Quantitative Representation of the Relative Position Between 3D

Spatial relationships play an important role in many domains of computer science, including computer vision, Geographic Information Systems (GIS), and medical imaging. In previous work, we introduced the notion of the histogram of forces. It is a quantitative representation of the relative position between two objects. It is sensitive to the shape, size, and orientation of the objects. The objects considered so far could be disjoint or intersecting, they could be bounded or unbounded, convex or concave, available in raster or in vector form, but they had to be two-dimensional. In this paper, we show that three-dimensional raster data can be handled as well. By adopting proper optimization procedures, the presented technique provides a fast and reliable way for representing the relative position between two 3D objects. The results of experiments conducted on synthetic and real data validate our approach