DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares (2003.10826v1)

Abstract: We propose a surface fitting method for unstructured 3D point clouds. This method, called DeepFit, incorporates a neural network to learn point-wise weights for weighted least squares polynomial surface fitting. The learned weights act as a soft selection for the neighborhood of surface points thus avoiding the scale selection required of previous methods. To train the network we propose a novel surface consistency loss that improves point weight estimation. The method enables extracting normal vectors and other geometrical properties, such as principal curvatures, the latter were not presented as ground truth during training. We achieve state-of-the-art results on a benchmark normal and curvature estimation dataset, demonstrate robustness to noise, outliers and density variations, and show its application on noise removal.

DeepFit: A Novel Approach to 3D Surface Fitting Using Neural Networks

The paper introduces DeepFit, a surface fitting method for unstructured 3D point clouds utilizing neural network-based weighted least squares. This approach addresses the challenges posed by traditional methods in estimating normals and curvatures, particularly in handling unstructured data, noise, and density variations.

Methodology

DeepFit employs a neural network to predict point-wise weights, facilitating weighted least squares polynomial surface fitting. This removes the traditional requirement for multi-scale neighborhood selection, which often involves a compromise between noise robustness and detail accuracy. The neural network is trained using a novel surface consistency loss that enhances the accuracy of point weight prediction.

Key components include:

• Point-wise Weight Estimation: A PointNet architecture computes both global and local representations of the point cloud to determine each point's weight in the fitting process.
• Geometric Quantities Extraction: From the fitted polynomial surface, normals and principal curvatures are derived without requiring additional ground truth data during training.
• Surface Consistency Loss: Combines weighted normal difference with regularization to ensure point weights remain informative, preventing convergence to trivial solutions.

Numerical Results and Comparative Analysis

The paper reports state-of-the-art results in normal and curvature estimation on benchmark datasets, demonstrating robustness to adverse conditions such as noise and uneven point cloud density. Several configurations are tested, with DeepFit consistently showing superior performance compared to existing methods like PCPNet, Nesti-Net, and traditional PCA and Jet methods. The method leverages its data-driven approach to adeptly manage sharp features and varying surfaces, outputting reliable and precise geometric estimates.

Practical and Theoretical Implications

DeepFit's ability to perform scale-independent fitting offers broad applicability in scenarios requiring accurate geometrical interpretations of 3D data. This can significantly enhance tasks like shape recognition, surface reconstruction, and segmentation in robotics and computer vision applications. By bypassing the iterative and often computationally intensive multi-scale analysis of traditional methods, DeepFit provides a more efficient mechanism conducive to real-time applications.

Future Prospects

The paper sets the stage for further exploration into more sophisticated neural architectures for geometric learning, potentially extending DeepFit to handle more complex differential properties or integrate seamlessly into larger-scale point cloud processing workflows. Future work could also focus on enhancing its adaptability and precision in even more challenging contexts, including dynamic environments where point cloud attributes change rapidly.

In summary, DeepFit presents an innovative, robust approach to 3D surface fitting, paving the way for improvements in a wide array of applications within AI-driven geometry processing and beyond.