Objective Surface reconstruction refers to the process of reconstructing a continuous 3D surface from discrete spatial point clouds data. Learning signed distance functions (SDFs) of an object through spatial discrete point clouds to reconstruct the implicit surface of an object is currently the main research strategy. Neural-pull (NP) is a method to obtain high-quality SDFs from discrete point clouds information to reconstruct original surface. The key lies in using the predicted SDFs and the gradient information of the query point to pull the query point onto the reconstructed surface (Fig.1). The advantage of this method is that the model training process does not require ground truth (GT) SDFs as supervision, and at the same time, the signed distance value and gradient information are updated simultaneously during the training process. However, due to the inevitable noise and defects in the actually obtained point cloud data, NP will cause edge defects on the reconstructed surface during reconstruction. Therefore, in order to improve the reconstruction effect of the algorithm, solve the edge defects problem occurs in NP's sparse point clouds reconstruction, this paper proposes an improvement strategy, called neural-pull based on edge enhancement (NPEE).

Methods In order to solve the NP edge overfitting problem, this paper proposes the NPEE framework (Fig.2). It consists of edge-construction network (EN) and NP network. EN (Fig.3) uses a residual learning mechanism to learn the edge SDFs of point clouds, ensuring sufficient edge accuracy while ensuring training efficiency. At the same time, based on the original point cloud, the edge factor \sigma is introduced, combined with the learned edge SDFs, to enhance the input point cloud through robust point cloud edge extraction (Fig.4). NPEE still retains the original neural network (Fig.5) for learning SDFs, so that the network that is prone to overfitting can obtain more surface details while ensuring the smoothness of the reconstructed surface.

Results and Discussions Using the ABC data set, Stanford scanning model and deep geometric prior data as the ground truth, ideal point clouds reconstruction experiments (Fig.7), sparse point clouds reconstruction experiments (Fig.8) and noisy points cloud reconstruction experiments (Fig.12) are designed to evaluate the algorithm capabilities. The reconstruction results of DeepSDF, Onsurface and NP are compared, and the chamfer distance (CD) of the three groups of experiments are calculated respectively. The experimental results are as follows (Tab.1-6). The reconstruction results of NPEE can show the complete reconstruction model and sufficient edge details.

Conclusions In order to improve the reconstruction effect of the algorithm, the edge defects problem occuring in NP's sparse point clouds reconstruction is solved, an improvement strategy is designed, called NPEE. To ensure the reconstructed surface is smooth while obtaining more surface details, on the basis of retaining the original neural network, a new network which uses the residual learning mechanism is designed for learning SDFs of the point cloud while ensuring training efficiency and getting sufficient edge accuracy. At the same time, on the basis of the original point cloud, the edge factor \sigma is introduced, to enhance the input point cloud through robust extraction of point cloud edges. Three sets of comparative experiments were designed using widely used ground truth data sets, namely ideal point cloud reconstruction experiment, sparse point cloud reconstruction experiment and noisy point cloud reconstruction experiment. Experimental results and evaluation index CD show that NPEE can effectively improve the defects of the NP algorithm in edge surface reconstruction, showing superiority compared with other algorithms.