RINO: Rotation-Invariant Non-Rigid Correspondences

Abstract

Dense 3D shape correspondence remains a central challenge in computer vision and graphics as many deep learning approaches still rely on intermediate geometric features or handcrafted descriptors, limiting their effectiveness under non-isometric deformations, partial data, and non-manifold inputs. To overcome these issues, we introduce RINO, an unsupervised, rotation-invariant dense correspondence framework that effectively unifies rigid and non-rigid shape matching. The core of our method is the novel RINONet, a feature extractor that integrates vector-based SO(3)-invariant learning with orientation-aware complex functional maps to extract robust features directly from raw geometry. This allows for a fully end-to-end, data-driven approach that bypasses the need for shape pre-alignment or handcrafted features. Extensive experiments show unprecedented performance of RINO across challenging non-rigid matching tasks, including arbitrary poses, non-isometry, partiality, non-manifoldness, and noise.

Figures (34)

• Figure 1: Our learned SO(3)-invariant features. We visualize the Euclidean distance to the blue surface point in the learned feature space (darker red means higher similarity). Semantic correspondences have a similar feature similarity pattern (left & mid.). The learned feature is invariant to rotations (mid. & right). Shape orientations are depicted by RGB frames.
• Figure 2: SO(3)-invariant correspondences. Our method is unaffected by shape orientations. In contrast, baselines (represented by DUOFM) perform well only when train and test shapes are pre-aligned (I/I), failing dramatically on unseen rotations (I/SO(3)).
• Figure 3: We propose RINONet, which learns SO(3)-invariant features $\mathbf{F}$ from input shape $\mathcal{X}$. Our novel network inherits all nice properties from DiffusionNet sharp2022diffusionnet, and learns smooth, high-quality per-point features, while additionally retaining invariant to SO(3) actions applied to input shapes by employing vector neurons as the feature representation in our hidden layers. The RINONet has a simple structure and contains four consecutive RINONet Blocks at its core, which is combined with VN-EdgeConv and VN-linear layers to achieve the desired I/O dimensionality. The VN-invariant layer is employed to convert SO(3)-equivariant features to invariant ones.
• Figure 4: Our RINONet block is the core of our RINONet, and it consists of three main modules: a VN-Diffusion layer, a VN-Gradient layer, and a VN-MLP. In contrast to the original DiffusionNet block sharp2022diffusionnet, ours is SO(3)-equivariant by design.
• Figure 5: Intrinsic symmetry. Ours fully resolves symmetry, while baselines suffer. Top: partial left-right (legs) and front-back (belly-back) flips. Bottom: full left-right flips (arms and legs).

Theorems & Definitions (6)

• Theorem 1
• Theorem 2
• proof
• proof
• Theorem 3
• proof