Warp-and-Project Tomography for Rapidly Deforming Objects Guangming - - PowerPoint PPT Presentation

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Warp-and-Project Tomography for Rapidly Deforming Objects Guangming - - PowerPoint PPT Presentation

Dec 12, 2023 117 likes •705 views

Warp-and-Project Tomography for Rapidly Deforming Objects Guangming Zang, Ramzi Idoughi, Ran Tao, Gilles Lubineau, Peter Wonka, Wolfgang Heidrich, King Abdullah University of Science And Technology Dynamic scene reconstruction [Wang et al.

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Warp-and-Project Tomography for Rapidly Deforming Objects

Guangming Zang, Ramzi Idoughi, Ran Tao, Gilles Lubineau, Peter Wonka, Wolfgang Heidrich, King Abdullah University of Science And Technology

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[Wang et al. 2009] [Li et al. 2013] [Zheng et al. 2017] [Innmann et al. 2016] [Dou et al. 2016]

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Dynamic scene reconstruction

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Dynamic X-ray tomography

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[Chen et al. 2012] Classical reconstruction

credit: austincc.edu

ECG gating

credit: RTK

[Mory et al. 2016]

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Optical means X-ray tomography

Cameras/ sensors One or more One Resolution Low High Reconstruction Surface Surface + internal structures Capture Speed Fast Slow Deformation type General Periodic or with Pattern Application fields General Medical, Security, Industry

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Dynamic scene reconstruction

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Optical means X-ray tomography

Cameras/ sensors One or more One Resolution Low High Reconstruction Surface Surface + internal structures Capture Speed Fast Slow Deformation type General Periodic or with Pattern Application fields General Medical, Security, Industry

High quality surface and internal reconstruction for fast deforming

  • bjects with general motion

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Dynamic scene reconstruction

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Motivation

Is it possible to scan rapidly deforming objects with internal details? Pills dissolving Hydro-gel balls

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Space time tomography

[Zang et al. SIGGRAPH18]

Shortcomings ?

  • Assumption: slow and smooth motion fields
  • Trade-off: spatial VS. temporal reconstruction quality
  • Sampling: costly uniform temporal sampling

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Motivation

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ST-Tomography [Zang et al. 2018] SART-ROF [Getreuer 2012] Warp-and-Project [Ours]

Motivation

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Image formation model

: X-ray path

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Image formation model

: X-ray path : Unknown field

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Image formation model

: X-ray path : Measurement : Unknown field

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Image formation model

: X-ray path : Measurement : Unknown field

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Image formation model

Each projection image has its own time stamp! : X-ray path : Measurement : Unknown field

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Linear system

  • Sparse system
  • Memory consuming
  • Ill-posed problem

Radon Transform Measurements Frames

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Linear system

  • Sparse system
  • Memory consuming
  • Ill-posed problem

Radon Transform Measurements Frames

Warp and project tomography

 Non-parametric and matrix-free  No assumption of the motion  A non-uniform temporal up-sampling

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Objective function

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Objective function

Data fitting (Forward / backward warping)

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Objective function

Volume correlation Data fitting (Forward / backward warping)

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Objective function

Volume correlation Volume smoothness Data fitting (Forward / backward warping)

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Objective function

Volume correlation Volume smoothness Deformation field smoothness Data fitting (Forward / backward warping)

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Optimization framework

Simulated plume data Volume size: 100x150x100 Time frames: 300

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Warping operator

?

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Warping operator

?

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Warping operator

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Warping operator

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Optimization framework

t1 X-Ray source

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Optimization framework

t1 t2 X-Ray source

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Optimization framework

t1 t2 t3 X-Ray source

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Optimization framework

t1 t2 t3 t4 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 t6 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9 X-Ray source

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

Forward warping Backward warping

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

Backward warping Forward warping

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

Backward warping Forward warping

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Optimization framework

t1 t2 t3 t4 t5 t6 t7 t8 t9

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Material deformation analysis

Sensor Compression stage X-ray source Controlled compression of a copper foam

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Stop-motion capture

  • Controlled compression
  • 192 intermediate states
  • 60 projections for each state

Reconstruction

  • Ground truth: 192*60 projections
  • Other reconstructions: only 192

projections

Ground truth reconstruction

After Before

Material deformation analysis

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Ground truth ST-Tomography [Zang et al. 2018] SART-ROF [Getreuer 2012] Warp-and-Project [Ours]

Material deformation analysis

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Ground truth Absolute error ST-Tomography [Zang et al. 2018] SART-ROF [Getreuer 2012] Warp-and-Project [Ours]

Material deformation analysis

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Rock porosity characterization

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Before After

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Rock porosity characterization

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Fungus re-hydration

Before After Capture duration: 38min # projections: 600

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Fungus re-hydration

30 key frames 30 key frames 30 key frames 64 key frames 128 key frames

Temporal sampling

ST-Tomography [Zang et al. 2018] SART-ROF [Getreuer 2012] Warp-and-Project [Ours]

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Hydro-gel balls

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Before After Capture duration: 43min # projections: 640

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Hydro-gel balls

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Frame 05 Frame 10 Frame 15 ST-Tomography [Zang et al. 2018] SART-ROF [Getreuer 2012] Warp-and-Project [Ours]

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Hydro-gel balls

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Summary

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  • A new 4D tomographic reconstruction for rapidly deforming objects
  • Well suited to graphics, and several scientific applications

Material deformation analysis Porosity characterization

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What is next ?

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  • Software engineering (memory, computation speed, etc.)
  • Combination with other tomography techniques (e.g. phase contrast

tomography)

  • Extension to other imaging modalities (e.g. electron microscopy)
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What is next ?

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Camera 1 Camera 2 Camera 3 Laser Camera 2

Applications: High speed 3D soot imaging

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Thank you !

Sponsorship: KAUST as part of VCC Center Competitive Funding. Project webpage: Code and data available soon