Selective sampling with Gromov–Hausdorff metric: Efficient dense-shape correspondence via Confidence-based sample consensus

Background

Functional mapping, despite its proven efficiency, suffers from a “chicken or egg” sce- nario, in that, poor spatial features lead to inadequate spectral alignment and vice versa during training, often resulting in slow convergence, high computational costs, and learning failures, particularly when small datasets are used.

Methods

A novel method is presented for dense-shape correspondence, whereby the spatial information transformed by neural networks is combined with the projections onto spectral maps to overcome the “chicken or egg” challenge by selectively sampling only points with high confidence in their alignment. These points then contribute to the alignment and spectral loss terms, boosting training, and accelerating convergence by a factor of five. To ensure full unsupervised learning, the Gromov–Hausdorff distance metric was used to select the points with the maximal alignment score displaying most confidence.

Results

The effectiveness of the proposed approach was demonstrated on several benchmark datasets, whereby results were reported as superior to those of spectral and spatial-based methods.

Conclusions

The proposed method provides a promising new approach to dense-shape correspondence, addressing the key challenges in the field and offering significant advantages over the current methods, including faster convergence, improved accuracy, and reduced computational costs.