On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Efficiently Computable Metric for Comparing Polygonal Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Similarity measure computation of convex polyhedra revisited
Digital and image geometry
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ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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PReMI'05 Proceedings of the First international conference on Pattern Recognition and Machine Intelligence
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This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the Brunn-Minkowski inequality. This means, in particular, that these measures are region-based, in contrast to most of the literature, where one considers contour-based 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 驴 is a piecewise concave function of 驴. 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 two-dimensional case, many of the theoretical results carry over almost directly to higher-dimensional spaces.