| Abstract: |
| 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. In this presentation, we present our recent works for surface reconstruction from point cloud data. Our model utilizes a mean curvature term as regularizer. When the data are incomplete or noisy, a Principal Component Analysis (PCA) based variational model is proposed. 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. An operator-splitting method is designed to effectively solve the proposed model. Through systematic experimentation, we demonstrate that our model is robust to noise, and successfully infers surface structures in data-missing regions and well reconstructs the underlying surfaces, outperforming existing methodologies. |
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