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Considering an grey-scale image as a function $z=f(x,y)$. (Specifically, I'm interested in $f=h*h*...*h$, where $h$ is the indicator function of a regular hexagon.) I am interested in finding places where $f$ fails to be smooth (or $k$-times continuously differentiable). This is the Singular Support of $f$.

Is there anything more sophisticated than applying GradientFilter a number of times - and the singular support will show up as white lines.

Edit: As requested here are some pictures for $h*h$. First, the function $h*h$: h*h and now applying the gradient filter: GradientFilter[h*h]

I'll try knocking up three for $h*h*h$.

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    $\begingroup$ I'm voting to close this question as off-topic because, as currently posed, it is really about image processing methodology and not about the use of Mathematica , $\endgroup$
    – m_goldberg
    Aug 27, 2015 at 9:57
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    $\begingroup$ I think this is an interesting question, but it would help if you would provide sample images and a minimal working example of your suggested GradientFilter approach. Hopefully, together with a little discussion on why it's not a full solution or where it breaks down. $\endgroup$
    – dionys
    Aug 27, 2015 at 10:18
  • $\begingroup$ How about migrating this to dsp.stackexchange.com $\endgroup$
    – pdmclean
    Aug 30, 2015 at 23:06
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    $\begingroup$ I'm voting to close this question as off-topic because without the Mathematica code involved it seems difficult to reproduce the OP results $\endgroup$
    – Dr. belisarius
    Feb 12, 2016 at 15:28
  • $\begingroup$ @m_goldberg Trying to close it ... again $\endgroup$
    – Dr. belisarius
    Feb 12, 2016 at 15:29

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