# SurfCut: Surfaces of Minimal Paths From Topological Structures

## TL;DR

SurfCut is a novel algorithm that accurately extracts smooth surfaces with unknown boundaries from noisy 3D images by leveraging topological structures and minimal path principles, outperforming existing methods in robustness and efficiency.

## Contribution

The paper introduces SurfCut, a new surface extraction algorithm based on topological and Morse theory insights, with improved accuracy and computational efficiency over prior approaches.

## Key findings

- Achieves higher accuracy than state-of-the-art methods.
- Demonstrates robustness on noisy 3D datasets.
- Reduces computational cost significantly.

## Abstract

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.