Authors: Žunić, Joviša 
Žunić, Dragiša
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Shape Interpretation of Second-Order Moment Invariants
Journal: Journal of Mathematical Imaging and Vision
Volume: 56
Issue: 1
First page: 125
Last page: 136
Issue Date: 1-Sep-2016
Rank: M21a
ISSN: 0924-9907
DOI: 10.1007/s10851-016-0638-8
This paper deals with the following problem: What can be said about the shape of an object if a certain invariant of it is known? Such a, herein called, shape invariant interpretation problem has not been studied/solved for the most of invariants, but also it is not known to which extent the shape interpretation of certain invariants does exist. In this paper, we consider a well-known second-order affine moment invariant. This invariant has been expressed recently Xu and Li (2008) as the average square area of triangles whose one vertex is the shape centroid while the remaining two vertices vary through the shape considered. The main results of the paper are (i) the ellipses are shapes which minimize such an average square triangle area, i.e., which minimize the affine invariant considered; (ii) this minimum is 1 / (16 π2) and is reached by the ellipses only. As by-products, we obtain several results including the expression of the second Hu moment invariant in terms of one shape compactness measure and one shape ellipticity measure. This expression further leads to the shape interpretation of the second Hu moment invariant, which is also given in the paper.
Keywords: Image processing | Moment invariants | Moments | Pattern recognition | Shape
Publisher: Springer Link
Project: Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
Representations of logical structures and formal languages and their application in computing 

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