SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation

In this paper, we propose SRIF, a novel Semantic shape Registration framework based on diffusion-based Image morphing and Flow estimation. More concretely, given a pair of extrinsically aligned shapes, we first render them from multi-views, and then utilize an image interpolation framework based on diffusion models to generate sequences of intermediate images between them. The images are later fed into a dynamic 3D Gaussian splatting framework, with which we reconstruct and post-process for intermediate point clouds respecting the image morphing processing. In the end, tailored for the above, we propose a novel registration module to estimate continuous normalizing flow, which deforms source shape consistently towards the target, with intermediate point clouds as weak guidance. Our key insight is to leverage large vision models (LVMs) to associate shapes and therefore obtain much richer semantic information on the relationship between shapes than the ad-hoc feature extraction and alignment. As a consequence, SRIF achieves high-quality dense correspondences on challenging shape pairs, but also delivers smooth, semantically meaningful interpolation in between. Empirical evidence justifies the effectiveness and superiority of our method as well as specific design choices. The code is released at https://github.com/rqhuang88/SRIF.

Spatially and Spectrally Consistent Deep Functional Maps

Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered state-of-the-art in non-rigid shape matching. We first justify that under certain conditions, the learned maps, when represented in the spectral domain, are already cycle consistent. Furthermore, we identify the discrepancy that spectrally consistent maps are not necessarily spatially, or point-wise, consistent. In light of this, we present a novel design of unsupervised Deep Functional Maps, which effectively enforces the harmony of learned maps under the spectral and the point-wise representation. By taking advantage of cycle consistency, our framework produces state-of-the-art results in mapping shapes even under significant distortions. Beyond that, by independently estimating maps in both spectral and spatial domains, our method naturally alleviates over-fitting in network training, yielding superior generalization performance and accuracy within an array of challenging tests for both near-isometric and non-isometric datasets. Codes are available at https://github.com/rqhuang88/Spatiallyand-Spectrally-Consistent-Deep-Functional-Maps.