Space-time Tomography
for Continuously Deforming Objects

Guangming Zang, Ramzi Idoughi, Ran Tao, Gilles Lubineau, Peter Wonka, Wolfgang Heidrich
Accepted to ACM Transactions on Graphics (Proc. SIGGRAPH), 2018

X-ray tomographic reconstruction of a rose undergoing significant wilting during the scan due to loss of water. Images (a) and (b) show photographs of the rose directly before and directly after the scanning process. Traditional CT reconstruction (c) from all 5520 projections in the scan sequence show significant distortions due to misalignment of features. When grouping the projections into 92 frames of 60 projections each (d), the deformation over each frame becomes negligible, but now the number of projections per frame is insufficient for high-quality reconstruction of the corresponding volumes (e, Y). By comparison, our full space-time reconstruction algorithm yields a time sequence of highly detailed volumes for different time steps (f, Y').


X-ray computed tomography (CT) is a valuable tool for analyzing objects with interesting internal structure or complex geometries that are not accessible with optical means. Unfortunately, tomographic reconstruction of complex shapes requires a multitude (often hundreds or thousands) of projections from different viewpoints. Such a large number of projections can only be acquired in a time-sequential fashion. This significantly limits the ability to use x-ray tomography for either objects that undergo uncontrolled shape change at the time scale of a scan, or else for analyzing dynamic phenomena, where the motion itself is under investigation.
In this work, we present a non-parametric space-time tomographic method for tackling such dynamic settings. Through a combination of a new CT image acquisition strategy, a space-time tomographic image formation model, and an alternating, multi-scale solver, we achieve a general approach that can be used to analyze a wide range of dynamic phenomena. We demonstrate our method with extensive experiments on both real and simulated data.

Main results

Wilting rose

A rose undergoing significant wilting was scanned during 9.5 hours.

High viscosity fluid flow

This experiment corresponds to the flow of a high viscosity transparent fluid over a 3D-printed mold. This fluid, with 20 million times the viscosity of water, has several included air bubbles that move and pop as the fluid fills the mold.
This flow was scanned during 2 hours and 12 minutes.

Rising dough

This rising dough is made from flour and yeast. A hazelnut is placed inside this dough, in order to have additional internal structures.
The process was scanned during 4 hours and 27 minutes.

Paper, code and video

paper [Zang2018Space-time.pdf (~35.6MB)] 
supplement [Zang2018Space-time.pdf(~8.4MB)] 
code and data [coming soon] 

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