3D particle volume tomographic reconstruction based on marked point process: Application to Tomo-PIV in fluid mechanics

In recent years, marked point processes have received a great deal of attention. They were applied with success to extract objects in large data sets as those obtained in remote sensing frameworks or biological studies. We propose in this paper a method based on marked point processes to reconstruct volumes of 3D particles from images of 2D particles provided by the Tomographic Particle Image Velocimetry (Tomo-PIV) technique. Unlike other reconstruction methods, our approach allows us to solve the problem in a parsimonious way. It facilitates the introduction of prior knowledge and naturally solves the memory problem which is inherent to pixel based approach used by classical tomographic reconstruction methods. The best reconstruction is found by minimizing an energy function which defines the marked point process. In order to avoid local minima, we use a simulated annealing algorithm. Results are presented on simulated data.

[1]  van Marie-Colette Lieshout,et al.  Markov Point Processes and Their Applications , 2000 .

[2]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

[3]  Josiane Zerubia,et al.  A Gibbs Point Process for Road Extraction from Remotely Sensed Images , 2004, International Journal of Computer Vision.

[4]  A. Baddeley,et al.  Stochastic geometry models in high-level vision , 1993 .

[5]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[7]  Julien Dombre,et al.  Simple Library of Image Processing (SLIP) , 2010 .

[8]  Jeffrey D. Scargle,et al.  An Introduction to the Theory of Point Processes, Vol. I: Elementary Theory and Methods , 2004, Technometrics.

[9]  Ulrike Goldschmidt,et al.  An Introduction To The Theory Of Point Processes , 2016 .

[10]  Robert T. Collins,et al.  Marked point processes for crowd counting , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  Bernhard Wieneke,et al.  Tomographic particle image velocimetry , 2006 .

[12]  B. Wieneke.  Iterative reconstruction of volumetric particle distribution , 2013 .

[13]  Josiane Zerubia,et al.  2D and 3D Vegetation Resource Parameters Assessment using Marked Point Processes , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[14]  Julio Soria,et al.  An efficient simultaneous reconstruction technique for tomographic particle image velocimetry , 2009 .

[15]  Nicholas A. Worth,et al.  Acceleration of Tomo-PIV by estimating the initial volume intensity distribution , 2008 .

[16]  Robert Azencott,et al.  Simulated annealing : parallelization techniques , 1992 .

[17]  A. Lent,et al.  Iterative reconstruction algorithms. , 1976, Computers in biology and medicine.

[18]  Olivier Alata,et al.  Grouping/degrouping point process, a point process driven by geometrical and topological properties of a partition in regions , 2011, Comput. Vis. Image Underst..

[19]  C. Preston.  Spatial birth and death processes , 1975, Advances in Applied Probability.

[20]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[21]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[22]  Hans-Gerd Maas,et al.  DETERMINATION OF VERY DENSE PARTICLE VELOCITY FIELDS BY TOMOGRAPHIC RECONSTRUCTION FROM FOUR CAMERA VIEWS AND VOXEL SPACE TRACKING , 2008 .

[23]  J. Mateu,et al.  Detection of cosmic filaments using the Candy model , 2004, astro-ph/0405370.

[24]  R. Gordon.  A tutorial on art (algebraic reconstruction techniques) , 1974 .

[25]  Robert T. Collins,et al.  Marked point processes for crowd counting , 2009, CVPR.

[26]  Olivier J. J. Michel,et al.  A Bayesian marked point process for object detection. Application to muse hyperspectral data , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).