Joint Reconstruction and Segmentation of Real 3D Data in Computed Tomography thanks to a Gauss-Markov-Potts Prior Model,

Computed Tomography is a powerful tool to reconstruct a volume in 3D and has a wide field of applications in industry for non-destructive testing. In these applications, the reconstruction process has a key importance to retrieve volumes that can be easily analyzed during the control. In this paper, in order to improve the reconstruction quality, we present a Gauss-Markov- Potts prior model for the object to reconstruct in a Bayesian framework. This model leads to a joint reconstruction and segmentation algorithm which is briefly described. The core of the paper is the application of the algorithm on real 3D data. We show that our method obtains better results than other state-ofart methods. We also propose reconstruction quality indicators without reference which uses both reconstruction and segmentation returned by the algorithm.

[1]  Michael Unser,et al.  Joint image reconstruction and segmentation using the Potts model , 2014, 1405.5850.

[2]  L. Bregman The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[3]  Thomas Rodet Algorithmes rapides de reconstruction en tomographie par compression des calculs : application à la tomofluoroscopie 3D , 2002 .

[4]  Jean-François Giovannelli Estimation of the Ising field parameter thanks to the exact partition function , 2010, 2010 IEEE International Conference on Image Processing.

[5]  Kennan T. Smith,et al.  Mathematical foundations of computed tomography. , 1985, Applied optics.

[6]  Keinosuke Fukunaga,et al.  A Graph-Theoretic Approach to Nonparametric Cluster Analysis , 1976, IEEE Transactions on Computers.

[7]  Ali Mohammad-Djafari,et al.  Joint NDT Image Restoration and Segmentation Using Gauss–Markov–Potts Prior Models and Variational Bayesian Computation , 2009, IEEE Transactions on Image Processing.

[8]  A. Kak,et al.  Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the Art Algorithm , 1984, Ultrasonic imaging.

[9]  Ali Mohammad-Djafari,et al.  Variational Bayes and Mean Field Approximations for Markov field unsupervised estimation , 2009, 2009 IEEE International Workshop on Machine Learning for Signal Processing.

[10]  Bülent Sankur,et al.  Color image segmentation using histogram multithresholding and fusion , 2001, Image Vis. Comput..

[11]  Ali Mohammad-Djafari,et al.  A 3D Bayesian Computed Tomography Reconstruction Algorithm with Gauss-Markov-Potts Prior Model and its Application to Real Data , 2017, Fundam. Informaticae.

[12]  Matthias Franz,et al.  Reducing non-linear artifacts of multi-material objects in industrial 3D computed tomography , 2008 .

[13]  G Demoment,et al.  Maximum entropy image reconstruction in X-ray and diffraction tomography. , 1988, IEEE transactions on medical imaging.

[14]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[15]  L. Feldkamp,et al.  Practical cone-beam algorithm , 1984 .

[16]  E. Sidky,et al.  Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle–Pock algorithm , 2011, Physics in medicine and biology.

[17]  Ali Mohammad-Djafari,et al.  Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data , 2005 .

[18]  P. Gilbert Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.