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. }-}-third, + 1; x < N; x++) { for (int y = N / 2 + 1; y < N; y++) { intermediaire_calcul = intermediaire_calcul + sym * (ip.getPixelValue(x, y) -offset) * matrix, symmetry or antisymmetry with respect to the origin point for

}. Quadrant, Axis of symmetry: y axis (m is odd: symmetry; m is even: antisymmetry) < N; x++) { for (int y = 0; y < N / 2; y++) { intermediaire_calcul = intermediaire_calcul -sym * (ip.getPixelValue(x, y) -offset) * matrix

}. Quadrant, With respect to origin: m is even?symmetry< N; y++) { intermediaire_calcul = intermediaire_calcul + sym * (ip.getPixelValue(x, y) -offset) * matrix, /

. }-}-the-executable-zernike_, java was written as a plugin for ImageJ, a public domain Java image processing program. As a consequence

, The subfolder matrices gathering all the files Zernnimj0.txt and Zernnimj1.txt must be placed in this folder as well. As any ImageJ plugin, Zernike_.java must be compiled once before using it, ImageJ/plugins/ before installing

, the following window appears: After filling these different fields (exposure time, offset value of the camera, etc.) another window comes out and asks "click on three points?, After opening an image, simply run the plugin (Plugins ? Zern ? Zernike)

, No" is chosen, three other points can be chosen on the same image, in order to restart the centring process, otherwise the cropped and centered image (1000 × 1000 pixels) appears and the calculation of invariants can start: Once all the invariants are computed

, Yes" another image will be opened, so as to restart the process on a new image. If "No", plugin and image will be closed. The invariants are stored as an arff file, called Resultats_DATE.arff and located in the same subfolder as the selected images