A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces

Weinrauch, Alexander; Seidel, Hans‐Peter; Mlakar, Daniel; Steinberger, Markus; Zayer, Rhaleb

doi:10.48550/arxiv.2105.13168

Cited by 1 publication

(1 citation statement)

References 14 publications

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“…Their method is computationally efficient, without requiring any 3D tessellation. More recently, Weinrauch et al [25] proposed a variational abstraction to the loop shrinking property for detection of handle and tunnel loops. Their method utilizes a succinct diffuse interface model for loop detection and a fully parallel algorithmic realization.…”

Section: Introductionmentioning

confidence: 99%

A Novel Robust Topological Denoising Method Based on Homotopy Theory for Virtual Colonoscopy

Ma,

Chen,

Lei

et al. 2023

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Virtual colonoscopy plays an important role in polyp detection of colorectal cancer. Noise in the colon data acquisition process can result in topological errors during surface reconstruction. Topological denoising can be employed to remove these errors on surfaces for subsequent geometry processing, such as surface simplification and parameterization. Many methods have been proposed for this task. However, many existing methods suffer from failure in computation of all the non-trivial loops, due to high genus or complex topological structures. In this paper, we propose a novel robust topological denoising method for surfaces based on homotopy theory. The proposed method was evaluated on two datasets of colon meshes. We compared our method with the State-of-the-Art persistent-homology-based method. Our method can successfully compute the loops on all colon data for topological denoising, whereas the persistent homology method fails on some colon data. Moreover, our method detects all loops with shorter lengths than those detected by the persistent homology method. Our experimental results show that the proposed method is effective and robust in topological denoising, and that it has the potential for practical application to virtual colonoscopy.

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Section: Introductionmentioning

confidence: 99%