Florian Bernard

Dongliang Cao, Paul Roetzer, Florian Bernard

We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting optimised functional maps alone, and then rely on off-the-shelf post-processing to obtain accurate point-wise maps during inference. However, this two-stage procedure for obtaining point-wise maps often yields sub-optimal performance. In contrast, building upon recent insights about the relation between functional maps and point-wise maps, we propose a novel unsupervised loss to couple the functional maps and point-wise maps, and thereby directly obtain point-wise maps without any post-processing. Our approach obtains accurate correspondences not only for near-isometric shapes, but also for more challenging non-isometric shapes and partial shapes, as well as shapes with different discretisation or topological noise. Using a total of nine diverse datasets, we extensively evaluate the performance and demonstrate that our method substantially outperforms previous state-of-the-art methods, even compared to recent supervised methods. Our code is available at https://github.com/dongliangcao/Unsupervised-Learning-of-Robust-Spectral-Shape-Matching.

Dongliang Cao, Paul Roetzer, Florian Bernard

We propose a novel unsupervised learning approach for non-rigid 3D shape matching. Our approach improves upon recent state-of-the art deep functional map methods and can be applied to a broad range of different challenging scenarios. Previous deep functional map methods mainly focus on feature extraction and aim exclusively at obtaining more expressive features for functional map computation. However, the importance of the functional map computation itself is often neglected and the relationship between the functional map and point-wise map is underexplored. In this paper, we systematically investigate the coupling relationship between the functional map from the functional map solver and the point-wise map based on feature similarity. To this end, we propose a self-adaptive functional map solver to adjust the functional map regularisation for different shape matching scenarios, together with a vertex-wise contrastive loss to obtain more discriminative features. Using different challenging datasets (including non-isometry, topological noise and partiality), we demonstrate that our method substantially outperforms previous state-of-the-art methods.

Dongliang Cao, Zorah Laehner, Florian Bernard

Most recent unsupervised non-rigid 3D shape matching methods are based on the functional map framework due to its efficiency and superior performance. Nevertheless, respective methods struggle to obtain spatially smooth pointwise correspondences due to the lack of proper regularisation. In this work, inspired by the success of message passing on graphs, we propose a synchronous diffusion process which we use as regularisation to achieve smoothness in non-rigid 3D shape matching problems. The intuition of synchronous diffusion is that diffusing the same input function on two different shapes results in consistent outputs. Using different challenging datasets, we demonstrate that our novel regularisation can substantially improve the state-of-the-art in shape matching, especially in the presence of topological noise.