Manifold Embedding for Fast and Accurate 3D Reconstruction

Duo Chen, Zixin Tang, Ke Song, Xingyu Peng, Wuque Cai, Hongze Sun, Dezhong Yao, Daqing Guo

Abstract: The goal of the fusion process in RGB-D reconstruction systems is to verify and update the 3D model while ensuring both completeness and accuracy. However, achieving precise dense correspondences in a point-to-point or pixel model during this process is challenging and computationally intensive. To address this challenge, we propose a Manifold Embedding framework that facilitates rapid point-to-surface fusion, removing the need for direct point-to-point or pixel correspondences. Our approach consists of three main steps: 1) Manifold Voxel: We transform discrete point sets into smooth surfaces using the Implicit Moving Least Squares (IMLS) method; 2) Two-Step Filtering: We enhance reconstruction accuracy through a two-step filtering technique that evaluates sampling points based on probabilistic measures; 3) Embedding for Smooth Surface: Lastly, we embed points into a smooth manifold surface represented via IMLS, ensuring high-quality reconstructed surfaces. Extensive experiments on both real and synthetic 3D scenes demonstrate the effectiveness of our Manifold Embedding framework. For instance, on the public Replica dataset, our method surpasses state-of-the-art fusion techniques regarding both completeness and accuracy. Our average accuracy is 2.11 cm and completeness is 2.80 cm, while NICE-SLAM achieves 2.85 cm and 3.00 cm, respectively (with lower values indicating better performance).