smallest rectangle within an elliptical ROI

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smallest rectangle within an elliptical ROI

CARL Philippe (LBP)
Dear all,

Is there an easy way to extract the "smallest rectangle ROI" found within an
elliptical ROI (i.e. similarly to Edit->Selection->To_bounding_box which
corresponds to the "biggest rectangle ROI").

I thank you very much in advance for your lightings.

My best regards,,

Philippe

 

Philippe CARL

Laboratoire de Biophotonique et Pharmacologie

UMR 7213 CNRS - Université de Strasbourg

Faculté de Pharmacie

74 route du Rhin

67401 ILLKIRCH

Tel : +33(0)3 68 85 41 84


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Re: smallest rectangle within an elliptical ROI

Peter Haub
Hallo Philippe,

there is no "smallest rectangle ROI" in an ellipse.

In an ellipse, defined by x*x/a*a + y*y/b*b = 1,
a rectangle is described by A = x*y = sqrt(a*a*x*x - x*x*x*x)*b/a .

A = 0 for x = 0 and for x = a.

The maximum rectangle inside the ellipse is where dA/dx = 0, which is
a*a*x*x - 2*x*x*x = sqrt(a*a*x*x - x*x*x*x) * a/b

So, if you are looking for the maximum rectangle ROI in an ellipse and
if you have the ellipse parameters you can calculate x for dA/dx=0 and
from that the y value.

Hope this helps.

Regards,

Peter


On 24.05.2016 15:46, Philippe CARL wrote:

> Dear all,
>
> Is there an easy way to extract the "smallest rectangle ROI" found within an
> elliptical ROI (i.e. similarly to Edit->Selection->To_bounding_box which
> corresponds to the "biggest rectangle ROI").
>
> I thank you very much in advance for your lightings.
>
> My best regards,,
>
> Philippe
>
>  
>
> Philippe CARL
>
> Laboratoire de Biophotonique et Pharmacologie
>
> UMR 7213 CNRS - Université de Strasbourg
>
> Faculté de Pharmacie
>
> 74 route du Rhin
>
> 67401 ILLKIRCH
>
> Tel : +33(0)3 68 85 41 84
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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ImageJ mailing list: http://imagej.nih.gov/ij/list.html