Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstruction

TL;DR

Shape Non-rigid Kinematics (SNK) addresses zero-shot non-rigid shape matching by overfitting a deformation to a single pair of shapes, guided by an unsupervised functional map and regularized by a PriMo-based prism decoder. It combines a DiffusionNet-based feature extractor with a two-stage functional-map pipeline and a novel prism decoder that enforces smooth, physically plausible deformations, trained per pair without pre-training. Across near-isometric and non-isometric benchmarks, SNK achieves state-of-the-art results among non-trained methods and competitive performance relative to supervised approaches, including strong Shrec dataset results. The approach offers practical advantages for data-scarce contexts and provides an online implementation, blending axiomatic robustness with learned priors to enable accurate, flexible non-rigid shape matching.

Abstract

We present Shape Non-rigid Kinematics (SNK), a novel zero-shot method for non-rigid shape matching that eliminates the need for extensive training or ground truth data. SNK operates on a single pair of shapes, and employs a reconstruction-based strategy using an encoder-decoder architecture, which deforms the source shape to closely match the target shape. During the process, an unsupervised functional map is predicted and converted into a point-to-point map, serving as a supervisory mechanism for the reconstruction. To aid in training, we have designed a new decoder architecture that generates smooth, realistic deformations. SNK demonstrates competitive results on traditional benchmarks, simplifying the shape-matching process without compromising accuracy. Our code can be found online: https://github.com/pvnieo/SNK

Figures (9)

• Figure 1: Method overview. Given two shapes as input, we deform a source shape to resemble the target. Our network can be trained using just a single pair of shapes and uses a combination of spatial and spectral losses, as well as a regularization on the decoder.
• Figure 2: PriMo construction. The mesh vertices are represented as white circles. The elastic joints are colored yellow.
• Figure 3: Prism Decoder. Our novel architecture, built upon DiffusionNet, initiates the process by extracting per-vertex features, which are subsequently consolidated into per-face features. These features are then processed by a Multilayer Perceptron (MLP) to generate per-face rotation and translation, which are used to rigidly transform the input faces. The transformed faces are then consolidated to produce the final reconstruction.
• Figure 4: Qualitative Results from the Shrec dataset. The correspondences are visualized by transferring a texture through the map. Our method results in visually superior outcomes.
• Figure 5: Examples of non-isometric and non-homeomorphic matching on the Smal and Shrec datasets, respectively.