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Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle
Institut für Innovationstransfer, University of Applied Sciences and Arts, Ricklinger Stadtweg 120,Hannover, 30459, Germany
Institut für Informationsverarbeitung, Gottfried Wilhelm Leibniz Universität Hannover, Appelstraße 9A, Hannover, 30167, Germany
* Author to whom correspondence should be addressed.
Received: 21 October 2012; in revised form: 14 December 2012 / Accepted: 17 December 2012 / Published: 21 December 2012
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
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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.
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.
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.