[Date Index]
[Thread Index]
[Author Index]
blurry ellipse
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92033] blurry ellipse
*From*: "Solomon, Joshua" <J.A.Solomon at city.ac.uk>
*Date*: Thu, 18 Sep 2008 06:11:07 -0400 (EDT)
*Organization*: Posted via ULCC Internet Services
NB: This is a mathematical problem, not necessarily a Mathematica problem.
I need a rasterized, blurry ellipse, i.e. an ellipse convolved with a
Gaussian. I already know how to make a blurry circle. You take the Fourier
transform of a circle (i.e. a Bessel function), the Fourier transform of a
Guassian, multiply them, and transform them back. No problem. Since an
ellipse is just a circle that has been squashed in one dimension, I figured
I could make a blurry one the same way as I make blurry circles. I just
needed to squash the Bessel function first. And I was right. The code below
works just fine, *except* the intensity varies as you go around the elipse.
If anyone could tell me how to fix that problem, I'd be very grateful!
BlurryEllipse[sizePix_, radiusPix_, sigmaPix_,stretchFactors_: {1, 1}] :=
Module[{half = sizePix/2, x, y, f, r, a, pr2},
f = 2*Pi*radiusPix/sizePix;
pr2 = -2 (Pi*sigmaPix/sizePix)^2;
RotateRight[
Abs[
Chop[
InverseFourier[
RotateRight[
Table[r1=
Abs[stretchFactors[[1]]*x+
stretchFactors[[2]]*I*y];
r2 = Abs[x + I*y];
BesselJ[0, f*r1] Exp[pr2 (r2^2)],
{y, -half, half-1} , {x, -half, half-1}],
{half, half}]]]], {half,half}]]
size = 64; rad = 24; scale = 3;
tmp = BlurryEllipse[size, rad, scale, {1, .5}];
Show[Graphics[Raster[tmp/Max[Max[tmp]]]], ImageSize -> 400]
Intensity varies around the elipse. We can compare amplitude (or power)
ratios between major and minor axes:
In[]:=Max[tmp[[33]]]/Max[Transpose[tmp][[33]]]
Out[]=1.93009
In[]:= Sqrt[Total[tmp[[33]]^2]/Total[Transpose[tmp][[33]]^2]]
Out[]= 1.98887
I was surprised these numbers weren't closer to 2. How can we make intensity
invariant around the ellipse?
Prev by Date:
**Re: Functional programming?**
Next by Date:
**Re: Functional programming?**
Previous by thread:
**Re: weird NMaximize behaviour**
Next by thread:
**Re: blurry ellipse**
| |