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The isotropicity definition clearly states uniform response on all orientation; hence, on images, the brightness magnitude should not be different for different dimensions. However, it is not clear for me how to test a given edge-detector-function for isotropicity.

For example, I'd like to test the following edge detector for isotropicity:

(Ex^2-Ey^2)ExEy-Exy(Exx-Eyy); (E being the intensity function (E(x,y)), while the Ex and Ey denote corresponding derivatives; as well as Exx and Eyy denoting second derivatives.)

TylerH
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ahmet
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1 Answers1

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Hum, you know, there is this thing called the scientific method: you formulate a hypothesis, design an experiment, perform it, and see how well your hypothesis explains its outcome.

In this particular case, anything wrong with using an appropriate natural or synthetic test image, and see how your detector responds on it?

This may be a good image to start: http://lowcadence.com/wp-content/uploads/2013/08/YinYang.jpg Don't forget to test at multiple resolutions, and after mirroring it. A light blur may help too.

Francesco Callari
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