DcMatch: Unsupervised Multi-Shape Matching with Dual-Level Consistency

TL;DR

DcMatch tackles unsupervised non-rigid multi-shape matching by unifying spectral functional maps with a shape graph attention-based universe learning framework. It enforces dual-level cycle consistency: spectral cycle consistency through $C_{ij}$ and spatial cycle consistency via shape-to-universe mappings $\Pi_i$, aligned in a robust shared universe space. The method introduces a shape graph attention module to capture manifold structure, a universe predictor to map shapes to a common universe, and joint spectral-spatial losses (including a Frobenius/cosine cycle loss) to guide end-to-end training. Across near-isometric, anisotropic, and non-isometric benchmarks, DcMatch achieves state-of-the-art accuracy and robustness, with ablations confirming the critical role of functional maps, universe learning, and cycle consistency.

Abstract

Establishing point-to-point correspondences across multiple 3D shapes is a fundamental problem in computer vision and graphics. In this paper, we introduce DcMatch, a novel unsupervised learning framework for non-rigid multi-shape matching. Unlike existing methods that learn a canonical embedding from a single shape, our approach leverages a shape graph attention network to capture the underlying manifold structure of the entire shape collection. This enables the construction of a more expressive and robust shared latent space, leading to more consistent shape-to-universe correspondences via a universe predictor. Simultaneously, we represent these correspondences in both the spatial and spectral domains and enforce their alignment in the shared universe space through a novel cycle consistency loss. This dual-level consistency fosters more accurate and coherent mappings. Extensive experiments on several challenging benchmarks demonstrate that our method consistently outperforms previous state-of-the-art approaches across diverse multi-shape matching scenarios.

Figures (8)

• Figure 1: Overview of mainstream multi-shape matching paradigms. (Left) The permutation synchronization paradigm, which consists of two stages: computing pairwise correspondences and enforcing cycle consistency via post-processing. (Right) The universe-based paradigm, which introduces a virtual universe shape and reduces the multi-shape matching problem to a set of pairwise mappings.
• Figure 2: Method Overview. Given a collection of shapes $\mathcal{S} = \{\mathcal{S}_i\}_{i=1}^n$, we first extract per-vertex features $\mathcal{F} = \{\mathcal{F}_i \} _{i=1}^n$ using DiffusionNet. These features are then used to compute bidirectional functional maps $\{C_{ij}\}$ and point-to-point correspondences $\{\Pi_{ij}\}$. Meanwhile, the shape graph attention module generates manifold-aware features for each shape, which are passed to the universe predictor to estimate the correspondences between each shape and a shared virtual universe. In addition to the spectral loss, we implement a cycle consistency loss to further align the spatial and spectral consistency in the shared universe space.
• Figure 3: Proportion of Correct Keypoints (PCK) curves and Area Under Curve (AUC) values on SHREC’19, SMAL, and DT4D-H inter-class, comparing our method with ULRSSM and HybridFMaps.
• Figure 4: Qualitative multi-shape matching results via texture transfer, comparing our method with HybridFMaps on SMAL (top) and DT4D-H inter-class (bottom).
• Figure 5: Qualitative examples on FAUST dataset.

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• proof