LIMP: Learning Latent Shape Representations with Metric Preservation Priors (2003.12283v2)

Abstract: In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.

• The paper introduces a novel metric interpolation loss that ensures linear latent traversals produce geometrically coherent 3D shapes.
• It employs differentiable intrinsic distances and a disentanglement loss to effectively separate style variations from pose transformations.
• Experimental results on datasets like FAUST and DFAUST demonstrate reduced interpolation and disentanglement errors, highlighting its efficacy in data-scarce scenarios.

Learning Latent Shape Representations with Metric Preservation Priors

The paper "LIMP: Learning Latent Shape Representations with Metric Preservation Priors" proposes a new methodology for learning latent representations of deformable 3D shapes, fundamentally utilizing metric preservation priors to guide the learning process. The paper introduces innovative techniques to integrate geometric priors within a generative model, particularly useful when dealing with limited datasets.

Overview

The core contribution of this paper lies in the introduction of a geometric distortion criterion that is directly applied to decoded shapes. This criterion essentially translates metric preservation on the decoding side to linear paths in the latent space. Current methodologies often rely on extensive datasets to achieve fidelity in generated shapes, which this paper argues is unnecessarily burdensome. Instead, the proposed metric preservation provides a structured approach to forming a latent space with minimized geometric distortion, allowing even data-scarce environments to produce high-quality synthetic samples.

Key Techniques

The paper unfolds the use of differentiable intrinsic distances utilized in backpropagating a geodesic loss in training. By leveraging these geometric priors, the approach aligns its utility especially in scenarios where training data is scarce. The effectiveness of this model is demonstrated through applications in style transfer, content generation, and shape completion. The method falls under the broader gamut of autoencoder-based generative models but emphasizes the integration of geometric priors as a new dimension of regularization.

Technical Implications

The framework proposes a novel loss formulation that couples the notions of metric preservation within the latent codes and decoded shapes. It introduces:

1. Metric Interpolation Loss: This controls how latent codes translate linearly into geometrically coherent shapes without distortion.
2. Disentanglement Loss: It separates intrinsic from extrinsic features, which allows for isolating style variations from pose transformations.

Moreover, the architecture employs a PointNet-based encoder and a fully connected decoder, highlighting the minimalist complexity yet robust capabilities provided by assimilating the proposed geometric priors.

Experimental Results

The authors conducted exhaustive experiments across multiple datasets, including FAUST, DFAUST, and COMA, illustrating the efficacy of their model. The framework not only showed lower metric distortion in interpolations between known shapes but also excelled in disentangling inputs into intrinsic and extrinsic factors. The paper establishes this superiority through both quantitative metrics, like interpolation error and disentanglement error, and qualitative evaluations, as evidenced by realistic generation of transitional shapes between sparse datasets.

Future Directions and Conclusions

This work opens avenues for further exploration in integrating intrinsic geometric properties within machine learning models for 3D shape representations. The potential applications in fields requiring high-fidelity generative models without the dependency on vast training datasets are notable. As datasets become increasingly scarce or expensive, methods like LIMP that effectively regularize and utilize available data are of paramount importance.

Future work could explore self-supervised adaptations where correspondences aren't strictly necessary, thus broadening the applicability across domains with high intra-class variability. Additionally, integrating more nuanced geometric priors or expanding into other data modalities where geometric coherence is significant might offer beneficial expansions of the proposed methodology.