{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:09Z","timestamp":1760243769571,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,12,21]],"date-time":"2012-12-21T00:00:00Z","timestamp":1356048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s130100137","type":"journal-article","created":{"date-parts":[[2012,12,21]],"date-time":"2012-12-21T11:06:37Z","timestamp":1356087997000},"page":"137-151","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle"],"prefix":"10.3390","volume":"13","author":[{"given":"Anja","family":"Frost","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Innovationstransfer, University of Applied Sciences and Arts, Ricklinger Stadtweg 120,Hannover, 30459, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eike","family":"Renners","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Innovationstransfer, University of Applied Sciences and Arts, Ricklinger Stadtweg 120,Hannover, 30459, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"H\u00f6tter","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Innovationstransfer, University of Applied Sciences and Arts, Ricklinger Stadtweg 120,Hannover, 30459, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00f6rn","family":"Ostermann","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informationsverarbeitung, Gottfried Wilhelm Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe 9A, Hannover, 30167, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TMI.2010.2060491","article-title":"Hybrid cone-beam tomographic reconstruction: Incorporation of prior anatomical models to compensate for missing data","volume":"30","author":"Sadowsky","year":"2011","journal-title":"IEEE Trans. Med. Imag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1109\/TBME.2005.857665","article-title":"A hierarchical statistical modeling approach for the unsupervised 3-D biplanar reconstruction of the scoliotic spine","volume":"52","author":"Benameur","year":"2005","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_3","unstructured":"Varga, L., Bal\u00e1zs, P., and Nagy, A. (2010). Advanced Concepts for Intelligent Vision Systems, Springer Verlag."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chan, M., Herman, G., and Levitan, E. (1999). Discrete Tomography: Foundations, Algorithms, and Applications, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-1568-4"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Herman, G., and Kuba, A. (2007). Advances in Discrete Tomography and Its Applications, Birkh\u00e4user.","DOI":"10.1007\/978-0-8176-4543-4"},{"key":"ref_6","unstructured":"Kunze, H. (2007). 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