Notes on shape orientation where the standard method does not work
Fieldsend, Jonathan E.
In this paper we consider some questions related to the orientation of shapes with particular attention to the situation where the standard method does not work. There are irregular and non-symmetric shapes whose orientation cannot be computed in a standard way, but in the literature the most studied situations are those where the shape under consideration has more than two axes of symmetry or where it is an n-fold rotationally symmetric shape with n>2.n>2. The basic reference for our work is [W.H. Tsai, S.L. Chou, Detection of generalized principal in rotationally symmetric shapes, Pattern Recognition 24 (1991) 95–104]. We give a very simple proof of the main result from [W.H. Tsai, S.L. Chou, Detection of generalized principal in rotationally symmetric shapes, Pattern Recognition 24 (1991) 95–104] and suggest a modification of the proposal on how the principal axes of rotationally symmetric shapes should be computed. We show some desirable property in defining the orientation of such shapes if the modified approach is applied. Also, we give some comments on the problems that arise when computing shape elongation.
Copyright © 2006 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition, Vol. 39 Issue 5 (2006), DOI: 10.1016/j.patcog.2005.11.010
Notes: This paper introduces a new method for shape orientation. This method, which uses Nth-order centralised moments (N>2), can be applied to cases, such as many-fold symmetric shapes, for which the standard method does not work. The paper proves several desirable properties of shape orientation defined in this way, and also corrects the previous approach where the central moments were treated equally independently of N. It shows that the situation is essentially different depending on whether N is an even or odd number. This corrects the previous work of Tsai and Chou (Pattern Recognition, vol. 24, pp.95-104, 1991), which up to then represented the state of the art in the field.
Vol. 39 (5), pp. 856 - 865