The distance between shape centroids is less than a quarter of the shape perimeter

Jovisa Zunic, Mehmet Ali Aktas, Carlos Martinez-Ortiz, and Antony Galton

Pattern Recognition, Volume 44 (2011), pages 2161-2169.
doi:10:1016/j.patcog.2011.03.003

Abstract

In this paper we consider the distance between the shape centroid computed from the shape interior points and the shape centroid computerd from the shape boundary points. We show that the distance between these centroids is upper bounded by the quarter of the perimeter of the shape considered. The obtained upper bound is sharp and cannot be improved.

Next, we introduce the shape centredness as a new shape descriptor which, informally speaking, should injdicate to which degree a shape has a uniquely defined centre. By expoiting the result mentioned above, we give a formula for the computation of the shape centredness. Such a computed centredness is invariant with respect to translation, rotation and scaling transformations.

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