Stochastic tomography and its applications in 3D imaging of mixing fluids

We present a novel approach for highly detailed 3D imaging of turbulent fluid mixing behaviors. The method is based on visible light computed tomography, and is made possible by a new stochastic tomographic reconstruction algorithm based on random walks. We show that this new stochastic algorithm is competitive with specialized tomography solvers such as SART, but can also easily include arbitrary convex regularizers that make it possible to obtain high-quality reconstructions with a very small number of views. Finally, we demonstrate that the same stochastic tomography approach can also be used to directly re-render arbitrary 2D projections without the need to ever store a 3D volume grid.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[3]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[4]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

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

[6]  Leonidas J. Guibas,et al.  Metropolis light transport , 1997, SIGGRAPH.

[7]  I. Grant Particle image velocimetry: A review , 1997 .

[8]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[9]  Kiriakos N. Kutulakos,et al.  Photo-consistent 3D fire by Flame-Sheet decomposition , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[10]  Marcus A. Magnor,et al.  Image-based tomographic reconstruction of flames , 2004, SIGGRAPH '04.

[11]  Marcus A. Magnor,et al.  Reconstructing the geometry of flowing water , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[12]  Parris K. Egbert,et al.  Energy redistribution path tracing , 2005, SIGGRAPH 2005.

[13]  Paul Debevec,et al.  Acquisition of time-varying participating media , 2005, SIGGRAPH 2005.

[14]  Kiriakos N. Kutulakos,et al.  Dynamic Refraction Stereo , 2005, ICCV.

[15]  Derek Bradley,et al.  Tomographic reconstruction of transparent objects , 2006, SIGGRAPH '06.

[16]  Kiriakos N. Kutulakos,et al.  Photo-Consistent Reconstruction of Semitransparent Scenes by Density-Sheet Decomposition , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Hans-Peter Seidel,et al.  Marker-less Deformable Mesh Tracking for Human Shape and Motion Capture , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[18]  Wojciech Matusik,et al.  Multi-scale capture of facial geometry and motion , 2007, ACM Trans. Graph..

[19]  D. Forsyth,et al.  Capturing and animating occluded cloth , 2007, SIGGRAPH '07.

[20]  Hans-Peter Seidel,et al.  Time-resolved 3d capture of non-stationary gas flows , 2008, SIGGRAPH 2008.

[21]  Derek Bradley,et al.  Markerless garment capture , 2008, SIGGRAPH 2008.

[22]  Hans-Peter Seidel,et al.  Performance capture from sparse multi-view video , 2008, ACM Trans. Graph..

[23]  Hengyong Yu,et al.  Compressed sensing based interior tomography , 2009, Physics in medicine and biology.

[24]  Paul Debevec,et al.  The Digital Emily project: photoreal facial modeling and animation , 2009, SIGGRAPH '09.

[25]  G. Turk,et al.  Physically guided liquid surface modeling from videos , 2009, SIGGRAPH 2009.

[26]  Derek Bradley,et al.  Synchronization and rolling shutter compensation for consumer video camera arrays , 2009, 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[27]  A. Srinivasan,et al.  Monte Carlo linear solvers with non-diagonal splitting , 2010, Math. Comput. Simul..

[28]  Xuanqin Mou,et al.  Statistical Interior Tomography , 2010, IEEE Transactions on Medical Imaging.

[29]  Radomír Mech,et al.  Metropolis procedural modeling , 2011, TOGS.

[30]  Gordon Wetzstein,et al.  Polarization fields: dynamic light field display using multi-layer LCDs , 2011, SA '11.

[31]  Gordon Wetzstein,et al.  Refractive shape from light field distortion , 2011, 2011 International Conference on Computer Vision.

[32]  Wolfgang Heidrich,et al.  Glare encoding of high dynamic range images , 2011, CVPR 2011.

[33]  Gordon Wetzstein,et al.  Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays , 2011, SIGGRAPH 2011.

[34]  R. Barbuzza,et al.  Metropolis monte carlo for tomographic reconstruction with prior smoothness information , 2011 .