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Henk J.A.M. Heijmans, Alexander V. Tuzikov, "Similarity and Symmetry Measures for Convex Shapes Using Minkowski Addition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 9, pp. 980993, September, 1998.  
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@article{ 10.1109/34.713363, author = {Henk J.A.M. Heijmans and Alexander V. Tuzikov}, title = {Similarity and Symmetry Measures for Convex Shapes Using Minkowski Addition}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {20}, number = {9}, issn = {01628828}, year = {1998}, pages = {980993}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.713363}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Similarity and Symmetry Measures for Convex Shapes Using Minkowski Addition IS  9 SN  01628828 SP980 EP993 EPD  980993 A1  Henk J.A.M. Heijmans, A1  Alexander V. Tuzikov, PY  1998 KW  Similarity measure KW  symmetry measure KW  convex set KW  Minkowski addition KW  BrunnMinkowski inequality. VL  20 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the BrunnMinkowski inequality. This means, in particular, that these measures are regionbased, in contrast to most of the literature, where one considers contourbased measures. All measures considered in this paper are invariant under translations; furthermore, they can be chosen to be invariant under rotations, multiplications, reflections, or the class of affine transformations. It is shown that the mixed volume of a convex polygon and a rotation of another convex polygon over an angle θ is a piecewise concave function of θ. This and other results of a similar nature form the basis for the development of efficient algorithms for the computation of the given measures. Various results obtained in this paper are illustrated by experimental data. Although the paper deals exclusively with the twodimensional case, many of the theoretical results carry over almost directly to higherdimensional spaces.
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