Guesgen, H. W. (1989). Spatial reasoning based on Allen's temporal logic. International Computer Science Institute technical report. TR-89-049. 1947 Center St, Suite 600, Berkeley, CA.

@TechReport{,
  author =       {Hans Werner Guesgen},
  title =        {Spatial reasoning based on Allen's temporal logic},
  institution =  {International Computer Science Institute},
  year =         {1989},
  OPTnumber =    {TR-89-049},
  OPTaddress =   {1947 Center St, Suite 600, Berkeley, CA},
}

Author of the summary: Jim Davies, 2003, jim@jimdavies.org

Cite this paper for:

• Each quantitative relation can be uniquely mapped to a qualitative one, while in general there are in infinite number of quantitative relations that correspond to a qualitative one. [7]

Constraints:

• represent imprecise relationships (e.g. "I'm sitting in the railway station")
• can handle uncertainty (e.g. you don't know the spatial relationship between two objects)
• Granularity depends on context (e.g. the distances referred to in "the moon rises over a field" and "a bridge over water" are different.)

• a is left of b
• a is attached to b
• a is overlaping b
• a is inside of b

It's reprensented with circular nodes (for objects) and rectangular labels (for relations). Spatial reasoning, on this count, is modifying the labels and inserting new rectangles.

Reasoning steps [6]:

• compute composition of spatial relations
• use constraint satisfaction to remove inconsistencies

Moving on two 2 and 3d

"Each quantitative relation can be uniquely mapped to a qualitative one, while in general there are in infinite number of quantitative relations that correspond to a qualitative one." [7]

To get to three dimensions, one can simply use three relations per pair of objects, each with respect to the x, y, and z axis. [10] The disadvantage is that certain ambiguities cannot be expressed tightly enough. Solving this problem by using sets of tuples improves it on this count, at the cost of a cubic disimprovement to the algorithm efficiency.

Summary author's notes:

• The third constraint (granularity) is related to viewing things at multiple levels of abstraction.
• This notion of spatial reasoning does not include adding objects to the image, which makes it limited for problem solving.