SurfCut: Surfaces of Minimal Paths from Topological Structures

Marei Algarni, Ganesh Sundaramoorthi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We present SurfCut, an algorithm for extracting a smooth, simple surface with an unknown 3D curve boundary from a noisy 3D image and a seed point. Our method is built on the novel observation that ridge curves of the Euclidean length of minimal paths ending on a level set of the solution of the eikonal equation lie on the surface. Our method extracts these ridges and cuts them to form the surface boundary. Our surface extraction algorithm is built on the novel observation that the surface lies in a valley of the eikonal equation solution. The resulting surface is a collection of minimal paths. Using the framework of cubical complexes and Morse theory, we design algorithms to extract ridges and valleys robustly. Experiments on three 3D datasets show the robustness of our method, and that it achieves higher accuracy with lower computational cost than state-of-the-art.

Original languageEnglish (US)
Article number8306823
Pages (from-to)726-739
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number3
StatePublished - Mar 1 2019

Bibliographical note

Publisher Copyright:
© 1979-2012 IEEE.


  • Morse-Smale complex
  • Segmentation
  • computational topology
  • cubical complex
  • minimal paths
  • surface extraction

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Applied Mathematics
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics


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