Robust Model Reconstruction Based on the Topological Understanding of Point Clouds Using Persistent Homology

TL;DR

This paper introduces a robust, topology-based method using persistent homology to automatically reconstruct multi-component models from noisy, unorganized point clouds, effectively distinguishing surfaces and generating high-quality models.

Contribution

It presents a novel approach combining persistent homology with surface reconstruction techniques to improve model reconstruction from noisy point clouds.

Findings

Effective separation of multiple surfaces in noisy point clouds

High-quality surface reconstruction achieved

Method demonstrates robustness to noise

Abstract

Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise that represent multiple closed surfaces with shared regions, making their automatic identification and separation inherently complex. In this paper, we propose an automatic method that uses the topological understanding provided by persistent homology, along with representative 2-cycles of persistent homology groups, to effectively distinguish and separate each closed surface. Furthermore, we employ Loop subdivision and least squares progressive iterative approximation (LSPIA) techniques to generate high-quality final surfaces and achieve complete model reconstruction. Our method is robust to noise in the point cloud, making it suitable for reconstructing models from such data. Experimental results demonstrate the effectiveness of our approach and highlight its potential for practical applications.