1 / 21

Reconstruction of objects containing circular cross-sections

Reconstruction of objects containing circular cross-sections. Lajos Rodek rodek@inf.u-szeged.hu. Supervisor: Attila Kuba Ph.D. University of Szeged, Hungary, Department of Applied Informatics. Zoltán Kiss kissz@inf.u-szeged.hu. SSIP 2003. The encountered problem. Tomography.

tory
Download Presentation

Reconstruction of objects containing circular cross-sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Reconstruction of objects containing circular cross-sections Lajos Rodek rodek@inf.u-szeged.hu Supervisor: Attila Kuba Ph.D. University of Szeged, Hungary, Department of Applied Informatics Zoltán Kiss kissz@inf.u-szeged.hu SSIP 2003

  2. The encountered problem • Tomography • Nondestructive substance examination • Neutron mapping Draft structure of the 3D object A cross-section to be reconstructed Result of a classic method • Using few projections (acquisition is time consuming and expensive)

  3. Reconstruction of 3D objects • Discrete tomography • Input: few projections (2-4) • a priori information: • geometrical structure (spheres) • range (attenuation coefficients) • Output: 3D model

  4. Reduction to 2D • Subproblem: reconstruction of 2D cross-sections • Assumptions: • known number of circles • at most four different substances

  5. Acquisition of projections • Projection: • Given: projections (p), directions, number of beams • Unknown: F, implicit parametric function to be reconstructed (4-valued)

  6. Parametres of F • Number of circles • Attenuation coefficients • Radii • Centres • Restrictions: • disjointness • minimal & maximal radii • circles are within the ring

  7. Mathematical description • Given:few projections with known number of circles & beams • Sought solution: configuration of parametres, which determines a function having projections of the best approximation of input data (p) ?

  8. Difficulties • Switching components • Superposition of projections • Noisy input data

  9. Implemented algorithm • Considered as optimization problem • Iteratively looking for a global optimum by random modification of parametres from an initial configuration

  10. Choosing a new configuration Adjustment of radius, centre or attenuation coef. of one of the circles, in agreement with the restrictions radius centre attenuation coefficient

  11. Optimization • Objective function: • Random choice of a new configuration • If , will be accepted • Else choosing another • Termination, if or no better solution is found in a certain number of iteration steps

  12. Simulated annealing • Fundaments: thermodynamic cooling process • Boltzmann-distribution: (1) • If , will be accepted in accordance with (1)

  13. Simulation studies

  14. Effects of changing the number of projections using 2, 3 & 4 noiseless projections Real conf. Initial conf. Reconstructed conf. Difference 2 projs 3 projs 4 projs

  15. Effects of noise Additive noise of uniform distribution 0% 5% 10% 20%

  16. Results from noisy projections using 4 projections, in case of 5, 20 & 40% of noise Real conf. Initial conf. Reconstructed conf. Difference Noise 5% 20% 40%

  17. Results on real measurements

  18. Encountered problems on real data • Precessing axis of revolution • Distorted, noisy projections • Low resolution • Too few quantization levels • Attenuation coefs are unknown  they should be estimated automatically

  19. Data from Berliner Hahn-Meitner Institut 0 45 90 135 Result of convolution backprojection from 60 projections Result of our method from 4 projections seen above

  20. Summary • A new reconstruction method has been implemented based on real physical measurements: • the effects of increasing the number of circles, projections & the amount of noise have been examined • Good results may be achieved from 4 projections even in case of greater amount of noise • Future plans: • extension to 3D • deformable models

  21. References • A. Kuba, L. Ruskó, Z. Kiss, L. Rodek, E. Balogh, S. Zopf, A. Tanács: Preliminary Results in Discrete Tomography Applied for Neutron Tomography, COST Meeting on Neutron Radiography, Loughborogh, England, 2002. • A. Kuba, L. Ruskó, L. Rodek, Z. Kiss: Preliminary Studies of Discrete Tomography in Neutron Imaging, IEEE Trans. on Nuclear Sciences, submitted • A. Kuba, L. Ruskó, L. Rodek, Z. Kiss: Application of Discrete Tomography in Neutron Imaging, Proc. of 7th World Conference on Neutron Radiography, Rome, Italy, 2002., accepted • Kiss Z., Kuba A., Rodek L.: Körmetszeteket tartalmazó tárgyak rekonstrukciója néhány vetületből, KÉPAF Konferencia kiadvány, Domaszék, Hungary 2002. Homepage of DIRECT: http://www.inf.u-szeged.hu/~direct

More Related