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Appl. Comput. Harmon. Anal. 17 (2004) 259276 www.elsevier.com/locate/acha

Summary: Appl. Comput. Harmon. Anal. 17 (2004) 259276
3D discrete X-ray transform
Amir Averbuch
, Yoel Shkolnisky 1
School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Received 5 April 2003; revised 29 April 2004; accepted 12 May 2004
Available online 5 August 2004
Communicated by the Editors
The analysis of 3D discrete volumetric data becomes increasingly important as computation power increases.
3D analysis and visualization applications are expected to be especially relevant in areas like medical imaging and
nondestructive testing, where elaborated continuous theory exists. However, this theory is not directly applicable
to discrete datasets. Therefore, we have to establish theoretical foundations that will replace the existing inexact
discretizations, which have been based on the continuous regime. We want to preserve the concepts, properties,
and main results of the continuous theory in the discrete case. In this paper, we present a discretization of the
continuous X-ray transform for discrete 3D images. Our definition of the discrete X-ray transform is shown to be
exact and geometrically faithful as it uses summation along straight geometric lines without arbitrary interpolation
schemes. We derive a discrete Fourier slice theorem, which relates our discrete X-ray transform with the Fourier
transform of the underlying image, and then use this Fourier slice theorem to derive an algorithm that computes the


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences