Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence (2003.14286v1)

Abstract: We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly across diverse datasets, our approach is both accurate and robust to changes in shape structure. Key to our method is a feature-extraction network that learns directly from raw shape geometry, combined with a novel regularized map extraction layer and loss, based on the functional map representation. We demonstrate through extensive experiments in challenging shape matching scenarios that our method can learn from less training data than existing supervised approaches and generalizes significantly better than current descriptor-based learning methods. Our source code is available at: https://github.com/LIX-shape-analysis/GeomFmaps.

• The paper presents a deep learning approach that integrates geometric functional maps to extract robust shape features for precise correspondence.
• It replaces traditional handcrafted descriptors with a feature-extraction network and a regularized spectral layer, enhancing matching accuracy.
• Evaluations on challenging datasets show the method's superior performance in reducing geodesic error even with minimal training data.

Overview of "Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence"

The paper "Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence," authored by Nicolas Donati, Abhishek Sharma, and Maks Ovsjanikov, introduces a novel approach in the field of shape matching within computer vision. The focus lies on learning-based techniques for computing correspondences between non-rigid 3D shapes, highlighting the importance of robustness and accuracy in diverse datasets. The innovative aspect of this research stems from learning directly from raw shape geometry and extending functional map representation into the feature extraction process.

Summary of Approach

This paper proposes an integrated system of geometric functional maps which combines two primary elements:

1. Feature-Extraction Network: The model learns directly from raw shape geometry, eschewing the necessity of handcrafted descriptors that often generalize poorly.
2. Regularized Functional Map Extraction Layer: The incorporation of a novel spectral correspondence extraction layer and loss ensures robust learning even from minimal training data compared to traditional descriptor-based methods.

The research demonstrated that this methodology, building consistent descriptors directly from point clouds, generates accurate pointwise correspondence between shapes. This is illustrated through extensive experiments in challenging shape-matching scenarios, affirming that the proposed approach surpasses current descriptor-based learning methods in generalization capability and efficiency.

Implications and Future Directions

The implications of this research are profound both theoretically and practically:

• Theoretical Implications:
  • The introduction of regularization into the learning process using spectral correspondence layers suggests new avenues to explore in spectral domain-based learning, potentially influencing other machine learning applications beyond shape matching.
• Practical Implications:
  • The reduced dependency on large annotated datasets presents significant potential for applications requiring efficient training, such as real-time processing and dynamic shape analysis.

The research also opens up discussion for future developments in AI and computer vision. The progression toward intrinsic and geometric representation learning could see applications expand into newer domains:

• Enhancement of machine learning algorithms for automated feature extraction directly from complex geometric structures, impacting areas like autonomous vehicle navigation and robotic manipulation.
• Extension to unsupervised learning models leveraging the spectral domain's intrinsic properties to discover shape correspondences without extensive labeled datasets.

Evaluation and Results

Evaluation metrics centered around geodesic error measurements emphasize the accuracy of correspondences. Quantitative and qualitative comparisons with existing methods showcased the superiority of the proposed system, particularly under conditions of minimal training data. The inclusion of novel refinement techniques further improved the maps' spatial accuracy.

Conclusion

The paper successfully articulates a clear advancement in 3D shape correspondence learning by leveraging functional map representations in a robust and efficient manner. By combining layer regularization with raw geometric feature extraction, the paper transcends traditional limitations associated with handcrafted descriptors and extensive training datasets. The advancements herald promising future applications across many facets of computer vision, presenting a significant leap in the domain of geometric learning. Future research could explore adapting the model for unsupervised learning and expanding its applicability beyond the current tested scenarios to broader, unexplored datasets.