Le but de cette étude est de comparer le respect de la morphologie canalaire après instrumentation à l’aide de trois systèmes de mise en forme canalaire différents : le One Shape NEW Generation®, le Wave One® et le Revo-S® grâce à une étude en Micro-tomographie assistée par ordinateur ou micro-CT (Computed Tomography). La mise en place d’une chaîne méthodologique totalement tridimensionnelle (3D) comprenant la reconstruction, le recalage et la segmentation a permis de traiter les images acquises et d’extraire les images recalées des canaux dentaires avant et après instrumentation. Les artéfacts de segmentation dus aux calcifications et aux débris dentinaires ont été traités. Une méthode d’estimation des zones non instrumentées a également été décrite.Le transport canalaire a été calculé pour chaque coupe de chaque tiers radiculaire, en comparant la position du centroïde avant et après instrumentation. La comparaison des moyennes de transport canalaire ne montre pas de différence significative entre les 3 systèmes d’instrumentation.Cette approche méthodologique en 4 parties a permis de valider un protocole d’imagerie 3D reproductible, qui pourra être appliqué in vitro en recherche endodontique dans l’analyse des effets instrumentaux. / The aim of this study is to compare the respect of the root canal morphology after instrumentation with different shaping systems (One Shape NEW Generation®, Wave One® and Revo-S®), by using Micro-Computed Tomography.We used a fully three-dimensional (3D) methodological process which involved the reconstruction, registration and segmentation. By this methodological process, images have been acquired and processed in order to extract registered canals images before and after the instrumentation. The segmentation artifacts like calcifications and debris have been taken into account. A method to estimate the non-instrumented zones is also described.The canal transportation was calculated for each slice of each root-third by comparing the position of the centroids before and after instrumentation. No significant difference was found between the three instrumentation systems when canal transport means were done.This 4-part methodological approach has enabled the validation of a reproducible 3D imaging protocol. This can be applied in vitro in endodontic research for analysis of the instrumental effects.

Filtered backprojection (FBP) reconstruction algorithms are very popular in the field of X-ray computed tomography (CT) because they give advantages in terms of the numerical accuracy and computational complexity. Ramp filter based fan-beam FBP reconstruction algorithms have the position dependent weight in the backprojection which is responsible for spatially non-uniform distribution of noise and resolution, and artifacts. Many algorithms based on shift variant filtering or spatially-invariant interpolation in the backprojection step have been developed to deal with this issue. However, these algorithms are computationally demanding. Recently, fan-beam algorithms based on Hilbert filtering with inverse distance weight and no weight in the backprojection have been derived using the Hamaker’s relation. These fan-beam reconstruction algorithms have been shown to improve noise uniformity and uniformity in resolution. In this thesis, fan-beam FBP reconstruction algorithms with inverse distance back-projection weight and no backprojection weight for 2D image reconstruction are presented and discussed for the two fan-beam scan geometries -equi-angular and equispace detector array. Based on the proposed and discussed fan-beam reconstruction algorithms with inverse distance backprojection and no backprojection weight, new 3D cone-beam FDK reconstruction algorithms with circular and helical scan trajectories for curved and planar detector geometries are proposed. To start with three rebinning formulae from literature are presented and it is shown that one can derive all fan-beam FBP reconstruction algorithms from these rebinning formulae. Specifically, two fan-beam algorithms with no backprojection weight based on Hilbert filtering for equi-space linear array detector and one new fan-beam algorithm with inverse distance backprojection weight based on hybrid filtering for both equi-angular and equi-space linear array detector are derived. Simulation results for these algorithms in terms of uniformity of noise and resolution in comparison to standard fan-beam FBP reconstruction algorithm (ramp filter based fan-beam reconstruction algorithm) are presented. It is shown through simulation that the fan-beam reconstruction algorithm with inverse distance in the backprojection gives better noise performance while retaining the resolution properities. A comparison between above mentioned reconstruction algorithms is given in terms of computational complexity. The state of the art 3D X-ray imaging systems in medicine with cone-beam (CB) circular and helical computed tomography scanners use non-exact (approximate) FBP based reconstruction algorithm. They are attractive because of their simplicity and low computational cost. However, they produce sub-optimal reconstructed images with respect to cone-beam artifacts, noise and axial intensity drop in case of circular trajectory scan imaging. Axial intensity drop in the reconstructed image is due to the insufficient data acquired by the circular-scan trajectory CB CT. This thesis deals with investigations to improve the image quality by means of the Hilbert and hybrid filtering based algorithms using redundancy data for Feldkamp, Davis and Kress (FDK) type reconstruction algorithms. In this thesis, new FDK type reconstruction algorithms for cylindrical detector and planar detector for CB circular CT are developed, which are obtained by extending to three dimensions (3D) an exact Hilbert filtering based FBP algorithm for 2D fan-beam beam algorithms with no position dependent backprojection weight and fan-beam algorithm with inverse distance backprojection weight. The proposed FDK reconstruction algorithm with inverse distance weight in the backprojection requires full-scan projection data while the FDK reconstruction algorithm with no backprojection weight can handle partial-scan data including very short-scan. The FDK reconstruction algorithms with no backprojection weight for circular CB CT are compared with Hu’s, FDK and T-FDK reconstruction algorithms in-terms of axial intensity drop and computational complexity. The simulation results of noise, CB artifacts performance and execution timing as well as the partial-scan reconstruction abilities are presented. We show that FDK reconstruction algorithms with no backprojection weight have better noise performance characteristics than the conventional FDK reconstruction algorithm where the backprojection weight is known to result in spatial non-uniformity in the noise characteristics. In this thesis, we present an efficient method to reduce the axial intensity drop in circular CB CT. The efficient method consists of two steps: the first one is reconstruction of the object using FDK reconstruction algorithm with no backprojection weight and the second is estimating the missing term. The efficient method is comparable to Zhu et al.’s method in terms of reduction in axial intensity drop, noise and computational complexity. The helical scanning trajectory satisfies the Tuy-smith condition, hence an exact and stable reconstruction is possible. However, the helical FDK reconstruction algorithm is responsible for the cone-beam artifacts since the helical FDK reconstruction algorithm is approximate in its derivation. In this thesis, helical FDK reconstruction algorithms based on Hilbert filtering with no backprojection weight and FDK reconstruction algorithm based on hybrid filtering with inverse distance backprojection weight are presented to reduce the CB artifacts. These algorithms are compared with standard helical FDK in-terms of noise, CB artifacts and computational complexity.

This work focuses on using the linear prediction based projection completion for the fan-beam and cone-beam reconstruction algorithm with no backprojection weight. The truncated data problems are addressed in the computed tomography research. However, the image reconstruction from truncated data perfectly has not been achieved yet and only approximately accurate solutions have been obtained. Thus research in this area continues to strive to obtain close result to the perfect. Linear prediction techniques are adopted for truncation completion in this work, because previous research on the truncated data problems also have shown that this technique works well compared to some other techniques like polynomial fitting and iterative based methods. The Linear prediction technique is a model based technique. The autoregressive (AR) and moving average (MA) are the two important models along with autoregressive moving average (ARMA) model. The AR model is used in this work because of the simplicity it provides in calculating the prediction coefficients. The order of the model is chosen based on the partial autocorrelation function of the projection data proved in the previous researches that have been carried out in this area of interest. The truncated projection completion using linear prediction and windowed linear prediction show that reasonably accurate reconstruction is achieved. The windowed linear prediction provide better estimate of the missing data, the reason for this is mentioned in the literature and is restated for the reader’s convenience in this work. The advantages associated with the fan-beam reconstruction algorithms with no backprojection weights compared to the fan-beam reconstruction algorithm with backprojection weights motivated us to use the fan-beam reconstruction algorithm with no backprojection weight for reconstructing the truncation completed projection data. The results obtained are compared with the previous work which used conventional fan-beam reconstruction algorithms with backprojection weight. The intensity plots and the noise performance results show improvements resulting from using the fan-beam reconstruction algorithm with no backprojection weight. The work is also extended to the Feldkamp, Davis, and Kress (FDK) reconstruction algorithm with no backprojection weight for the helical scanning geometry and the results obtained are compared with the FDK reconstruction algorithm with backprojection weight for the helical scanning geometry.