Warp-and-Project Tomography
for Rapidly Deforming Objects

Guangming Zang, Ramzi Idoughi, Ran Tao, Gilles Lubineau, Peter Wonka, Wolfgang Heidrich
Accepted to ACM Transactions on Graphics (Proc. SIGGRAPH), 2019

We introduce a CT reconstruction method for objects that undergo rapid deformation during the scan. Shown here is a copper foam crumpling under a compressive force during the scan. The whole complex animation is reconstructed using only 192 projection images that all correspond to different deformation states of the foam.


Computed tomography has emerged as the method of choice for scanning complex shapes as well as interior structures of stationary objects. Recent progress has also allowed the use of CT for analyzing deforming objects and dynamic phenomena, although the deformations have been constrained to be either slow or periodic motions.
In this work we improve the tomographic reconstruction of time-varying geometries undergoing faster, non-periodic deformations. Our method uses a warp-and-project approach that allows us to introduce an essentially continuous time axis where consistency of the reconstructed shape with the projection images is enforced for the specific time and deformation state at which the image was captured. The method uses an efficient, time-adaptive solver that yields both the moving geometry as well as the deformation field.
We validate our method with extensive experiments using both synthetic and real data from a range of different application scenarios.

Main results

Hydro-gel balls

3D rendering of water absorption by Hydro-gel balls, with a slice comparison of the ST-tomography approach (lower left) and our method (upper right).

Compression of the copper foam

(a-b): The height (in mm) of the copper foam before and after the compression process, respectively. The total displacement during the compression is 3.77mm, uniformly distributed over 192 scans. 60 projections are obtained for each scan. (c): the states of the foam after 192 scans. (d) The Micro-CT setup for the in-situ compressions of the foam. (e):Algorithm comparison for the compression of copper foam. First row: results from different reconstruction methods compared to the ground truth; Second row: the absolute error for time frame 150. The dynamic range of density values is (0, 4600).

Capillarity effect in porous rock

Reconstruction results for the porous rock dataset. Images (a) and (c) represent respectively the rock before and after the scan. Some representative CT projections are given in (b). The rendering results in (d) show the absorption of liquid over time.

Pills dissolved in water

Pills dissolving in water. This is our fastest dataset with only 30 projections captured in 3 minutes.

Paper and video

Paper [Zang2019WarpAndProject.pdf ~14.9 MB] 

Code and dataset

Source code  [Github] 


  title={Warp-and-Project Tomography for Rapidly Deforming Objects},
  author={Zang, Guangming and Idoughi, Ramzi and Tao, Ran and Lubineau, Gilles and Wonka, Peter and Heidrich, Wolfgang},
  journal={ACM Transactions on Graphics (TOG)},