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Subject: Re: 3D reconstruction from 2D CT images
Date: Tue, 2 Dec 2008 10:22:01 +0000 (UTC)
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First, we need to clarify the question. Are you asking:

"I have 2D slices from a fully 3D CT dataset and I need to do something with them"

-OR-

"I have 2D image data which I wish to put together in order to create a 3D image"

??? Have a think, I'll presume the second answer in the meantime...

The originally posted question can be rephrased 'How different projections of an object be used to reconstruct it's 3D shape?.' This is the subject of tomography ('tomos' in greek is a 'section, slice or cutting' according to wikipedia!).

Now, there are a number of different types of tomography - my PhD is based around one, MART (Multiplicative Algebraic Reconstruction Technique) which I could help you to understand. However, I don't actually think that this is right for you. To my knowledge, Computerised Tomography (CT) for medical purposes is often done by means of a Radon Transform - one of the other posters gives a link to a radon transform site which might be useful.

Sorry, I don't know the details of radon transforms - but I can point you to exactly the right textbook to get you under way. The guru of the field is Gabor T Herman; check out one of his books:

Image Reconstruction from Projections: Fundamentals of Computed Tomography
G. T. Herman
Academic press 1981
ISBN-13:  978-0123420503

OR

Discrete Tomography: Foundations, Algorithms and Applications
G. T. Herman and A. Kuba
Birkhauser Verlag AG 1999
ISBN-13:  978-3764341015


... The latter is more up to date, so likely to be a bit more relevant for modern computing tasks. It's also cheaper.

Be warned that tomography can be incredibly computationally expensive. To give you an idea I've just bought a quad-core machine with 20Gb of ram to cope... although requirements vary wildly depending on the resolution you require, the number of elevations/sections you have, and the size of the 3D volume itself.

Hope this kicks you off...

Tom Clark