mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 15:06:42 +08:00
Pieter Holtzhausen
110 lines
2.6 KiB
Plaintext
110 lines
2.6 KiB
Plaintext
***************
|
|
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.
|
|
|
|
For more information:
|
|
http://en.wikipedia.org/wiki/Radon_transform
|
|
http://www.clear.rice.edu/elec431/projects96/DSP/bpanalysis.html
|
|
|
|
Forward transform
|
|
=================
|
|
|
|
First we load the Schepp-Logan phantom, a classic test image representing a tomographic scan.
|
|
|
|
.. ipython::
|
|
|
|
In [1]: from scikits.image.io import imread
|
|
|
|
In [1]: from scikits.image import data_dir
|
|
|
|
In [2]: from scikits.image.transform import radon, iradon
|
|
|
|
In [3]: from scikits.image.color import rgb2gray
|
|
|
|
In [4]: import matplotlib.pyplot as plt
|
|
|
|
In [5]: import matplotlib.cm as cm
|
|
|
|
In [6]: image = rgb2gray(imread(data_dir + "/phantom.png"))
|
|
|
|
In [7]: plt.title("original image");
|
|
|
|
In [8]: plt.imshow(image, cmap=cm.Greys_r)
|
|
|
|
@savefig radon_original_image.png width=4in
|
|
In [9]: plt.show()
|
|
|
|
|
|
Let us illustrate the transform by looking at projections taken at specific angles.
|
|
|
|
.. ipython::
|
|
|
|
In [10]: projections = radon(image, theta=[0, 45, 90])
|
|
|
|
In [11]: plt.plot(projections);
|
|
|
|
In [12]: plt.title("radon projections");
|
|
|
|
In [13]: plt.xlabel("projection axis");
|
|
|
|
In [14]: plt.ylabel("intensity");
|
|
|
|
@savefig radon_projection_plot1.png width=4in
|
|
In [15]: plt.show()
|
|
|
|
We are going to reconstruct an image from 180 (the default) of these projections.
|
|
|
|
.. ipython::
|
|
|
|
In [16]: projections = radon(image)
|
|
|
|
In [17]: plt.figure()
|
|
|
|
In [18]: plt.title("radon projections");
|
|
|
|
In [19]: plt.xlabel("projection axis");
|
|
|
|
In [20]: plt.ylabel("intensity");
|
|
|
|
In [21]: plt.plot(projections)
|
|
|
|
@savefig radon_projection_plot2.png width=4in
|
|
In [22]: plt.show()
|
|
|
|
|
|
We have now constructed various projections, line integrals of an image, at specific angles. This image is called a sinogram.
|
|
|
|
.. ipython::
|
|
|
|
In [23]: plt.figure()
|
|
|
|
In [24]: plt.title("sinogram");
|
|
|
|
In [25]: plt.xlabel("projection axis");
|
|
|
|
In [26]: plt.ylabel("intensity");
|
|
|
|
In [27]: plt.imshow(projections)
|
|
|
|
@savefig radon_sinogram.png width=4in
|
|
In [28]: plt.show()
|
|
|
|
Inverse transform
|
|
=================
|
|
To reconstruct the image from this sinogram, we apply the inverse transform.
|
|
|
|
.. ipython::
|
|
|
|
In [29]: reconstruction = iradon(projections)
|
|
|
|
In [30]: plt.title("reconstructed image");
|
|
|
|
In [31]: plt.imshow(reconstruction, cmap=cm.Greys_r)
|
|
|
|
@savefig radon_reconstructed_image.png width=4in
|
|
In [32]: plt.show()
|
|
|
|
|