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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
Received: 21 October 2012; in revised form: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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.

AMA Style

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(1):137-151.

Chicago/Turabian Style

Frost, Anja; Renners, Eike; Hötter, Michael; Ostermann, Jörn. 2013. "Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle." Sensors 13, no. 1: 137-151.



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