MOTIVATION: Serial section electron microscopy (ssEM) is essential for studying biological cell structures at nanometer resolution. However, supporting film folding (SFF) degradation frequently occurs during sample preparation, causing structural distortions and information loss that severely impair downstream analyses such as 3D reconstruction and neuron segmentation. RESULTS: We propose RegInpaint, a novel recovery framework that jointly addresses deformation correction and missing-information restoration caused by SFF degradation. RegInpaint formulates SFF recovery as a joint problem of 3D elastic registration and image inpainting, providing a generalizable solution for ssEM restoration. Experiments on four EM datasets show that RegInpaint consistently outperforms existing methods in image restoration quality and significantly improves neuron segmentation accuracy. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/zhangzhenbang2021/RegInpaint.git.

Series Section Electron Microscopy (ssEM) is a crucial technique for visualizing three-dimensional (3D) biological structures, which involves collecting electron microscopy images from a series of biological sections along the z-axis and reconstructing the 3D structure. 3D registration is an essential step in ssEM, designed to eliminate axial misalignment and nonlinear distortions introduced during sample sectioning. A significant challenge in 3D registration is eliminating nonlinear distortions while preserving natural deformations. In this paper, we present a new formulation of the 3D registration problem from a frequency domain perspective and propose a Gaussian filtering-based 3D registration method, which defines 3D registration as a superposition problem of high-frequency and low-frequency components. We extend the concept of a one-dimensional Gaussian filter to three-dimensional image stacks and integrate it with optical flow networks to consolidate the deformation field within the receptive field. Extensive experiments demonstrate that our method can successfully decouple nonlinear distortions and natural deformations in the frequency domain, proving superior to existing methods in rapidly and accurately eliminating nonlinear distortions and restoring biological structures, and has the potential to be extended to large datasets.

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. A key strength of our method is its fully unsupervised training, which avoids reliance on ground truth and suits ssEM scenarios where annotations are difficult to obtain. Extensive experiments on multiple datasets spanning diverse tissue types demonstrate our method's superior performance in structural restoration accuracy and cross-tissue robustness.