Comparing convex shapes using Minkowski addition
This report deals with similarity measures for convex shapes whose definition is based on Minkowski addition and the Brunn-Minkowski inequality. All measures considered here are invariant under translations. In addition, they may be invariant under rotations, multiplications, reflections, or affine transformations. Restricting oneselves to the class of convex polygons, it is possible to develop efficient algorithms for the computation of such similarity measures. These algorithms use a special representation of convex polygons known as the perimetric measure. Such representations are unique for convex sets and linear with respect to Minkowski addition. Although the paper deals exclusively with the 2-dimensional case, many of the results carry over almost immediately to higher-dimensional spaces.
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