|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Shape elongation from optimal encasing rectangles||Journal:||Computers and Mathematics with Applications||Volume:||60||Issue:||7||First page:||2035||Last page:||2042||Issue Date:||1-Oct-2010||Rank:||M21||ISSN:||0898-1221||DOI:||10.1016/j.camwa.2010.07.043||Abstract:||
Let S be a shape with a polygonal boundary. We show that the boundary of the maximally elongated rectangle R(S) which encases the shape S contains at least one edge of the convex hull of S. Such a nice property enables a computationally efficient construction of R(S). In addition, we define the elongation of a given shape S as the ratio of the length of R(S) (determined by the longer edge of R(S)) and the width of R(S) (determined by the shorter edge of R(S)) and show that a so defined shape elongation measure has several desirable properties. Several examples are given in order to illustrate the behavior of the new elongation measure. As a by-product, of the method developed here, we obtain a new method for the computation of the shape orientation, where the orientation of a given shape S is defined by the direction of the longer edge of R(S).
|Keywords:||Computational geometry | Elongation | Encasing rectangle | Image processing | Shape||Publisher:||Elsevier||Project:||Serbian Ministry of Science and Technology, grant ON144018|
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