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.
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