coordinate-frame alignment

This work addresses the problem of automatically generating low-distortion, orthogonal quadrilateral surface meshes that satisfy user-specified feature alignment and sizing constraints. The authors propose a novel approach based on integrable orthogonal frame fields, where the symmetry of the frames is implicitly modeled using three-dimensional orthogonally decomposable (odeco) tensors. Within a finite element framework, the method jointly optimizes area and stretch distortion while enforcing shear-free orthogonality constraints. A key contribution is the extension of two-dimensional odeco integrability to three dimensions, coupled with an automatic singularity placement strategy that ensures global integrability without manual intervention or greedy heuristics. Experimental results demonstrate that the method consistently outperforms existing techniques on both smooth surfaces and complex CAD models, achieving significantly reduced mesh distortion under strict sizing control.

This paper addresses the robust alignment of two rotation sets in SO(3) under challenging conditions: no point-wise correspondences, temporal asynchrony, high outlier ratios (up to 90%), and inconsistent axis conventions. We propose the Permutation- and Sign-Invariant (PASI) framework, which decomposes rotations into spherical basis vectors and achieves axis-level decoupled matching via exhaustive enumeration of the 24 valid sign permutations—bypassing conventional correspondence search. PASI integrates weighted correlation scoring, spherical point-set matching (SPMC/FRS), and projection-based or Karcher mean estimation to ensure globally consistent alignment. The algorithm exhibits linear time complexity, achieving 6–60× speedup over state-of-the-art methods. It requires neither initial correspondences nor temporal synchronization. Extensive experiments on synthetic and real-world data demonstrate significant accuracy improvements over baseline approaches.

Medical image registration across heterogeneous imaging devices suffers from fragmented and nontraceable transformation information, impeding clinical diagnosis and collaborative workflows. To address this, we propose a tree-structured documentation framework for multimodal image registration, unifying coordinate transformations—spanning diverse devices and modalities—within a patient-specific reference frame. We introduce the .dpw (Digital Patient Workspace) proprietary file format, enabling hierarchical storage, reversible provenance tracking, and cross-platform reproducibility of transformation chains. Furthermore, we develop dpVision, a software tool supporting interactive visualization, validation, and management of registration workflows. Evaluated in orthodontic analysis, our approach significantly enhances interpretability, reproducibility, and clinical audit efficiency of complex registration pipelines. The method provides a standardized, interoperable foundation for multicenter medical imaging collaboration.

Three-dimensional (3D) mappings are fundamental in computational mechanics (CAE), computer graphics, and medical imaging; however, conventional vertex-coordinate-based representations struggle to simultaneously ensure geometric fidelity and intuitive, controllable editing. To address this, we propose the first theoretically rigorous and computationally tractable 3D quasiconformal representation—extending the Beltrami coefficient to three dimensions—to characterize local scaling distortion in a mathematically sound manner. We further design an invertible reconstruction algorithm that stably and accurately recovers the original mapping from its distortion representation. Our approach integrates 3D quasiconformal theory, partial differential equation (PDE)-based modeling, and numerical optimization. Experiments demonstrate that our method significantly outperforms state-of-the-art alternatives in 3D mapping reconstruction, keyframe interpolation, and compression—achieving superior accuracy, robustness, and editability while preserving theoretical guarantees.

Existing directional statistics tools are seldom adopted in engineering and computer science due to terminological barriers and lack of practical interfaces for modeling orientation data—such as angles, unit vectors, rotation matrices, and quaternions—in applications ranging from robotics to 3D vision. Method: We introduce the first comprehensive, practitioner-oriented reference guide for probability distributions over multi-degree-of-freedom orientation domains (1D–3D), employing a unified, engineering-friendly notation. The guide systematically presents density functions, maximum-likelihood parameter estimation procedures, and inverse-transform or rejection-sampling algorithms for six canonical directional distributions. Contribution/Results: We release an open-source Python library (built on NumPy/SciPy) supporting distribution fitting and random sampling. Empirical validation on robot pose calibration and 3D point cloud normal estimation demonstrates its practical efficacy, substantially bridging the gap between theoretical directional statistics and real-world engineering deployment.

This work addresses the challenge of achieving sub-pixel registration accuracy for images undergoing translation, scaling, and rotation. To this end, a two-stage decoupled estimation framework is proposed: first, scale and rotation parameters are estimated in the log-polar domain using the Fourier magnitude spectrum; subsequently, high-precision sub-pixel translation is estimated in the spatial domain by integrating an auxiliary function method with phase correlation. By effectively combining the Fourier–Mellin transform with auxiliary-function-based phase correlation, the approach successfully decouples the parameters of the similarity transformation. Experimental results demonstrate that the proposed method significantly outperforms conventional discrete cross-correlation–based Fourier–Mellin approaches in terms of estimation accuracy for scale, rotation, and translation.

This study addresses the trade-off in image–point cloud registration between insufficient inliers and an excessively high outlier ratio caused by suboptimal point cloud density, which limits registration accuracy. It presents the first systematic analysis of how point cloud density affects cross-modal registration and introduces a cross-coordinate correspondence pruning mechanism. Specifically, coarse correspondences are projected into the image coordinate system, where a lightweight network fuses geometric and feature information to predict inlier confidence scores for effective outlier rejection. Furthermore, a multi-density point cloud ensemble strategy is employed to enhance inlier recall. The proposed method consistently outperforms existing approaches across multiple benchmarks, achieving a registration recall improvement of at least 8.6%.

This work addresses the significant performance degradation of existing deep image matching methods under large in-plane rotations. Through systematic investigation of where to best incorporate rotation invariance within sparse feature matching pipelines, extensive training, and multi-benchmark evaluation, the study demonstrates that introducing rotation invariance solely at the descriptor stage achieves robustness comparable to that of rotation-invariant matchers while being more computationally efficient. Moreover, it shows that, with sufficient training data, rotation invariance does not compromise general matching performance and highlights the critical role of data scale in enabling robust rotation generalization. The released models achieve state-of-the-art results on benchmarks including WxBS, HardMatch, and SatAst, substantially improving matching robustness across multimodal, extreme-viewpoint, and satellite imagery scenarios.

Existing neural operators rely on fixed Eulerian coordinates, which struggle to capture evolving physical structures and often lead to spatial misalignment, amplified non-local mappings, and excessive smoothing in regions with sharp transitions. To address this limitation, this work proposes the Adaptive Coordinate Transformation (ACT) module—a plug-and-play component that learns data-driven coordinate transformations and integrates differentiable sampling to reconstruct feature representations, enabling neural operators to model dynamic processes in more suitable coordinate systems. Inspired by adaptive meshing techniques in classical PDE solvers, ACT introduces, for the first time, end-to-end learnable coordinate systems into neural operators, thereby overcoming the constraints of fixed grids. Extensive experiments across multiple PDE benchmarks and mainstream architectures—including FNO and DeepONet—demonstrate that ACT consistently enhances predictive accuracy, underscoring the critical role of coordinate learning in improving operator generalization.