CAINE-2010, 23nd International Conference on Computer Applications in Industry and Engineering, Sponsored by the International Society for Computers and Their Applications (ISCA), Las Vegas, Nevada USA, pp.74-79, 2010, RCC-3D: Qualitative Spatial Reasoning in 3D Julia Albath Jennifer L. Leopold Chaman L. Sabharwal Anne M. Maglia Computer Science Dept Computer Science Dept Computer Science Dept Biological Sciences Dept Missouri University S&T Missouri University S&T Missouri University S&T Missouri University S&T Rolla, MO-65409,USA Rolla, MO-65409,USA Rolla, MO-65409,USA Rolla, MO-65409,USA jgadkc@mst.edu leopoldj@mst.edu chaman@mst.edu magliaa@mst.edu Abstract Qualitative Spatial Reasoning (QSR) theories have applications in areas such as Geographic Information Systems (GIS), robotics, biomedicine, and engineering. However, existing QSR theories primarily have been applied only to 2D data. Herein we introduce a 3D reasoning system that is based on Generalized 2D Region Connection Calculus (GRCC). Our theory, RCC-3D, supports a priori knowledge of the extent of each object. It also provides occlusion support by considering the projections of 3D objects on 2D space. Further, we demonstrate how this model is applied to a particular domain such as anatomy. 1 Introduction Consider an everyday task such as merging onto a busy highway. Drivers do not necessarily require quantitative information about the other traffic, such as "car A is approaching the driver’s lane at 59.7 mph." However, drivers do require qualitative information, such as "car A is rapidly approaching in the driver’s lane." The concepts of spatial representation and reasoning can be applied to problems that require qualitative and/or quantitative information about the spatial relations that hold between pairs of objects. Today many GIS systems employ some degree of spatial reasoning [1]. Although reasoning over two dimensions is sufficient for many such applications [2], other spatial reasoning problems need to consider information in more than two dimensions. For example, a morphologist may need to examine a species from the dorsoventral (front to back), anteroposterior (head to toe), and left-right perspectives. A 2D QSR system cannot be utilized for these tasks. Further, in order to determine occlusion, the view reference point, the plane of projection, and the type of projection must be known. Herein we introduce a novel approach for spatial reasoning in 3D that is based on the Generalized 2D Region Connection Calculus (GRCC) system [8]. Our system, RCC-3D, provides Omni-view support by assuming a priori knowledge of the extent of each object. It also provides occlusion support by considering orthographic projections on principal planes to detect occlusion. We describe the qualitative reasoning functionality for RCC-3D and implement it using a quantitative computational layer. We then discuss the application of this model to a particular domain, anatomy. 2 Existing QSR Theories Parthood [3] is a relation that exists between two objects whenever one is a subpart of the other. Mereology, which is the study of Parthood, is the foundation for many QSR theories. Parthood is sufficient for defining spatial relations such as overlap and disjointness. However, Parthood is not adequate to define spatial relations that need to take connectedness into consideration. Topology is the study of Connectivity and Continuous deformations, and, unlike mereology, is based upon the mathematical concepts of points, lines, regions, and objects. Because neither mereology nor topology alone is sufficient for doing a broad spectrum of qualitative spatial reasoning [4], the two fields are often combined to form mereotopology, which defines each spatial relation in terms of Parthood and/or Connectivity. For a detailed study of mereotopology, the reader may consult a text such as [5]. An extensive survey of work on qualitative spatial representation and reasoning is based on various mereotopological theories [6]. The authors of [6] further suggest a logical classification of QSR theories based on Connectivity, Parthood, and other necessary axioms. Such theories can be modeled using a Region Connection Calculus (RCC) that defines a number of jointly exhaustive and pairwise disjoint (JEPD) relations. RCC-5 has the following five relations: DR (Disjoint Relation), PO (Proper Overlap), PP (Proper