DALM, Deformable Attenuation-Labeled Mesh for Tomographic Reconstruction and Segmentation

Most X-ray tomographic reconstruction methods represent a solution as an image on a regular grid. Such representation may be inefficient for reconstructing homogeneous objects from noisy or incomplete projections. Here, we propose a mesh-based method for reconstruction and segmentation of homogeneous objects directly from sinogram data. The outcome of our proposed method consists of curves outlining the regions of constant attenuation, and this output is represented using a labeled irregular triangle mesh. We find the solution by deforming the mesh to minimize the residual given by the sinogram data. Our method supports multiple materials, and allows for topological changes during deformation. An integral part of our algorithm is an efficient forward projection of the labeled mesh onto the sinogram domain. We initialize our algorithm based on graph total variation, also here taking advantage of the mesh representation. Experimental results on simulated datasets show that our method gives a compact representation of the reconstruction and also accurate segmentation results for challenging data with e.g. large noise, a small number of angles or problems with limited angle. We also demonstrate the result on real fan-beam data. The proposed geometric solution shows a further step towards using alternative representations for tomographic reconstruction.

[1]  Per Christian Hansen,et al.  Computing segmentations directly from x-ray projection data via parametric deformable curves , 2018 .

[2]  Kees Joost Batenburg,et al.  SDART: An algorithm for discrete tomography from noisy projections , 2014, Comput. Vis. Image Underst..

[3]  Gabor T. Herman,et al.  Fundamentals of Computerized Tomography: Image Reconstruction from Projections , 2009, Advances in Pattern Recognition.

[4]  Kees Joost Batenburg,et al.  TVR-DART: A More Robust Algorithm for Discrete Tomography From Limited Projection Data With Automated Gray Value Estimation , 2016, IEEE Transactions on Image Processing.

[5]  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.

[6]  W. Clem Karl,et al.  Variable splitting techniques for discrete tomography , 2016, 2016 IEEE International Conference on Image Processing (ICIP).

[7]  W. Clem Karl,et al.  Graph-Cut Based Discrete-Valued Image Reconstruction , 2015, IEEE Transactions on Image Processing.

[8]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[9]  Christopher V. Alvino,et al.  Tomographic reconstruction of piecewise smooth images , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[10]  Long Wei,et al.  A Joint Reconstruction and Segmentation Method for Limited-Angle X-Ray Tomography , 2018, IEEE Access.

[11]  Yongyi Yang,et al.  Tomographic image reconstruction based on a content-adaptive mesh model , 2004, IEEE Transactions on Medical Imaging.

[12]  A Sitek,et al.  Practical implementation of tetrahedral mesh reconstruction in emission tomography. , 2013, Physics in medicine and biology.

[13]  Christoph Schnörr,et al.  TomoGC: Binary Tomography by Constrained GraphCuts , 2015, GCPR.

[14]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[15]  Kees Joost Batenburg,et al.  A semi-automatic algorithm for grey level estimation in tomography , 2011, Pattern Recognit. Lett..

[16]  Pierre Vandergheynst,et al.  Adaptive Graph-Based Total Variation for Tomographic Reconstructions , 2016, IEEE Signal Processing Letters.

[17]  Eric L. Miller,et al.  Parametric Level Set Methods for Inverse Problems , 2010, SIAM J. Imaging Sci..

[18]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[19]  R. Fahrig,et al.  Simultaneous segmentation and reconstruction: a level set method approach for limited view computed tomography. , 2010, Medical physics.

[20]  Samuli Siltanen,et al.  Tomographic X-ray data of carved cheese , 2017, 1705.05732.

[21]  A. Pressley Elementary Differential Geometry , 2000 .

[22]  Jakob Andreas Bærentzen,et al.  Topology-adaptive interface tracking using the deformable simplicial complex , 2012, TOGS.

[23]  T. Pan Computed Tomography: from Photon Statistics to Modern Cone-Beam CT , 2009, Journal of Nuclear Medicine.

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

[25]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[26]  Tai Sing Lee,et al.  Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation , 1995, Proceedings of IEEE International Conference on Computer Vision.

[27]  Sylvie Sevestre,et al.  Adapted sampling for 3D X-ray computed tomography , 2015, ArXiv.

[28]  Daniel J Ching,et al.  XDesign: an open-source software package for designing X-ray imaging phantoms and experiments. , 2017, Journal of synchrotron radiation.

[29]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[30]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[31]  Ronald H. Huesman,et al.  Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud , 2006, IEEE Transactions on Medical Imaging.

[32]  Jan Sijbers,et al.  Fast and flexible X-ray tomography using the ASTRA toolbox. , 2016, Optics express.

[33]  Kees Joost Batenburg,et al.  The reconstructed residual error: A novel segmentation evaluation measure for reconstructed images in tomography , 2014, Comput. Vis. Image Underst..

[34]  François Lauze,et al.  Simultaneous Reconstruction and Segmentation of CT Scans with Shadowed Data , 2017, SSVM.

[35]  Kees Joost Batenburg,et al.  DART: A Practical Reconstruction Algorithm for Discrete Tomography , 2011, IEEE Transactions on Image Processing.

[36]  Ross T. Whitaker,et al.  A direct approach to estimating surfaces in tomographic data , 2002, Medical Image Anal..

[37]  Kees Joost Batenburg,et al.  A Parametric Level-Set Method for Partially Discrete Tomography , 2017, DGCI.

[38]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[39]  A Sitek,et al.  Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method. , 2010, Physics in medicine and biology.