Topology-Constrained Surface Reconstruction From Cross-sections

SIGGRAPH 2015, ACM Transactions on Graphics
Ming Zou1, Michelle Holloway1, Nathan Carr2, Tao Ju1
1Washington University in St. Louis, 2Adobe

Teaser: Non-parallel cross-section curves delineating a developing chicken heart from a CT volume (a) and the reconstructed surfaces using the method of Lu et al. [2008] (b), method of Bermano et al. [2011] (c), and our method with genus-1 constraint without utilizing the CT volume (d). The first two surfaces contain numerous topological tunnels, while ours correctly captures the shell-like shape of the object.

Gallery: Reconstructions from input cross-sections (a) using the method of Lu et al. [2008] (b), method of Bermano et al. [2011] (c), and our method with prescribed genuses without additional image data (showing running times) (d).


In this work we detail the first algorithm that provides topological control during surface reconstruction from an input set of planar cross-sections. Our work has broad application in a number of fields including surface modeling and biomedical image analysis, where surfaces of known topology must be recovered. Given curves on arbitrarily oriented cross-sections, our method produces a manifold interpolating surface that exactly matches a user-specified genus. The key insight behind our approach is to formulate the topological search as a divide-and-conquer optimization process which scores local sets of topologies and combines them to satisfy the global topology constraint. We further extend our method to allow image data to guide the topological search, achieving even better results than relying on the curves alone. By simultaneously satisfying both geometric and topological constraints, we are able to produce accurate reconstructions with fewer input cross-sections, hence reducing the manual time needed to extract the desired shape.


+ Paper
[PDF 4M]
+ Slides
[KEYNOTE 30M] (recommended) [PDF 22M]
+ Code+Data   
[ZIP 17M]


The source code is currently distributed under the license MPL2, which is a simple weak copyleft license.
Please check the MPL2 FAQ for more information, and contact me if you have any question.

Release Notes

Our source code as well as the executable files are provided for research use.
The code is written in C++ and tested on Windows 8 with Visual Studio 2012.

Version 1.0.0 (Sep 2015)
+ The first distribution. Run with command line. A README is included.


This work is supported in part by NSF grants (IIS-1302200 and IIS-0846072) and a gift from Adobe.


title={Topology-constrained surface reconstruction from cross-sections},
author={Zou, Ming and Holloway, Michelle and Carr, Nathan and Ju, Tao},
journal={ACM Transactions on Graphics (TOG)},