions; these relationshave been an ongoing focus of optimization and refinementin the implementation as a QSR system [9]. The obscurationportion of the composite relations are refinements on the basicconcepts of no obscuration (nObs), partial obscuration (pObs),equal obscuration (eObs), and complete obscuration (cObs).