Series Section Electron Microscopy (ssEM) has emerged as a pivotal technology for deciphering nanoscale biological architectures. Three-dimensional (3D) registration is a critical step in ssEM, tasked with rectifying axial misalignments and nonlinear distortions introduced during serial sectioning. The core scientific challenge lies in achieving distortion mitigation without erasing the natural morphological deformations of biological tissues, thereby enabling faithful reconstruction of 3D ultrastructural organization. In this study, we present a paradigm-shifting optimization framework that rethinks 3D registration through the lens of manifold trajectory optimization. We propose the first continuous trajectory dynamics formulation for 3D registration and introduce a novel optimization strategy. Specifically, we introduce a dual optimization objective that inherently balances global trajectory smoothness with local structural preservation, while developing a solver that combines Gauss-Seidel iteration with Neural ODEs to systematically integrate biophysical priors with data-driven deformation compensation. Extensive experiments on multiple datasets spanning diverse tissue types demonstrate our method's superior performance in structural restoration accuracy and cross-tissue robustness.

Determining the 3D pose of a patient from a limited set of 2DX-ray images is imaging a critical (e.g., task CT and in interv MRI) entional provides settings.

Point Cloud Interpolation confronts challenges from point sparsity, complex spatiotemporal dynamics, and the difficulty of deriving complete 3D point clouds from sparse temporal information. This paper presents NeuroGauss4D-PCI, which excels at modeling complex non-rigid deformations across varied dynamic scenes. The method begins with an iterative Gaussian cloud soft clustering module, offering structured temporal point cloud representations. The proposed temporal radial basis function Gaussian residual utilizes Gaussian parameter interpolation over time, enabling smooth parameter transitions and capturing temporal residuals of Gaussian distributions. Additionally, a 4D Gaussian deformation field tracks the evolution of these parameters, creating continuous spatiotemporal deformation fields. A 4D neural field transforms low-dimensional spatiotemporal coordinates ($x,y,z,t$) into a high-dimensional latent space. Finally, we adaptively and efficiently fuse the latent features from neural fields and the geometric features from Gaussian deformation fields.NeuroGauss4D-PCI outperforms existing methods in point cloud frame interpolation, delivering leading performance on both object-level (DHB) and large-scale autonomous driving datasets (NL-Drive), with scalability to auto-labeling and point cloud densification tasks.

The method begins with an iterative Gaussian cloud soft clustering module, offering structured temporal point cloud representations.

Modeling dynamic scenes is important for many applications such as virtual reality and telepresence. Despite achieving unprecedented fidelity for novel view synthesis in dynamic scenes, existing methods based on Neural Radiance Fields (NeRF) suffer from slow convergence (i.e., model training time measured in days). In this paper, we present DeVRF, a novel representation to accelerate learning dynamic radiance fields. The core of DeVRF is to model both the 3D canonical space and 4D deformation field of a dynamic, non-rigid scene with explicit and discrete voxel-based representations. However, it is quite challenging to train such a representation which has a large number of model parameters, often resulting in overfitting issues. To overcome this challenge, we devise a novel static-to-dynamic learning paradigm together with a new data capture setup that is convenient to deploy in practice. This paradigm unlocks efficient learning of deformable radiance fields via utilizing the 3D volumetric canonical space learnt from multi-view static images to ease the learning of 4D voxel deformation field with only few-view dynamic sequences. To further improve the efficiency of our DeVRF and its synthesized novel view's quality, we conduct thorough explorations and identify a set of strategies. We evaluate DeVRF on both synthetic and real-world dynamic scenes with different types of deformation.

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks.