Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform

1991 ◽  
pp. 66-97 ◽  
Author(s):  
Pierre Grangeat
Keyword(s):  
3D Reconstruction ◽  
Radon Transform ◽  
Cone Beam ◽  
Mathematical Framework ◽  
First Derivative

NDT Applications of the 3D Radon Transform Algorithm for Cone Beam Reconstruction

1990 ◽  
Vol 217 ◽  
Author(s):  
P. Sire ◽  
P. Grangeat ◽  
P. Lemasson ◽  
P. Mélennec ◽  
P. Rizo
Keyword(s):  
Basic Principle ◽  
Radon Transform ◽  
Cone Beam ◽  
Imaging Processing ◽  
X Ray ◽  
First Derivative ◽  
X Ray Imaging ◽  
Cone Beam Reconstruction ◽  
Scientific Computer ◽  
Theoretical Developments

ABSTRACTThe paper describes our 3D X-ray CT algorithm “RADON” using attenuation measurements acquired with a bidimensional detector. Our inversion diagram uses the first derivative of the Radon transform synthesis then its inversion. The potentiality of that new method, particularly for the large aperture, prompted us to develop an optimized software offering convenience and high performances on a modem scientific computer. After a brief recall of the basic principle of X-ray imaging processing, we will introduce the theoretical developments resulting in the present inversion diagram. A general algorithm structure will be proposed afterwards. As a conclusion we will present the performances and the results obtained with ceramic rotors examination.

scholarly journals Evaluation of accuracy of 3D reconstruction images using multi-detector CT and cone-beam CT

2012 ◽  
Vol 42 (1) ◽  
pp. 25 ◽  
Author(s):  
Mija Kim ◽  
Kyung-Hoe Huh ◽  
Won-Jin YI ◽  
Min-Suk Heo ◽  
Sam-Sun Lee ◽  
...  
Keyword(s):  
3D Reconstruction ◽  
Cone Beam Ct ◽  
Cone Beam

scholarly journals Cone Beam Computed Tomography 3D Reconstruction of the Mandibular Condyle

2008 ◽  
Vol 78 (5) ◽  
pp. 880-888 ◽  
Author(s):  
Brian Schlueter ◽  
Ki Beom Kim ◽  
Donald Oliver ◽  
Gus Sortiropoulos
Keyword(s):  
Computed Tomography ◽  
Soft Tissue ◽  
3D Reconstruction ◽  
Cone Beam Computed Tomography ◽  
Three Dimensional ◽  
Mandibular Condyle ◽  
Cone Beam ◽  
Low Density ◽  
Mineral Density ◽  
Linear Measurements

Abstract Objective: To determine the ideal window level and width needed for cone beam computed three-dimensional (3D) reconstruction of the condyle. Materials and Methods: Linear dimensions were measured with a digital caliper to assess the anatomic truth for 50 dry human mandibular condyles. Condyles were scanned with the i-CAT cone beam computed tomography (CBCT) and 3D-models were reconstructed. Three linear three-dimensional measurements were made on each of the 50 condyles at 8 different Hounsfield unit (HU) windows. These measurements were compared with the anatomic truth. Volumetric measurements were also completed on all 50 condyles, at 23 different window levels, to define the volumetric distribution of bone mineral density (BMD) within the condyle. Results: Significant differences were found in two of the three linear measurement groups at and below the recommended viewing window for osseous structures. The most accurate measurements were made within the soft tissue range for HU window levels. Volumetric distribution measurements revealed that the condyles were mostly comprised of low-density bone, and that condyles exhibiting significant changes in linear measurements were shown to have higher percentages of low-density bone than those condyles with little change from the anatomic truth. Conclusions: CBCT assessment of the mandibular condyle, using the 3D reconstruction, is most accurate when accomplished at density levels below that recommended for osseous examination. However, utilizing lower window levels which extend into the soft tissue range, may compromise one's capacity to view the bony topography.

scholarly journals Impacts of Thresholds of Gray Value for Cone-Beam Computed Tomography 3D Reconstruction on the Accuracy of Image Matching with Optical Scan

2020 ◽  
Vol 17 (17) ◽  
pp. 6375 ◽  
Author(s):  
Se-Won Park ◽  
Ra Gyoung Yoon ◽  
Hyunwoo Lee ◽  
Heon-Jin Lee ◽  
Yong-Do Choi ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Image Registration ◽  
3D Reconstruction ◽  
Cone Beam Computed Tomography ◽  
Cone Beam ◽  
Dental Arch ◽  
Arch Model ◽  
3D Mesh ◽  
Optical Scan ◽  
Reconstruction Model

In cone-beam computed tomography (CBCT), the minimum threshold of the gray value of segmentation is set to convert the CBCT images to the 3D mesh reconstruction model. This study aimed to assess the accuracy of image registration of optical scans to 3D CBCT reconstructions created by different thresholds of grey values of segmentation in partial edentulous jaw conditions. CBCT of a dentate jaw was reconstructed to 3D mesh models using three different thresholds of gray value (−500, 500, and 1500), and three partially edentulous models with different numbers of remaining teeth (4, 8, and 12) were made from each 3D reconstruction model. To merge CBCT and optical scan data, optical scan images were registered to respective 3D reconstruction CBCT images using a point-based best-fit algorithm. The accuracy of image registration was assessed by measuring the positional deviation between the matched 3D images. The Kruskal–Wallis test and a post hoc Mann–Whitney U test with Bonferroni correction were used to compare the results between groups (α = 0.05). The correlations between the experimental factors were calculated using the two-way analysis of variance test. The positional deviations were lowest with the threshold of 500, followed by the threshold of 1500, and then −500. A significant interaction was found between the threshold of gray values and the number of remaining teeth on the registration accuracy. The most significant deviation was observed in the arch model with four teeth reconstructed with a gray-value threshold of −500. The threshold for the gray value of CBCT segmentation affects the accuracy of image registration of optical scans to the 3D reconstruction model of CBCT. The appropriate gray value that can visualize the anatomical structure should be set, especially when few teeth remain in the dental arch.

3D reconstruction images of cone beam computed tomography applied to maxillofacial fractures: A case study and mini review

2018 ◽  
Vol 26 (1) ◽  
pp. 115-123 ◽  
Author(s):  
Liyun Bai ◽  
Linlin Li ◽  
Kexin Su ◽  
Anthony Bleyer ◽  
Yuanyuan Zhang ◽  
...  
Keyword(s):  
Computed Tomography ◽  
3D Reconstruction ◽  
Cone Beam Computed Tomography ◽  
Cone Beam ◽  
Maxillofacial Fractures

Comparison of three 3D-Reconstruction Methods from Cone-Beam Data

1996 ◽  
pp. 3-18 ◽  
Author(s):  
Caroline Axelsson-Jacobson ◽  
Regis Guillemaud ◽  
Per-Erik Danielsson ◽  
Pierre Grangeat ◽  
Michel Defrise ◽  
...  
Keyword(s):  
3D Reconstruction ◽  
Cone Beam ◽  
Reconstruction Methods

scholarly journals The Formula of Grangeat for Tensor Fields of Arbitrary Order innDimensions

2007 ◽  
Vol 2007 ◽  
pp. 1-4 ◽  
Author(s):  
T. Schuster
Keyword(s):  
Radon Transform ◽  
Tensor Field ◽  
Arbitrary Order ◽  
Cone Beam ◽  
Inversion Method ◽  
Tensor Fields ◽  
Arbitrary Tensor

The cone beam transform of a tensor field of orderminn≥2dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of then-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces form=0andn=3to the well-known formula of Grangeat. In that sense, the paper contains a generalization of Grangeat's formula to arbitrary tensor fields in any dimension. We further briefly explain the importance of that formula for the problem of tensor field tomography. Unfortunately, form>0, an inversion method cannot be derived immediately. Thus, we point out the possibility to calculate reconstruction kernels for the cone beam transform using Grangeat's formula.

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