Jennifer L. Leopold

Spatial relations between 3D objects

With the proliferation of 3D image data comes the need for advances in automated spatial reasoning. One specific challenge is the need for a practical mapping between spatial reasoning and human cognition, where human cognition is expressed through natural-language terminology. With respect to human understanding, researchers have found that errors about spatial relations typically tend to be metric rather than topological; that is, errors tend to be made with respect to quantitative differences in spatial features. However, topology alone has been found to be insufficient for conveying spatial knowledge in natural-language communication. Based on previous work that has been done to define metrics for two lines and a line and a 2D region in order to facilitate a mapping to natural-language terminology, herein we define metrics appropriate for 3D regions. These metrics extend the notions of previously defined terms such as splitting, closeness, and approximate alongness. The association between this collection of metrics, 3D connectivity relations, and several English-language spatial terms was tested in a human subject study. As spatial queries tend to be in natural language, this study provides preliminary insight into how 3D topological relations and metrics correlate in distinguishing natural-language terms. Defined 3D dependencies and intra-relationships between topological relations and metrics.Association between metrics, 3D connectivity relations, and natural-language terms tested.Found three metric equivalence classes that could define natural-language terms for 3D objects.Found that using topological relation with metrics made no difference in terms of accuracy.

Evolution of Region Connection Calculus to VRCC-3D+

Qualitative spatial reasoning (QSR) is useful for deriving logical inferences when quantitative spatial information is not available. QSR theories have applications in areas such as geographic information systems, spatial databases, robotics, and cognitive sciences. The existing QSR theories have been applied primarily to 2D. The ability to perform QSR over a collection of 3D objects is desirable in many problem domains. Here we present the evolution (VRCC-3D+) of RCC-based QSR from 2D to both 3D (including occlusion support) and 4D (a temporal component). It is time consuming to construct large composition tables manually. We give a divide-and-conquer algorithm to construct a comprehensive composition table from smaller constituent tables (which can be easily handcrafted). In addition to the logical consistency entailment checking that is required for such a system, clearly there is a need for a spatio-temporal component to account for spatial movements and path consistency (i.e. to consider only smooth transitions in spatial movements over time). Visually, these smooth movement phenomena are represented as a conceptual neighborhood graph. We believe that the methods presented herein to detect consistency, refine uncertainty, and enhance reasoning about 3D objects will provide useful guidelines for other studies in automated spatial reasoning.

Triangle-Triangle Intersection Determination and Classification to Support Qualitative Spatial Reasoning

In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model. Detection of possible intersection between objects can be based on the objects boundaries (i.e., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection detection algorithm for both cross and coplanar intersections. For qualitative spatial reasoning, a general-purpose algorithm is desirable for accurately differentiating the relations in a region connection calculus, a task that requires consideration of intersection between objects. Herein we present a complete uniform integrated algorithm for both cross and coplanar intersection. Additionally, we present parametric methods for classifying and computing intersection points. This work is applicable to most region connection calculi, particularly VRCC-3D+, which detects intersections between 3D objects as well as their projections in 2D that are essential for occlusion detection.

Efficient determination of spatial relations using composition tables and decision trees

In order for Qualitative Spatial Reasoning applications to be both useful and usable, the information feedback loop between the computational engine and the user must be as seamless as possible. Inherently, computational geometry can be quite expensive, and every effort must be made to avoid inefficient or unnecessary calculations. Within the field of Region Connection Calculi, the 9-Intersection model often is used to determine the spatial relation between two regions. Consequently, optimization efforts typically focus on calculations involving the intersections between the interiors, boundaries, and exteriors of the regions, or the use of composition tables to narrow down the possibilities for the relations that can hold between two regions. The few implementations of spatial reasoners that have been attempted have been simply proofs-of-concept and/or have been limited to two dimensions. Herein we present a novel approach that combines the use of composition tables and decision trees to efficiently determine the spatial relation between two objects in 3D considering both connectivity and obscuration. This approach has been fully implemented for the VRCC-3D+ spatial reasoning system, and benchmarks are included to corroborate our claims of efficiency.

Smooth transition neighborhood graphs for 3D spatial relations

Distance between two relations can be defined by using some metric based on the qualitative or quantitative representation of the relations [1]. However, qualitative distances cannot be expressed by conventional measures. Most differentiating measures are derived from observation and experience in an ad hoc manner. The outcomes are cognitively acceptable only if they match the users concept of distance. We have designed an algorithm based on heuristics to derive a conceptual neighborhood supporting smooth transitions between the relations. Herein we present the results of applying the algorithm to the well-known region connection calculus, RCC-8, and to an additional model, VRCC-3D+, that considers both 3D connectivity and obscuration.

Scaffolding Version Control into the Computer Science Curriculum.

Version control systems (VCS) are widely-used in the software industry. They provide a powerful, collaborative framework that allows software engineers to work together effectively. VCS allow users to track changes and merge ongoing work into concurrently evolving software projects. Distributed VCS such as Git, allow a great degree of flexibility, and provide powerful options for managing personal code and evolving collaborative content. Power incurs responsibility, and introducing collaborative coding and version control tools to new developers can create many challenges. Yet these tools, once mastered, are crucial skills for professional developers. In this paper, the authors introduce VCS to computer science students both in a custom environment specifically designed to support new developers and in a commercially-available native environment suitable for more experienced students. Results show that proper introduction of these powerful tools can make early exposure a positive and valued experience.

Modeling Cardinal Direction Relations in 3D for Qualitative Spatial Reasoning

Many fundamental geoscience concepts and tasks require advanced spatial knowledge about the topology, orientation, shape, and size of spatial objects. Besides topological and distance relations, cardinal directions also can play a prominent role in the determination of qualitative spatial relations; one of the facets of spatial objects is the determination of relative positioning of objects. In this paper, we present an efficient approach to representing and determining cardinal directions between free form regions. The development is mathematically sound and can be implemented more efficiently than the existing models. Our approach preserves converseness of direction relations between pairs of objects, while determining directional relations between gridded parts of the complex regions. All the essential details are in 2D. Yet the extension to 3D is seamless; it needs no additional formulation for transition from 2D to 3D. Furthermore, the extension to 3D and construction of a composition table has no adverse impact on the computational efficiency, as the technique is akin to 2D.

VeCVL: A Visual Language for Version Control.

Version control systems (VCS), such as Subversion and Git, are pervasive in industry; they are invaluable tools for collaborative development that allow software engineers to track changes, monitor issues, merge work from multiple people, and manage releases. These tools are most effective when they are a part of a developer’s habitual workflow. Unfortunately, the use of these powerful tools is often taught much later in a developer’s educational career than other tools like programming languages or databases. Even an experienced student’s first experience with version control can be unpleasant. In this paper, the authors analyze the workflow of two common Version Control Systems with different version controls (Subversion and Git) to build a common visual language for these systems (Version Control Visual Language, or VeCVL), and show that the same visual language applies to other version control systems. Keywordscomputer science education, education technology, pedagogy, version control, visual language

Dual graph partitioning for Bottom-Up BVH construction

Bounding Volume Hierarchies (BVHs) are essential tools in performing collision detection on three-dimensional information. They reduce the number of expensive calculations required to determine whether or not two geometrical entities collide by using inexpensive calculations to rule out parts of the objects that could not possibly intersect. Quickly producing a high quality BVH is an important aspect of three-dimensional multimedia analysis. As such a powerful optimization, efficient and high quality BVHs are still an active area of research. Herein, the authors present a novel BVH representation that reduces the redundancy in the tree structure by allowing a node to contain an arbitrary number of children, as well as compressing non-unique nodes and combining their children. A new partitioning scheme using a graphical representation of the object is also presented to improve the quality of the generated BVH. HighlightsWe present a way to partition triangulated faces for BVH construction.A representation of an AABB tree that exploits a hashmap is examined.BVH representation and partitioning increase quality of BVH.

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

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).