bug in radon transform?

[Emmanuelle Gouillart]

Yes, it looks weird. I don't have access to the corresponding toolbox in
Matlab either. I could "symmetrize" the result by the following change in
radon:
-    shift0 = np.array([[1, 0, -w/2.],
-                       [0, 1, -h/2.],
+    shift0 = np.array([[1, 0, -w/2. + 0.5],
+                       [0, 1, -h/2. + 0.5],
                        [0, 0, 1]])
 
-    shift1 = np.array([[1, 0, w/2.],
-                       [0, 1, h/2.],
+    shift1 = np.array([[1, 0, w/2. - 0.5],
+                       [0, 1, h/2. - 0.5],
                        [0, 0, 1]])

but then I'm not sure whether the behavior of iradon is correct either,
so I haven't committed this change yet. Pieter, if you're around, would
you mind having a quick look?

Also, iradon crashes for arrays with less than 64 lines (due to an int
that should be a float, resulting in a division by zero error -- I just
made a small pull request to correct that).

I also noticed that for the array used in
test_radon_transform.test_radon_iradon, applying radon and then iradon
does not give back the correct original array, but an array that looks
shifted by one line and one column. Try for example
>>> from skimage.transform import radon, iradon
>>> size = 70
>>> image = np.tri(size) + np.tri(size)[::-1]
>>> reconstructed = iradon(radon(image), filter="ramp",
>>> interpolation="linear")
>>> close('all')
>>> plt.matshow(image)
<matplotlib.image.AxesImage object at 0x42f9b90>
>>> plt.matshow(reconstructed)
<matplotlib.image.AxesImage object at 0x494a5d0>

I very much suspect that the center of rotation is not correct either in
radon, or in iradon, or maybe in both... I started having a look at the
code, but maybe it would be easier for Pieter than for me to fix it...

Cheers,
Emmanuelle

On Wed, Apr 04, 2012 at 03:53:38PM -0700, St�fan van der Walt wrote:
> On Wed, Apr 4, 2012 at 2:31 PM, Emmanuelle Gouillart
> <emmanuelle.gouillart at nsup.org> wrote:
> > � � � �I have the impression that the center of rotation used for
> > computing the radon transform (skimage.transform.radon) is not correct:

> In [8]: tf.radon(z, theta=[0, 90])
> Out[8]:
> array([[ 0.,  0.],
>        [ 0.,  0.],
>        [ 0.,  1.],
>        [ 0.,  0.],
>        [ 0.,  0.],
>        [ 0.,  0.],
>        [ 1.,  0.],
>        [ 0.,  0.],
>        [ 0.,  0.],
>        [ 0.,  0.]])

> Hrm, you're right; that looks fishy.  I wonder if this has to do with
> the padding that happens beforehand?  I don't have access to
> MATLAB--does their "radon" give similar results?

> St�fan