Supervised Fitting of Geometric Primitives to 3D Point Clouds (1811.08988v4)

Abstract: Fitting geometric primitives to 3D point cloud data bridges a gap between low-level digitized 3D data and high-level structural information on the underlying 3D shapes. As such, it enables many downstream applications in 3D data processing. For a long time, RANSAC-based methods have been the gold standard for such primitive fitting problems, but they require careful per-input parameter tuning and thus do not scale well for large datasets with diverse shapes. In this work, we introduce Supervised Primitive Fitting Network (SPFN), an end-to-end neural network that can robustly detect a varying number of primitives at different scales without any user control. The network is supervised using ground truth primitive surfaces and primitive membership for the input points. Instead of directly predicting the primitives, our architecture first predicts per-point properties and then uses a differential model estimation module to compute the primitive type and parameters. We evaluate our approach on a novel benchmark of ANSI 3D mechanical component models and demonstrate a significant improvement over both the state-of-the-art RANSAC-based methods and the direct neural prediction.

• The paper introduces the Supervised Primitive Fitting Network (SPFN), a novel end-to-end neural network for accurately and efficiently fitting geometric primitives to 3D point clouds.
• In evaluations, SPFN significantly outperformed state-of-the-art RANSAC methods across various metrics including segmentation accuracy, primitive type prediction, and fitting precision.
• This method enables practical applications in CAD modeling and 3D scanning, offering a significant advance for the field by uniting machine learning with geometric modeling.

Supervised Fitting of Geometric Primitives to 3D Point Clouds

The paper "Supervised Fitting of Geometric Primitives to 3D Point Clouds" introduces a novel approach called the Supervised Primitive Fitting Network (SPFN) designed to efficiently fit geometric primitives to 3D point cloud data. This method is aimed at addressing the limitations of traditional RANSAC-based methods, which require extensive per-input parameter tuning and subsequently struggle to efficiently scale across large datasets with diverse shape categories.

Overview of SPFN

The SPFN architecture is an end-to-end neural network framework capable of detecting a varying number of primitives such as planes, spheres, cylinders, and cones in a given point cloud. The network is supervised using ground truth data consisting of primitive surfaces, primitive membership for input points, and point normals. Instead of directly predicting the parameters of the primitives, SPFN first estimates per-point properties which aid in determining primitive types and their characteristics, utilizing a differential model estimation module. This process allows for robust and accurate extraction of primitives without manual intervention.

Key Contributions

1. End-to-End Training: SPFN is designed to be completely trainable bottom-up, allowing it to leverage readily available per-point properties as a supervisory signal during training to maximize the accuracy of primitive detection.
2. Differential Estimator: The model estimation module employs a series of linear least-square problems to compute the primitive parameters. This module is differentiable, ensuring that the fitting loss can be propagated back through the network. This allows the use of a neural network that efficiently estimates complex shapes in a scalable manner.
3. Novel Dataset: To evaluate SPFN, the authors introduced a novel dataset comprising ANSI 3D mechanical component models. This dataset consists of thousands of CAD models, utilized to benchmark the performance of SPFN against existing methods.

Numerical Results and Evaluation

In rigorous empirical evaluations, SPFN was shown to outperform state-of-the-art RANSAC-based methods in several metrics including segmentation accuracy, primitive type prediction accuracy, point normal difference, and primitive axis difference. Notably, SPFN demonstrated superior fitting precision, achieving high coverage and low residual errors even with input shapes from unseen categories during training.

The network's ability to consistently achieve high $\{\mathbf{S}_k\}$ coverage across various scales of primitives further underscores its effectiveness in parsing complex shapes. Furthermore, the incorporation of the direct supervision of per-point properties such as normals and membership enhances the network's fitting precision when compared to direct parameter prediction networks.

Implications and Future Directions

SPFN's success highlights significant advances in computer vision, particularly in the domain of 3D geometric data processing. Practically, this approach can be applied to tasks such as CAD model editing, 3D scanning, and even in automating aspects of computer-aided design. Theoretically, the proposed architecture opens new avenues for research, presenting the potential for more sophisticated models to be built over its foundation.

In terms of future developments, ongoing advancements in AI could enable SPFN to incorporate more sophisticated geometric primitives, potentially expanding its applications to more versatile 3D modeling tasks. The integration of large-scale datasets beyond mechanical component models could also improve SPFN’s generalizability, facilitating its usage in more diverse domains.

In conclusion, the SPFN model marks a substantial contribution to the field by effectively uniting machine learning with geometric modeling, circumventing historical limitations and setting a precedent for future research initiatives.