Spatial relations between 3D objects: The association between natural language, topology, and metrics

• 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.

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.