3D Tilted projection

Is there any Matlab script to get 2D projections of a 3D matrix after rotating the 3D matrix X degrees over it self?

Actually I need to build a simulator for the Electron Tomography Image acquisition, In which a 2D images of an object are taken every time the object is rotated over it self for X degree from -A to +A Degree, as in the Image below. http://media.wiley.com/CurrentProtocols/PS/ps1702/ps1702-fig-0009-1-full.jpg

http://vis.lbl.gov/Vignettes/KDowning-Tomo/rays.jpg

I would very grateful for your help.

wish you a nice weekend.

Alan

Answer 1

[Bjorn Gustavsson]

From the looks of your figures it seems as if you have parallel beam projection geometry. For the 2-D-to-1-D case your projections would be calculated with the Radon transform. Slightly depending on your exact geometry you might get away with a number of stacked radon transforms, all for various slices along your axis of rotation. Or you might have to make a 3-D version of radon.

HTH.

[Alan AF]

How can we change the parameters of Radon transform, I mean can we do Radon based on exponent function ?

Thank you

[Bjorn Gustavsson]

Perhaps:

I = radon(log(f))

Then your Radon-inverse of I will give you log(f).

Answer 2

[bym]

if you have the image processing toolbox take a look at

maketform()

[Alan AF]

Thank you for the reply

but I still dont know how it can be used in my case?

Is it possible to use it in a loop and taking 2D projections of a image stack (3d matrix) from angle -60 to 60?

[bym]

is your stack like a MRI in this demo? http://www.mathworks.com/products/image/demos.html?file=/products/demos/shipping/images/ipexmri.html

If it is, then I would say no, you can't slice it at an arbitrary angle

Answer 3

[Sean de Wolski]

doc iradon

will likely be your friend.