Daily Papers

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle (<5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

Existing methods for capturing datasets of 3D heads in dense semantic correspondence are slow, and commonly address the problem in two separate steps; multi-view stereo (MVS) reconstruction followed by non-rigid registration. To simplify this process, we introduce TEMPEH (Towards Estimation of 3D Meshes from Performances of Expressive Heads) to directly infer 3D heads in dense correspondence from calibrated multi-view images. Registering datasets of 3D scans typically requires manual parameter tuning to find the right balance between accurately fitting the scans surfaces and being robust to scanning noise and outliers. Instead, we propose to jointly register a 3D head dataset while training TEMPEH. Specifically, during training we minimize a geometric loss commonly used for surface registration, effectively leveraging TEMPEH as a regularizer. Our multi-view head inference builds on a volumetric feature representation that samples and fuses features from each view using camera calibration information. To account for partial occlusions and a large capture volume that enables head movements, we use view- and surface-aware feature fusion, and a spatial transformer-based head localization module, respectively. We use raw MVS scans as supervision during training, but, once trained, TEMPEH directly predicts 3D heads in dense correspondence without requiring scans. Predicting one head takes about 0.3 seconds with a median reconstruction error of 0.26 mm, 64% lower than the current state-of-the-art. This enables the efficient capture of large datasets containing multiple people and diverse facial motions. Code, model, and data are publicly available at https://tempeh.is.tue.mpg.de.

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no correspondence annotation during training. Our key insight is to incorporate neural features learned by deep learning-based shape matching networks into an iterative, geometric shape registration pipeline. The advantage of our approach is two-fold -- On one hand, neural features provide more accurate and semantically meaningful correspondence estimation than spatial features (e.g., coordinates), which is critical in the presence of large non-rigid deformations; On the other hand, the correspondences are dynamically updated according to the intermediate registrations and filtered by consistency prior, which prominently robustify the overall pipeline. Empirical results show that, with as few as dozens of training shapes of limited variability, our pipeline achieves state-of-the-art results on several benchmarks of non-rigid point cloud matching and partial shape matching across varying settings, but also delivers high-quality correspondences between unseen challenging shape pairs that undergo both significant extrinsic and intrinsic deformations, in which case neither traditional registration methods nor intrinsic methods work.