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Sensors 2013, 13(1), 137-151; doi:10.3390/s130100137
Article

Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle

1,* , 1
,
1
 and
2
1 Institut für Innovationstransfer, University of Applied Sciences and Arts, Ricklinger Stadtweg 120,Hannover, 30459, Germany 2 Institut für Informationsverarbeitung, Gottfried Wilhelm Leibniz Universität Hannover, Appelstraße 9A, Hannover, 30167, Germany
* Author to whom correspondence should be addressed.
Received: 21 October 2012 / Revised: 14 December 2012 / Accepted: 17 December 2012 / Published: 21 December 2012
(This article belongs to the Special Issue State-of-the-Art Sensors Technology in Germany 2012)
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Abstract

An important part of computed tomography is the calculation of a three-dimensional reconstruction of an object from series of X-ray images. Unfortunately, some applications do not provide sufficient X-ray images. Then, the reconstructed objects no longer truly represent the original. Inside of the volumes, the accuracy seems to vary unpredictably. In this paper, we introduce a novel method to evaluate any reconstruction, voxel by voxel. The evaluation is based on a sophisticated probabilistic handling of the measured X-rays, as well as the inclusion of a priori knowledge about the materials that the object receiving the X-ray examination consists of. For each voxel, the proposed method outputs a numerical value that represents the probability of existence of a predefined material at the position of the voxel while doing X-ray. Such a probabilistic quality measure was lacking so far. In our experiment, false reconstructed areas get detected by their low probability. In exact reconstructed areas, a high probability predominates. Receiver Operating Characteristics not only confirm the reliability of our quality measure but also demonstrate that existing methods are less suitable for evaluating a reconstruction.
Keywords: X-ray; computed tomography; discrete tomography; three-dimensional image reconstruction; limited data; Dempster–Shafer theory; data fusion; probability calculus X-ray; computed tomography; discrete tomography; three-dimensional image reconstruction; limited data; Dempster–; Shafer theory; data fusion; probability calculus
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Frost, A.; Renners, E.; Hötter, M.; Ostermann, J. Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle. Sensors 2013, 13, 137-151.

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