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Pieter Holtzhausen
2011-08-22 14:08:45 +02:00
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doc/source/tutorials/radon_transform.txt
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Radon transform
***************
The radon transform is a technique widely used in tomography, where you reconstruct an object from its different projections. A projection for example the scattering data obtained as the output of a tomographic scan.
The radon transform is a technique widely used in tomography, where you
reconstruct an object from its different projections. A projection for example
the scattering data obtained as the output of a tomographic scan.
For more information:
http://en.wikipedia.org/wiki/Radon_transform
@@ -11,7 +13,8 @@ For more information:
Forward transform
=================
First we load the Schepp-Logan phantom, a classic test image representing a tomographic scan.
First we load the Schepp-Logan phantom, a classic test image representing a
tomographic scan.
.. ipython::
@@ -37,7 +40,8 @@ First we load the Schepp-Logan phantom, a classic test image representing a tomo
In [9]: plt.show()
Let us illustrate the transform by looking at projections taken at specific angles.
Let us illustrate the transform by looking at projections taken at specific
angles.
.. ipython::
@@ -54,7 +58,8 @@ Let us illustrate the transform by looking at projections taken at specific angl
@savefig radon_projection_plot1.png width=4in
In [15]: plt.show()
We are going to reconstruct an image from 180 of these projections (the default).
We are going to reconstruct an image from 180 of these projections (the
default).
.. ipython::
@@ -74,7 +79,8 @@ We are going to reconstruct an image from 180 of these projections (the default)
In [22]: plt.show()
We have now constructed various projections, line integrals of an image, at specific angles. This image is called a sinogram.
We have now constructed various projections, line integrals of an image, at
specific angles. This image is called a sinogram.
.. ipython::
@@ -91,6 +97,7 @@ We have now constructed various projections, line integrals of an image, at spec
@savefig radon_sinogram.png width=4in
In [28]: plt.show()
Inverse transform
=================
To reconstruct the image from this sinogram, we apply the inverse transform.