Manifold Embedding for Fast and Accurate 3D Reconstruction

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) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Manifold Voxel</i>: We transform discrete point sets into smooth surfaces using the Implicit Moving Least Squares (IMLS) method; 2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Two-Step Filtering</i>: We enhance reconstruction accuracy through a two-step filtering technique that evaluates sampling points based on probabilistic measures; 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Embedding for Smooth Surface</i>: 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Replica</i> 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). Overall, our proposed method provides superior reconstruction quality and enhanced computational efficiency (See Fig. 1).