A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds

Point cloud data represents a crucial category of information for mathematical modeling, and surface reconstruction from such data is an important task across various disciplines. However, during the scanning process, the collected point cloud data may fail to cover the entire surface due to factors such as high light-absorption rate and occlusions, resulting in incomplete datasets. Inferring surface structures in data-missing regions and successfully reconstructing the surface poses a challenge. In this paper, we present a Principal Component Analysis (PCA) based model for surface reconstruction from incomplete point cloud data. Initially, we employ PCA to estimate the normal information of the underlying surface from the available point cloud data. This estimated normal information serves as a regularizer in our model, guiding the reconstruction of the surface, particularly in areas with missing data. Additionally, we introduce an operator-splitting method to effectively solve the proposed model. Through systematic experimentation, we demonstrate that our model successfully infers surface structures in data-missing regions and well reconstructs the underlying surfaces, outperforming existing methodologies.