Parameter-sparse modification of Fourier methods to analyse the shape of closed contours with application to otolith outlines
Alf HarbitzInstitute of Marine Research, Sykehusveien 23, PO Box 6404, N-9294 Tromsø, Norway. Email: alf.harbitz@imr.no
Marine and Freshwater Research 67(7) 1049-1058 https://doi.org/10.1071/MF15087
Submitted: 1 March 2015 Accepted: 3 November 2015 Published: 5 February 2016
Journal Compilation © CSIRO Publishing 2016 Open Access CC BY-NC-ND
Abstract
Elliptical Fourier descriptors (EFDs) have been used extensively in shape analysis of closed contours and have a range of marine applications, such as automatic identification of fish species and discrimination between fish stocks based on EFDs of otolith contours. A recent method (the ‘MIRR’ method) transforms the two-dimensional contour to a one-dimensional function by mirroring (reflecting) the lower half of the contour around a vertical axis at the right end of the contour. MIRR then applies the fast Fourier transform (FFT) to the vertical contour points corresponding to equidistant coordinate values along the horizontal axis. MIRR has the advantage of reducing the number of Fourier coefficients to two coefficients per frequency component compared with four EFDs. However, both Fourier methods require several frequency components to reproduce a pure ellipse properly. This paper shows how the methods can be easily modified so that a virtually perfect reproduction of a pure ellipse is obtained with only one frequency component. In addition, real otolith examples for cod (Gadus morhua) and Greenland halibut (Reinhardtius hippoglossoides) are used to demonstrate that the modified methods give better approximations to the large-scale shape of the original contour with fewer coefficients than the traditional Fourier methods, with negligible additional computing time.
Additional keywords: cod otoliths, Greenland halibut otoliths, modified Fourier method, shape analysis.
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