Authors: Žunić, Dragiša
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Shape ellipticity from Hu moment invariants
Journal: Applied Mathematics and Computation
Volume: 226
First page: 406
Last page: 414
Issue Date: 2014
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2013.10.062
Abstract: 
In this paper we derive an explicit formula which uses the first two Hu moment invariants to compute a shape ellipticity measure, i.e. to evaluate how much a planar shape differs from an ellipse. The ellipticity measure computed by this formula is invariant with respect to translation, rotation and scaling transformations. Also, the highest possible value is obtained if and only if the shape considered is an ellipse. Several experiments are also provided to confirm the theoretical observations. A by product, of the derivations made in this paper, is an implicit interpretation of geometric/shape meaning of the second Hu moment invariant. A formula which connects the shape ellipticity and the first Hu moment invariant (both having a well understood behavior) and the second Hu moment invariant is derived.
Keywords: Image processing | Moment invariants | Shape | Shape descriptors | Shape ellipticity
Publisher: Elsevier
Project: Representations of logical structures and formal languages and their application in computing 
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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