scholarly journals A general scheme for constructing inversion algorithms for cone beam CT

2003 ◽  
Vol 2003 (21) ◽  
pp. 1305-1321 ◽  
Author(s):  
Alexander Katsevich

Given a rather general weight functionn0, we derive a new cone beam transform inversion formula. The derivation is explicitly based on Grangeat's formula (1990) and the classical 3D Radon transform inversion. The new formula is theoretically exact and is represented by a 2D integral. We show that if the source trajectoryCis complete in the sense of Tuy (1983) (and satisfies two other very mild assumptions), then substituting the simplest weightn0≡1gives a convolution-based FBP algorithm. However, this easy choice is not always optimal from the point of view of practical applications. The weightn0≡1works well for closed trajectories, but the resulting algorithm does not solve the long object problem ifCis not closed. In the latter case one has to use the flexibility in choosingn0and find the weight that gives an inversion formula with the desired properties. We show how this can be done for spiral CT. It turns out that the two inversion algorithms for spiral CT proposed earlier by the author are particular cases of the new formula. For general trajectories the choice of weight should be done on a case-by-case basis.

2017 ◽  
Vol 46 (7) ◽  
pp. 20170030 ◽  
Author(s):  
Cosimo Nardi ◽  
Cinzia Talamonti ◽  
Stefania Pallotta ◽  
Paola Saletti ◽  
Linda Calistri ◽  
...  

Author(s):  
Aditya Shetty ◽  
Raksha Bhat ◽  
Bessy Babu ◽  
Mithra N. Hegde ◽  
Chitharanjan Shetty ◽  
...  

Abstract Introduction Molars have been known to display varied morphologies. Maxillary first molar is the tooth with the largest volume and most complex root and root canal anatomy; also, possibly the most treated and least understood posterior tooth. The present study aimed to investigate the occurrence and morphology of MB2 canals in maxillary first molars in an Indian subpopulation (Dakshina kannada) using cone beam CT (CBCT) imaging. Materials and Methods A total of 330 maxillary molars were placed on “U-” shaped modelling wax template, mimicking the natural arch and digitally scanned, of which 196 scans met the inclusion criteria and were analyzed for unusual root canal anatomy by CBCT. To analyze the occurrence and morphology of the canals, the acquired data was examined by two endodontists and discussed till an agreement was reached. Results The results were subjected to descriptive analysis. The majority of patients 103 (52.6%) teeth showed the presence of MB2 canals. As much as 83.5% of teeth depicted Vertucci's type II morphology, and 16.5% teeth presented with Vertucci's type IV morphology. Conclusion CBCT overcomes the limitations of conventional radiography. However, the decision to use CBCT in the management of endodontic problems must be based on a case-by-case basis and only when sufficient diagnostic information is not obtained from diagnostic tests.


Author(s):  
Miet Loubele ◽  
Frederik Maes ◽  
Filip Schutyser ◽  
Guy Marchal ◽  
Reinhilde Jacobs ◽  
...  

2013 ◽  
Vol 791-793 ◽  
pp. 2053-2057
Author(s):  
Li Sun ◽  
Ya Juan Guo ◽  
Xiao Ju Liu ◽  
Hong Bo Li ◽  
Lin Liu ◽  
...  

Objectives The aim of this study was to compare 3D accuracy of tooth image reconstruction from three kinds of CT scans using 3D superimpositional method. Methods 18 sound extracted human teeth were scanned by 3D optical system, spiral CT, micro-CT, and cone-beam CT scanner. The digital teeth images reconstructed from three kinds of CT scans were superimposed onto the standard image from optical scans respectively. Distribution patterns of shape discrepancy were presented using histogram, as well as showed in different colors on the superimposed imagines. The ratio of voluminal discrepancy versus the volume of the standard image (RVD/VS) was calculated and analyzed, using the matched-pair t-test and rank sum test. Results Compared with the standard tooth image, the average RVD/VS of digital teeth images by the micro-CT, cone-beam CT, spiral CT scans were 5.11%, 20.73%, 24.60% respectively, and there were statistically significant difference among the three kinds of CT scans (P<0.01). Significant difference were also found among the anterior teeth, bicuspids, and molars (P<0.01). Histogram gave the description about the counts and magnitude of the discrepancies. Marked by difference colors, the superimposed images could give visualized information about the magnitude and distribution patterns of discrepancies. Conclusions The digital teeth models reconstructed from the spiral CT, micro-CT, cone-beam CT images are inhomogeneous enlarged, compared with the original models. As the only realizable way to individualized FEM analysis, tooth modeling by CT scans needs more efforts and refinements to improve its accuracy.


2000 ◽  
Vol 19 (5) ◽  
pp. 361-375 ◽  
Author(s):  
S. Schaller ◽  
F. Noo ◽  
F. Sauer ◽  
K.C. Tam ◽  
G. Lauritsch ◽  
...  

2011 ◽  
Vol 23 (2) ◽  
pp. 83 ◽  
Author(s):  
Kai Zeng ◽  
Zhiqiang Chen

Long-object problem and short-object problem both deal with reconstruction problems with truncated conebeam CT projections acquired with a helical path. They have significantly less practical limitations than original exact cone-beam CT reconstruction algorithms which the cone-beam must cover the whole object. The short-object problem can be defined as reconstruction of the whole object having a finite support in the axial direction with helical scan extends a little bit above and below the object's support. However the longobject problem is to reconstruct the central region of interest (ROI) of a long object having an infinite support in the axial direction with helical scan extends a little a bit above and below the ROI. Although the short-object problem is more difficult to solve than the conventional exact reconstruction with non-truncated projections, the long-object problem presents greater challenge to researchers. Recently, with the great development of panel detector technology and computer technology, more and more researchers have been inspired to work on it. Because of great practical value of long-object algorithms, this paper focuses on the review and discussion of recent developments in long-object algorithms. All Long-object algorithms are classified as exact and approximate algorithms. After going briefly over the history of cone-beam algorithms, some novel cone-beam long-object algorithms are introduced, such as: Tam's algorithm, PImethod, PHI-method, etc. Then, the methods described are being compared and discussed.


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