# SurfCut: Surfaces of Minimal Paths From Topological Structures

arXiv: https://arxiv.org/abs/1705.00301 · HTML: https://mlsanity.com/paper/1705.00301/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2017.

## Built on by (most cited first, 2 of 2)

- [A Local Iterative Approach for the Extraction of 2D Manifolds from Strongly Curved and Folded Thin-Layer Structures](https://mlsanity.com/paper/2308.07070/) (2023)
- [Virtually Unrolling the Herculaneum Papyri by Diffeomorphic Spiral Fitting](https://mlsanity.com/paper/2512.04927/) (2025)

## Abstract (arXiv)

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 certain ridge curves of a function defined on a front propagated using the Fast Marching algorithm lie on the surface. Our method extracts and cuts these ridges to form the surface boundary. Our surface extraction algorithm is built on the novel observation that the surface lies in a valley of the distance from Fast Marching. We show that the resulting surface is a collection of minimal paths. Using the framework of cubical complexes and Morse theory, we design algorithms to extract these critical structures 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.